SudokuSolver Forum http://www.rcbroughton.co.uk/sudoku/forum/ |
|
Texas Jigsaw Killer Archive http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=1078 |
Page 6 of 7 |
Author: | Andrew [ Tue Apr 29, 2014 7:03 pm ] |
Post subject: | Texas Jigsaw Killer Archive |
A New Jigsaw Killer (aka TJK 36) by manu (January 2009) here Puzzle Diagrams: Jigsaw nonet design: ZigZag by Gérard Coteau. Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration: Cages with cells in 2 jigsaw nonets: green, yellow and brown Code: Select, Copy & Paste into solver: SumoCueV1=26J0+0J0=13J0=15J0=27J1+4J2+4J2+4J2=27J2=20J0+0J0+2J3+3J0+3J1+4J1+4J2+8J2+8J2+9J0+0J3+2J3=14J4=10J1+22J1=11J1=11J2+8J5+9J0+0J3+2J3+21J4+21J4+24J1+24J1+25J2=20J5=13J3=13J3=17J6=25J4+39J4+39J4+39J1+25J5+35J5+36J3+37J7+38J6+38J6=9J4+49J4+49J5=22J5+35J8=9J3+37J7=27J6+56J6=16J6+58J4+52J5+52J5+35J8+54J7+54J7=23J7+56J6+58J6=12J8=8J5=10J8+70J8+65J7+65J7+65J7+56J7+58J6+68J8+69J8=7J8+79J8 Solution: +-------+-------+-------+ Quote: manu: This is a new jigsaw killer. It is not really difficult (rated at 1.06 SSscore), but it might keep busy the killer fans (and the other ones of course !) until the next Assassin 140. I have not inserted it into the "Texas jigsaw killer" series carried on by Para because I have no experience in creating such puzzles : please, advices are welcome ! Have fun with it SS v3.6 score 1.35 Para: I would just name it Texas Jigsaw Killer 36. It was quite fun. It's not my TJK series. It's Ruud's series. I just continued the legacy. One thing. The picture's just a bit easier to see if you select thick nonet lines in the sumocue option. Ed: Very worthy of Para's christening as "TJK 36"! I'd like to see these again on a regular basis, perhaps as a monthly puzzle. I'll get the next one ready for November. I made very heavy going of this puzzle the first time through (earlier this year). This time, I managed to find steps 1 & 7 which made a huge difference. But still took quite a while to find perhaps because there are so many other places to look and make real progress. Thanks manu! Andrew (in 2013): This cage pattern is very good for Law of Leftovers (LoL) based on the columns. Since the SS(v3.6.2) score is more than 1.25, I’ve used LoL from a fairly early stage. It seems appropriate to me that manu, who lives in France, selected a jigsaw design by a Frenchman Gérard Coteau. That may just be coincidence. My solving path is fairly short, but Ed's is shorter still. He did excellent work in columns 8 and 9; I wish I'd spotted his step 1. The way I solved it felt fairly easy, partly because I'm used to using this jigsaw cage pattern for solving jigsaw sudokus. Ed's walkthrough: manu wrote: I have not inserted it into the "Texas jigsaw killer" series .. because I have no experience in creating such puzzles : please, advices are welcome ! Very worthy of Para's christening as "TJK 36"! I'd like to see these again on a regular basis, perhaps as a monthly puzzle. I'll get the next one ready for November. I made very heavy going of this puzzle the first time through (earlier this year). This time, I managed to find steps 1 & 7 which made a huge difference. But still took quite a while to find perhaps because there are so many other places to look and make real progress. Thanks manu! Partial Walkthrough for Jigsaw killer (AKA TJK 36) NOTE: this is an optimised way in to my solution so some obvious eliminations are left out. However, clean-up is done as sub-steps as I go. Please let me know of any corrections or clarifications. Prelims i. 13(4)r1c3: no 8,9 ii. 27(4)r1c9: no 1,2 iii. 20(3)r2c1: no 1,2 iv. 10(2)r3c5: no 5 v. 11(3)r3c7 and r3c8: no 9 vi. 13(2)r5c1: no 1,2,3 vii. 9(3)r6c5: no 7,8,9 viii. 22(3)r6c8: no 1,2,3,4 ix. 9(3)r7c1: no 7,8,9 x. 27(4)r7c3: no 1,2 xi. 12(2)r8c6: no 1,2,6 xii. 8(2)r8c7: no 4,8,9 xiii. 10(2)r8c8: no 5 xiv. 7(2)r9c8: no 7,8,9 1. "45" c89: 1 outie r7c7 - 7 = 1 innie r1c8. 1a. r7c7 = (89), r1c8 = (12) 2. 22(3)r6c8 = 9{58/67}: 9 locked for Nr3c9 2a. must have 7 or 8 2b. must have 5 or 6 in c8 (important for later) 3. "45" r1234: 1 outie r5c8 + 6 = 1 innie r4c9 3a. r5c8 = (12), r4c9 = (78) 4. Killer pair 7,8 in r4c9 & 22(3)r6c8 (step 2a) both locked for Nr3c9 4a. no 1 in r9c7 5. naked pair {12} in r15c8: both locked for c8 5a. no 8 or 9 in r8c9 5b. no 5 or 6 in r9c9 6. "45" c9: 2 outies r29c8 - 9 = 1 innie r8c9 6a. no 9 in r2c8 (IOU) 6b. max. 2 outies = [86] = 14 -> max. r8c9 = 5 6c. no 3 or 4 in r8c8 7. "45" c9: 1 outie r2c8 - 2 = 2 innies r89c9 7a. min. 2 innies = 3 -> min. r2c8 = 5 8. "45" c9: 3 outies r289c8 = 19 = {379/469/478}(no 5) ({568} blocked by r67c8 step 2b) 8a. must have 3 or 4 which is only in r9c8 -> r9c8 = (34) 9. 7(2)r9c8 = {34}: both locked for r9 & Nr6c9 9a. r8c8 = (89) 10. 12(2)r8c6 = {57}: both locked for c6 and Nr6c9 10a. no 3 in r3c5 11. 8(2)r8c7 = {26}: both locked for c7 11a. no 2 in r8c9 CPE (I love jigsaws!) Puzzle is cracked. Enjoy! Andrew's walkthrough: This cage pattern is very good for Law of Leftovers (LoL) based on the columns. Since the SS(v3.6.2) score is more than 1.25, I’ve used LoL from a fairly early stage. It seems appropriate to me that manu, who lives in France, selected a jigsaw design by a Frenchman Gérard Coteau. That may just be coincidence. My solving path is fairly short, but Ed's is shorter still. He did excellent work in columns 8 and 9; I wish I'd spotted his step 1. The way I solved it felt fairly easy, partly because I'm used to using this jigsaw cage pattern for solving jigsaw sudokus. Here is my walkthrough for TJK 36 Thanks Ed for a couple of corrections Prelims a) R3C56 = {19/28/37/46}, no 5 b) R56C1 = {49/58/67}, no 1,2,3 c) R89C6 = {39/48/57}, no 1,2,6 d) R89C7 = {17/26/35}, no 4,8,9 e) R8C89 = {19/28/37/46}, no 5 f) R9C89 = {16/25/34}, no 7,8,9 g) 20(3) cage at R2C1 = {389/479/569/578}, no 1,2 h) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9 i) 11(3) cage at R3C8 = {128/137/146/236/245}, no 9 j) 9(3) cage at R6C5 = {126/135/234}, no 7,8,9 k) 22(3) cage at R6C8 = {589/679} l) 9(3) cage at R7C1 = {126/135/234}, no 7,8,9 m) 13(4) cage at R1C3 = {1237/1246/1345}, no 8,9 n) 27(4) cage at R1C9 = {3789/4689/5679}, no 1,2 o) 27(4) cage at R7C3 = {3789/4689/5679}, no 1,2 Steps resulting from Prelims 1a. 13(4) cage at R1C3 = {1237/1246/1345}, 1 locked for C3 1b. 22(3) cage at R6C8 = {589/679}, 9 locked for NR3C9 1c. 27(4) cage at R7C3 = {3789/4689/5679}, CPE no 9 in R6C4 2. 45 rule on R1234 1 innie R4C9 = 1 outie R5C8 + 6, R4C9 = {78}, R5C8 = {12} 2a. Killer pair 7,8 in R4C9 and 22(3) cage, locked for NR3C9, clean-up: no 1 in R9C7 2b. 4 in NR3C9 only in R35C9 + R6C7, CPE no 4 in R6C9 2c. 27(4) cage at R1C9 = {3789/4689/5679}, 9 locked for NR1C6 2d. 3 of {3789} must be in R3C9 -> no 3 in R1C9 + R2C89 3. 45 rule on C1 4 innies R1789C1 = 12 = {1236/1245}, no 7,8,9 3a. 20(3) cage at R2C1 = {389/479/578} (cannot be {569} which clashes with R1789C1), no 6 4. 45 rule on NR5C3 2 outies R7C6 + R9C4 = 15 = {69/78} 4a. Min R7C6 = 6 -> max R789C5 = 10, no 8,9 in R789C5 5. Law of Leftovers (LoL) for C1234 three outies R789C5 must exactly equal three innies R345C4, no 8,9 in R789C5 -> no 8,9 in R345C4 6. LoL for C789 three outies R189C6 must exactly equal three innies R345C7 6a. R89C6 = 12 -> two of the cells in R345C7 must total 12, cannot be R34C7 because they are part of 11(3) cage at R3C7) -> R5C7 must be part of this hidden 12(2) cage, no 1,2,6 in R5C7 7. 45 rule on NR3C9 + NR6C9 3 innies R3C9 + R5C8 + R6C7 = 11 = {146/236/245} 7a. R5C8 = {12} -> no 1,2 in R6C7 7b. Killer pair 5,6 in R3C9 + R6C7 and 22(3) cage at R6C8, locked for NR3C9, clean-up: no 2,3 in R9C7 8. 45 rule on C12 2 outies R89C3 = 14 = {59/68} 8a. 45 rule on C12 2 innies R9C12 = 9 = [18/27]/{36/45}, no 1,2,9 in R9C2 9. 45 rule on C123 4 outies R6789C4 = 26 = {2789/3689/4589/4679/5678}, no 1 9a. 1 in NR5C3 only in R789C5, locked for C5,clean-up: no 9 in R3C6 9b. LoL (step 5), 1 in NR5C3 only in R789C5 -> 1 in R345C4, locked for C4 and NR3C4 10. 9(3) cage at R6C5 = {234} (only remaining combination), locked for R6, 2 also locked for NR3C4, clean-up: no 9 in R5C1 10a. R3C9 + R5C8 + R6C7 (step 7) = {146/236/245} 10b. 5,6 only in R3C9 -> R3C9 = {56} 11. LoL (step 5) no 2 in R345C4 -> no 2 in R789C5 11a. 16(4) cage at R7C5 = {1348/1357/1456}, no 9, clean-up: no 6 in R9C4 (step 4) 11b. R7C6 = {678} -> no 6,7 in R789C5 11c. LoL (step 5), no 6,7 in R789C5 -> no 6,7 in R345C4 12. R5C3 = 2 (hidden single in NR5C3), R5C8 = 1, R4C9 = 7 (step 2), both placed for NR3C9, clean-up: no 6 in 22(3) cage at R6C8, no 3 in R8C8, no 9 in R8C9. no 7 in R9C7, no 6 in R9C9 12a. R5C8 = 1 -> R34C8 = 10 = {28/46}/[73], no 5, no 3 in R3C8 12b. R3C9 = 6 (hidden single in NR3C9), clean-up: no 4 in R3C56, no 4 in R4C8, no 4 in R8C8 12c. R8C7 = 2 (hidden single in NR3C9), R9C7 = 6, placed for NR6C9, clean-up: no 8 in R8C3 (step 8), no 8 in R8C8, no 4,8 in R8C9, no 1 in R9C9 13. Naked quint {12345} in R345C4 + R6C56, locked for NR3C4, 5 also locked for C4 13a. LoL (step 5), 5 in R345C4 -> 5 in R789C5, locked for C5 and NR5C3 13b. 1 in C4 only in R34C4 -> 14(3) cage at R3C4 = {149/158}, no 3,6 14. 13(4) cage at R1C3 = {1345} (only remaining combination), locked for C3, clean-up: no 9 in R89C3 (step 8) 14a. R89C3 = [68], placed for NR6C2, clean-up: no 7 in R7C6 (step 4), no 4 in R8C6, no 1,3 in R9C1 (step 8a), no 3 in R9C2 (step 8a) 14b. Naked pair {79} in R67C3, locked for NR5C3 14c. R7C3 + R9C4 = {79} = 16 -> R78C4 = 11 = {38}, locked for C4 and NR5C3 -> R6C4 = 6, R6C3 = 9 (cage sum), R7C3 = 7, R9C4 = 9, placed for NR6C2, R7C6 = 6 (step 4), placed for NR3C4, clean-up: no 4,7 in R5C1, no 3 in R8C6 15. Naked triple {145} in R345C4, locked for C4 and NR3C4 15a. Naked pair {23} in R6C56 -> R6C7 = 4, placed for NR3C9, R5C9 = 3, R8C9 = 1, R8C8 = 9, placed for NR6C9, clean-up: no 3 in R9C6, no 4 in R9C8 15b. Naked triple {145} in R789C5, locked for C5 16. Naked pair {27} in R12C4, locked for NR1C1, R2C5 = 6 (cage sum) 17. 25(4) cage at R5C4 = {4579} (only remaining combination) -> R5C4 = 4, R5C7 = 5, placed for NR1C5, R5C56 = {79}, locked for R5 and NR3C4, R4C5 = 8, clean-up: no 2 in R3C6, no 2 in R3C8 (step 12a), no 8 in R6C1 18. 20(3) cage at R2C1 (step 3a) = {389} (only remaining combination), locked for C1 and NR1C1 -> R5C1 = 6, R6C1 = 7, both placed for NR3C2, R5C2 = 8, R67C2 = 5 = [14], placed for NR6C2, R2C2 = 5, placed for NR1C1, R1C2 = 6, R8C12 = [53], R7C1 = 1 (cage sum), R1C13 = [41], R9C12 = [27], R78C4 = [38], R8C6 = 7, R9C6 = 5, placed for NR5C9, R6C9 = 8, R9C89 = [34], R12C9 = [59], R2C8 = 7 (cage sum), placed for NR1C6, R67C8 = [58], R1C8 = 2, R12C4 = [72] 19. Naked pair {38} in R1C67, locked for R1 and 27(6) cage at R1C5 -> R1C5 = 9, R2C67 = [41] and the rest is naked singles, without using the nonets. One surprising thing about my solving path is that, although there are many LoLs available for the columns, I only used two of them, one of which I used repeatedly. |
Author: | Andrew [ Thu May 01, 2014 12:31 am ] |
Post subject: | Texas Jigsaw Killer Archive |
Texas Jigsaw Killer 37 by Ed (31st October/1st November 2009) here Puzzle Diagrams: Jigsaw nonet design: Double Mirror by Fer van Niewenhuizen. Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration: Cages with cells in 3 jigsaw nonets: pink and orange Code: Select, Copy & Paste into solver: SumoCueV1=9J0=14J0+1J0=15J0+3J1+3J2=14J2+6J2=14J2+0J0+1J0=20J0+11J1+3J1=19J1+14J2+6J2+8J2=14J0+18J3+11J1+11J1=30J1+14J1+14J1=20J4+25J2+18J0=14J3=15J3+29J5+22J5=6J5+32J4=15J4+25J2+28J3+28J3=11J3+38J5+22J5=14J5+41J4+34J4+34J4=17J6+28J3=15J3+47J5+22J5=7J5+50J4+34J4=14J7+45J6+45J3=17J8+56J8+22J8=25J8+59J8+53J4+53J7=15J6=14J6+56J6+56J8=15J8+59J8+59J7=15J7=7J7+63J6+64J6+64J6+67J6+67J8+67J7+70J7+70J7+71J7 Solution: +-------+-------+-------+ Quote: Ed: A monthly Texas Jigsaw Killer (TJK) would be great. Mind twisting guaranteed. As it turns out, November's does it nicely! I found it really hard yet my optimised solution cracks it very, very quickly with two nice tricks. It's been a long time since I solved a killer with an SSscore this high. If you want a Liter version with this cage pattern, just ask. It's ready. SSscore: 1.68 manu: Glad that the TJK's series is not dead ! I have much enjoyed this one since involved moves are really characteristic of this kind of puzzle. Thanks Ed ; please, continue !! Ed: Thanks! Great to have your interest. I really enjoyed this one so will get one ready for December. Thanks for your walkthrough. Very quick too compared to my months for yours! We did mine very differently (though many of the moves were familiar from my first tries at it) but we both used a really nice cloning trick. I added two more dimensions to that basic idea which I hope are correct (steps 5 & 7) [edit: manu has validated them. Thanks!]. Andrew (in 2013): Loved the cage pattern! Neat interactions between the horizontal LoLs and the 3-cell cages! Nice solving paths by both manu and Ed! I particularly liked manu's step 2c and Ed's step 7a! My solving path was somewhat longer, possibly using simpler steps. manu's walkthrough: Glad that the TJK's series is not dead ! I have much enjoyed this one since involved moves are really characteristic of this kind of puzzle. Thanks Ed ; please, continue !! Edit : some corrections have been added. Thanks Ed T J K 37 Walkthrough I have used some useful LOL's and clones cells (again !) , but the decisive step seems to be the hidden killer quad {6789} at n6 (step 4)d)) which leads to r6c7=6 1)a) Outies for c12 : r19c3=h7(2) at c3 : no 7,8,9 b) Innies for c1234 : r19c4=h5(2) at c4 : no 5,6,7,8,9. c) L.O.L for n147 : {r1c4, r9c4} = {r3c3, r7c3} : r37c3=h5(2)at c3 ={14/23} d) h7(2)c3<>{34} since this combination would block combination of h5(2)c3. e) Killer pair {12} locked for c3 at h5(2)+h7(2) 2)a) 11(2)r5 <> {56} since {56} block combinations of 14(2)r5 b) Innies-outies for c1 : r3c2+r7c2=10+r5c1 >= 11 : r37c2<>1. c) « 45 »-rule for n4 : r4c3+r5c3+r6c3=31 – (r3c2+r7c2) <= 20 :since the sum of 3 of {6789} is more than 20, r456c3 must contain at least one of (34), only possible at r5c3 since r46c3=(6789) => r5c34=[38/47] d) Killer pair {34} locked for c3 at r5c3+ h5(2) 3)a) Innies-outies for n7 : r7c2=1+r8c3+r9c4 >= 1+5+1=7 => r7c2=(789) => r8c3<>8,9 => r9c4<>4, r1c4<>1 b) L.O.L for n123 : {r4c1, r4c9}={r3c2, r3c8}. r4c1 cannot equal r3c2 since they share a cage, idem for r3c8 and r4c9, so => r4c1=r3c8 : no 1,2 => r3c2=r4c9 : no 2 c) 14(4)n4<>{2345} blocked by r5c3=(34) => 14(4) contains one of {6789} d) Killer quad {6789} locked for n4 at 14(4)+r46c3+r7c2 => r3c2<>6,7,8,9 : r3c2=(345)=r4c9 (step 3)b) ) e) Max r4c9=5 => Min (r3c8+r3c9)=15 : r3c89=(6789) => r4c1=(6789) 4)a) L.O.L for n789 : {r6c1, r6c9}={r7c2, r7c8} => r6c1=r7c8, and r6c9=r7c2=(789) b) Innies-outies for r789 : r6c1+r6c9=4+r7c5 <= 13 c) r6c19<>{67} which would block combinations of 15(2)r6 Since r6c1+r6c9 <=13 and r6c19<>{67}, r6c19 contain one of {12345} => r6c1=(12345), so r7c8=(12345) d) 15(4)n6 contain exactly one of {6789} => Hidden killer quad {6789} locked for n6 at 15(4)+r3c8+r5c7+r6c7 => r6c7=6 The puzzle is now cracked 5)a) 7(2)r6=[16], 15(2)r6={78} locked for r6 b) r6c9=9 => r7c2=9 (step 4)a)) c) Naked pair {78} locked for c4 and n5 at r56c4 => 15(2)r4=[69] d) 14(2)n3={68} locked for n3 and c9 => r3c9=7 e) h7(2)c3={25}=r19c3 locked for c3 f) h5(2)c3={14}=r37c3 locked for c3 g) 11(2)n4=[38], 15(2)r6=[87], 14(2)r5=[59] i) Innie for n4 : r3c2=5=r4c9 j) r3c8=8=r4c1 => cage sum r3c1=1 k) Hidden single for c3 : r2c3=9 => r8c3=7 l) Innie for n1 : r1c4=4 => r9c4=1 m) 15(2)n7={69} locked for n7 and c1 n) 9(2)n1={27} locked for n1 and c1 o) r7c8+r7c9=5 : r7c8<>5 => r6c1<>5 p) Last combo : r67c1=[35] => r7c8=3 The rest is straightforward Ed's walkthrough: manu wrote: Glad that the TJK's series is not dead ! I have much enjoyed this one since involved moves are really characteristic of this kind of puzzle. Thanks Ed ; please, continue !! Thanks! Great to have your interest. I really enjoyed this one so will get one ready for December. Thanks for your walkthrough. Very quick too compared to my months for yours! We did mine very differently (though many of the moves were familiar from my first tries at it) but we both used a really nice cloning trick. I added two more dimensions to that basic idea which I hope are correct (steps 5 & 7) [edit: manu has validated them. Thanks!]. It's cracked by step 9. Texas Jigsaw Killer 37 Walkthrough 19 steps Prelims i. 9(2)r1c1: no 9 ii. 14(2)r1c9 & r5c6 = {59/68} iii. 20(3)r3c8: no 1,2 iv. 14(4)r4c2: no 9 v. 15(2)r4c3 & r6c3 & r8c1 = {69/78} vi. 6(2)r4c6 = {15/24} vii. 11(2)r5c3: no 1 viii. 7(2)r6c6 & r8c9: no 7,8,9 1. "45" on c123: 2 innies r19c4 = 5 = {14/23} 2. "45" on Nr1c1: 1 outie r3c2 + 8 = 2 innies r1c4 + r2c3 2a. max. 2 innies = 13 -> max r3c2 = 5 3. LOL on nonets lined up with r123: 2 outies r4c19 = 2 innies r3c28 3a. but r3c2 cannot equal r4c1 since they have a common cage -> r3c2 = r4c9 = (345) 3b. same deal with r3c8 = r4c1 (no 1,2) 4. 20(3)r3c8: min. r3c89 = 15 (no 3,4,5) 4a. no 3,4,5 in r4c1 (step 3b) 5. We know that r3c2=r4c9 and r4c1=r3c8 (step 3a.b) -> the only cells left in the 14(3)r3c1 and 20(3)r3c8 to make up the difference in the cage totals (6) are r3c1 and r3c9 -> r3c1 + 6 = r3c9 5a. ->r3c1 = (123), r3c9 = (789) 6. "45" on r123: 2 outies r4c19 - 4 = 1 innie r3c5 6a. min. 2 outies = 9 -> min. r3c5 = 5 7. Combining steps 3b and 6.: -> r3c8 + r4c9 - 4 = r3c5 7a. -> no 4 in r4c9 (Clone IOU)! 7b. -> no 4 in r3c2 (step 3a) 8. "45" on r12 8a. four outies r3c3467 = 15 and must have 4 for r3 = {1248/1347/2346}(no 5,9) 8b. note: has two of 1,2,3 9. Killer triple 1,2,3 in r3c1 & h15(4)r3 (step 8b): locked for r3 The puzzle is cracked. 10. r3c2 = 5, r4c9 = 5 (step 3a) 11. 14(2)r1c9 = {68}: both locked for c9 & Nr1c6 11a. r3c1, no 2 (step 5) 12. r3c89 = 15 = [69/87]: r3c8 = (68) 12a. ->r4c1 = (68) (step 3b) 13. "45" on Nr1c1: 2 remaining innies r1c4 + r2c3 = 13 = [49] 13a. no 5 in 9(2)r1c1 14. Killer pair 6,8 in r4c1 & 15(2)r8c1: both locked for c1 15. 9(2)r1c1 = {27}: both locked for Nr1c1 & c1 16. 15(2)r8c1 = {69}: both locked for c1 & Nr6c1 17. r4c1 = 8, r3c1 = 1 (cage sum) 18. r3c8 = 8 (step 3b), r3c9 = 7 (cage sum) 19. r3c5 = 9 (hidden single r3) Enjoy the rest! Andrew's walkthrough: Loved the cage pattern! Neat interactions between the horizontal LoLs and the 3-cell cages! Nice solving paths by both manu and Ed! I particularly liked manu's step 2c and Ed's step 7a! My solving path was somewhat longer, possibly using simpler steps. Thanks Ed for your comment and corrections; I've added some more I found while going through my walkthrough again. Prelims a) R12C1 = {18/27/36/45}, no 9 b) R12C9 = {59/68} c) R4C34 = {69/78} d) R4C67 = {15/24} e) R5C34 = {29/38/47/56}, no 1 f) R5C67 = {59/68} g) R6C34 = {69/78} h) R6C67 = {16/25/34}, no 7,8,9 i) R89C1 = {69/78} j) R89C9 = {16/25/34}, no 7,8,9 k) 20(3) cage at R3C8 = {389/479/569/578}, no 1,2 l) 14(4) cage at R4C2 = {1238/1247/1256/1346/2345}, no 9 1. 45 rule on C12 2 outies R19C3 = 7 = {16/25/34}, no 7,8,9 2. 45 rule on C1234 2 innies R19C4 = 5 = {14/23} 3. 45 rule on C6789 2 innies R19C6 = 10 = {19/28/37/46}, no 5 4. 45 rule on C89 2 outies R19C7 = 9 = {18/27/36/45}, no 9 5. 45 rule on C1 2 outies R37C2 = 1 innie R5C1 + 10 5a. Max R37C2 = 17 -> max R5C1 = 7 5b. Min R37C2 = 11, no 1 in R37C2 6. 45 rule on C9 2 outies R37C8 = 1 innie R5C9 + 10 6a. Max R37C8 = 17 -> max R5C9 = 7 6b. Min R37C8 = 11, no 1 in R7C8 7. Law of Leftovers (LoL) for C123 two outies R19C4 must exactly equal two innies R37C3, R19C4 = {14/23} -> R37C3 = {14/23} 7a. R19C3 = 7 = {16/25} (cannot be {34} which clashes with R37C3), no 3,4 7b. Killer pair 1,2 in R19C3 and R37C3, locked for C3, clean-up: no 9 in R5C4 7c. R5C34 = {38/47}/[92] (cannot be {56} which clashes with R5C67), no 5,6 in R5C34 8. LoL for C789 two outies R19C6 must exactly equal two innies R37C7, no 5 in R19C6 -> no 5 in R37C7 9. LoL for R123 two outies R4C19 must exactly equal two innies R3C28 but R3C2 + R4C1 are in the same cage and R3C8 + R4C9 are in the same cage -> R3C2 = R4C9 and R3C8 = R4C1, no 1,2 in R3C2 + R4C1 [There’s the obvious Min R3C2 + R4C1 = 7 -> max R3C1 = 7, however one can get more out of this LoL …] 9a. R3C2 = R4C9 and R3C8 = R4C1 -> R3C9 = R3C1 + 6 (difference between 14(3) and 20(3) cages) -> R3C1 = {123}, R3C9 = {789} 9b. 20(3) cage at R3C8 = {389/479/569/578} 9c. 3 of {389} must be in R4C9 (R34C9 cannot be {89} which clashes with R12C9) -> no 3 in R3C8, clean-up: no 3 in R4C1 (LoL) 9d. 6 of {569} must in R3C8 (R34C9 cannot be [96] which clashes with R12C9) -> no 6 in R4C9, clean-up: no 6 in R3C2 (LoL) 10. 45 rule on NR1C1 2 innies R1C4 + R2C3 = 1 outie R3C2 + 8 10a. Max R1C4 + R2C3 = 13 -> max R3C2 = 5, clean-up: max R4C9 = 5 (LoL, step 9) 10b. Min R3C2 = 3 -> min R1C4 + R2C3 = 11 -> min R1C4 = 2, min R2C3 = 7, clean-up: no 4 in R9C4 (step 2) 10c. Max R3C12 = 8 -> min R4C1 = 6, clean-up: min R3C8 = 6 (LoL, step 9) 11. 45 rule on NR1C6 1 outie R3C8 = 2 innies R1C6 + R2C7 + 3 11a. Max R1C6 + R2C7 = 6, no 6,7,8,9 in R1C6 + R2C7, clean-up: no 1,2,3,4 in R9C6 (step 3) 12. LoL for R789 two outies R6C19 must exactly equal two innies R7C28 but R6C1 + R7C2 are in the same cage and R6C9 + R7C8 are in the same cage -> R6C1 = R7C2 and R6C9 = R7C8, no 1 in R6C19 12a. R6C1 = R7C8 and R6C9 = R7C2 -> R7C1 = R7C9 + 3 (difference between 17(3) and 14(3) cages), no 1,2,3 in R7C1, no 7,8,9 in R7C9 13. R37C2 = 1 innie R5C1 + 10 (step 5) 13a. Max R37C2 = 14 -> max R5C1 = 4 13b. Min R37C2 = 11 -> min R7C2 = 6, clean-up: min R6C9 = 6 (LoL, step 12) 13c. Min R7C12 = 10 -> max R6C1 = 7, clean-up: max R7C8 = 7 (LoL, step 12) 13d. 5 in NR3C2 only in R3456C2, locked for C2 14. 45 rule on NR6C1 1 outie R7C2 = 2 innies R8C3 + R9C4 + 1 14a. Max R8C3 + R9C4 = 8, no 8,9 in R8C3 15. 45 rule on NR6C9 2 innies R8C7 + R9C6 = 1 outie R7C8 + 9 15a. Min R7C8 = 2 -> min R8C7 + R9C6 = 11, no 1 in R8C7 16. 1,2 in NR3C2 only in 14(4) cage at R4C2 = {1238/1247/1256} 16a. Killer quad 6,7,8,9 in 14(4) cage, R46C3 and R7C2, locked for NR3C2, clean-up: no 2,3,4 in R5C4 16b. Killer pair {34} in R37C3 and R5C3, locked for C3 17. R7C2 = R8C3 + R9C4 + 1 (step 14) 17a. Min R8C3 + R9C4 = 6 -> min R7C2 = 7, clean-up: min R6C9 = 7 (LoL, step 12) 17b. Min R6C1 + R7C2 = 9 -> max R7C1 = 8, clean-up: max R7C9 = 5 (step 12a) 17c. Min R7C12 = 11 -> max R6C1 = 6, clean-up: max R7C8 = 6 (LoL, step 12) 17d. R37C8 = R5C9 + 10 (step 6) 17e. Max R37C8 = 15 -> max R5C9 = 5 18. 45 rule on R12 4 outies R3C3467 = 15 = {1248/1257/1347/1356/2346} (cannot be {1239} which clashes with R3C1), no 9 18a. Killer quint 1,2,3,4,5 in R3C12 and R3C3467, locked for R3 19. Hidden killer quad 1,2,3,4 in R12C1, 14(3) cage at R1C2, R1C4 and R3C1 for NR1C1, R12C1 contains one of 1,2,3,4, R1C4 = {234}, R3C1 = {123} -> 14(3) cage must contain one of 1,2,3,4 = {158/167/257/356} (other combinations contain two of 1,2,3,4), no 4,9 19a. 5 of {257} must be in R1C3 -> no 2 in R1C3, clean-up: no 5 in R9C3 (step 1) 19b. 9 in NR1 only in R2C3 + R4C1, CPE no 9 in R4C3, clean-up: no 6 in R4C4 20. 14(3) cage at R8C2 = {149/239/248} (cannot be {167} which clashes with R89C1, cannot be {347} because R9C3 only contains 1,2,6), no 6,7, clean-up: no 1 in R1C3 (step 1) 20a. R9C3 = {12} -> no 1,2 in R89C2 20b. Killer pair 8,9 in R89C1 and 14(3) cage, locked for NR6C1, clean-up: no 5 in R7C9 (step 12a) 20c. 1 in NR6C1 only in R9C34, locked for R9, clean-up: no 8 in R1C7 (step 4), no 6 in R8C9 21. 9 in C2 only in R789C2 -> 17(3) cage at R6C1 and 14(3) cage at R8C2 form a combined cage without any repeated candidates (but note that R7C2 doesn’t “see” R89C1) 21a. 14(3) cage at R8C2 (step 20) = {149/239/248} 21b. 17(3) cage at R6C1 = {359/368/458/467} (cannot be {269} which clashes with 14(3) cage, cannot be {278} because {278} + 14(3) cage = {149} clashes with R89C1), no 2, clean-up: no 2 in R7C8 (LoL, step 12) [Ed commented that an alternative way to eliminate {278} is 7 in R7C1 clashes with R89C1 = {78} since R7C2 repeats in R89C1.] 21c. 7 of {467} must be in R7C2 -> no 7 in R7C1, clean-up: no 4 in R7C9 (step 12a) 21d. R9C34 = {12} (hidden pair in NR6C1), locked for R9, clean-up: no 2 in R1C4 (step 2), no 7 in R1C7 (step 4), no 5 in R8C9 21e. 3 in NR6C1 only in R6C1 + R89C2, CPE no 3 in R6C2 [Can also eliminate {368}from the 17(3) cage, using LoL interaction with 14(3) cage at R6C9, but I’ll leave that for now in the hope that there’s a simpler way and because it doesn’t eliminate any candidates.] 22. 17(3) cage at R6C1 (step 21b) = {359/368/458/467} 22a. 5 in C1 only in R12C1 = {45} or in 17(3) cage = {359/458} -> 17(3) cage = {359/368/458} (cannot be {467}, locking-out cages), no 7, clean-up: no 7 in R6C9 (LoL, step 12) 22b. Killer pair 8,9 in R6C34 and R6C9, locked for R6 22c. Killer pair 8,9 in R7C2 and 14(3) cage at R8C2, locked for C2 23. R3C9 = 7 (hidden single in C9), placed for NR1C6, R3C1 = 1 (step 9a), placed for NR1C1, clean-up: no 8 in R12C1, no 7 in R4C1 (LoL, step 9) 23a. 20(3) cage at R3C8 = {479/578}, no 3,6 23b. 14(3) cage at R3C1 = {149/158}, no 3,6 23c. R2C3 + R4C1 = {89} (hidden pair in NR1C1) 23d. Killer pair 4,5 in R4C67 and R4C9, locked for R4 24. 14(4) cage at R4C2 (step 16) = {1247/1256}, no 3 24a. R5C3 = 3 (hidden single in NR3C2), R5C4 = 8, placed for NR4C4, clean-up: no 7 in R4C3, no 6 in R5C67, no 7 in R6C3 24b. Naked pair {59} in R5C67, locked for R5 [Cracked. The rest is fairly straightforward.] 25. LoL (step 7), no 3 in R37C3 -> no 3 in R1C4 25a. R1C4 = 4, placed for NR1C1, R9C4 = 1 (step 2), clean-up: no 5 in R12C1, no 6 in R9C6 (step 3), no 5 in R9C7 (step 4) 25b. R9C3 = 2, R3C3 = 4, placed for NR1C5, R7C3 = 1, placed for NR7C3, R3C2 = 5, R4C1 = 8 (cage sum), placed for NR1C1, R2C3 = 9, R4C3 = 6, R6C3 = 8, both placed for NR3C2, R4C4 = 9, R6C4 = 7, both placed for NR4C4, R5C6 = 5, placed for NR4C4, R5C7 = 9, placed for NR3C8, R3C8 = 8, R4C9 = 5 (cage sum), placed for NR1C6, R6C9 = 9, placed for NR6C9, R7C2 = 9, R1C3 = 5, R8C3 = 7, placed for NR6C1, clean-up: no 1 in R1C6 (step 3), no 1 in R4C67, no 2 in R6C7, no 2 in R8C9, no 4 in R9C7 (step 4) 25c. LoL (step 8), R9C6 = {78} -> R7C7 = {78} and R1C6 = {23} -> R3C7 = {23} 26. Naked pair {69} in R89C1, locked for C1, clean-up: no 3 in R12C1 26a. Naked pair {27} in R12C1, locked for C1 and NR1C1 -> R5C1 = 4, R7C1 = 5 R6C1 = 3, placed for NR6C1, clean-up: no 4 in R6C67 27. R6C9 = 9 -> R7C89 = 5 = {23} -> R7C8 = 3, R7C9 = 2, placed for NR6C9, R7C4 = 6, R8C4 = 3 (cage sum), both placed for NR7C3, R3C4 = 2, placed for NR1C5, R2C4 = 5, R5C9 = 1, placed for NR3C8, R8C9 = 4, placed for NR6C9, R9C9 = 3, clean-up: no 6 in R6C6 28. R3C7 = 3, placed for NR1C5 28a. R1C6 = 3 (hidden single in NR1C6), R9C6 = 7 (step 3), R1C2 = 6, R12C9 = [86] 29. 14(3) cage at R1C7 = {149} (only remaining combination) -> R2C8 = 4, R1C8 = 9, R1C7 = 1, R9C7 = 8 (step 4) 30. R23C7 = [23] = 5 -> R23C6 = 14 = [86] and the rest is naked singles, without using the nonets. |
Author: | Andrew [ Thu May 15, 2014 4:15 am ] |
Post subject: | Texas Jigsaw Killer Archive |
Texas Jigsaw Killer 38 by Ed (December 2009) here Puzzle Diagrams: Jigsaw nonet design: Tornado by Kathleen R. Nichol. Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration: Cages with cells in 3 jigsaw nonets: pink and orange Code: Select, Copy & Paste into solver: SumoCueV1=8J0=16J0+1J0+1J0=23J1+4J2=14J2=13J2+7J2+0J0=24J0=9J0=15J1+4J1+6J3+6J2+7J2=9J2+10J0+10J1+11J1+12J1+4J3=22J3+23J3+23J3+17J2=10J0=15J1+11J4+12J4+23J3+23J3=20J3+33J3+33J2+27J1+28J1+28J4+28J4=24J4=18J4+41J4+41J5=10J5=19J6+45J7+45J7+40J7+40J7=8J4=18J4+41J5+44J8+45J6=23J7+55J7+40J7=14J7+50J5+51J5=21J5+61J8+55J6+55J6=15J6+65J7+58J5+50J5+51J8+61J8=10J8=10J6+72J6+65J6+58J6+58J5=17J8+77J8+77J8+71J8 Solution: +-------+-------+-------+ Quote: Ed: This puzzle started out as Texas Jigsaw Killer 39 (TJK39), but it turned out so good it had to come forward to TJK38! It may be just co-incidence, but the TJKs I like to make seem to have a cage (I make) and nonet (from SumoCue) structure that DON'T give high SudokuSolver Scores (SSscore). So, all I need to do is try the puzzle that JSudoku generates within that structure that has the highest score and it has been the one. Easy! TJK39 will be a posted about the 4th of January. But first, SSscore: 1.43 manu: Ouah! It was so good to have another great TJK ! My Wt is short, but I must admit I had to take a long time to find the cracking move. Ed: Congratulations manu on finding a brilliant solution to this puzzle!! Love it. BTW - Andrew is finally going to post a puzzle( )...so now TJK39 will be on the 1st of January. Stay tuned. Andrew (in 2013): I agree completely! It was brilliant to combine two different LoLs in that way! I'd got each of them, and the hidden cage, but hadn't thought to put them together. Congratulations to manu for finding a short solving path. I had to work very hard to solve it. TJK 37 and TJK 38 both have the same score 1.60 (using SS v3.6.1). However this was a lot harder than TJK 37. Thanks Ed for the pics, explaining manu's breakthrough and your breakthrough, which I did find. My walkthrough is fairly long, but I found some interesting steps. manu's walkthrough: Ouah! It was so good to have another great TJK ! My Wt is short, but I must admit I had to take a long time to find the cracking move. Thanks Ed . A walkthough for TJK 38 Jigsaw nonets : n1 at r1c1 n2 at r1c5 n3 at r1c6 n4 at r2c6 n5 at r4c3 n6 at r5c8 n7 at r6c1 n8 at r6c2 n9 at r6c9 1) a) Innies-outies for n1 : « 45 rule » => r3c2 = r2c3 + r4c1 + 3 r3c2=(789) => r2c3+r4c1=4/5/6 : r2c3=(12345), r4c1=(1234) b) Cage sum for 10(2) ; r5c1=(6789) 2)a) Innies-outies for c12345 : r1c6=r4c5 b) hcage h23(4) = r1234c5 since r1c6=r4c5. c) Outies for n34 : r12c5=h11(2) => r34c5= h12(2). d) Outies for n78 : r589c5=h15(3). e) Innies for c5 : r67c5= h7(2). 3)a) LOL for r1234 (or for n1234) : {r5c12}={r4c34} b) LOL for c1234 (or for n1278) : {r1267c5} = {r4c34+r5c34} The following is the cracking move : c){r4c34} ={r5c12} from step 3)a), so digits at r4c34 must be different of any digit of {r12c5} since they share n4 with {r5c12} => {r4c34} = {r67c5} (from step 3)b)) = h7(2) (from step 2)e)) => {r4c34}={r5c12}=h7(2) : r5c1=6, r5c2=1 d) r4c1=4 (cage sum) e) Innie for r1234 : r4c2=3 f) From step 3)c) : r4c34={16} locked for r4 and n5 and r67c5={16} locked for c5 and n8. g) Cage 20(3) at r4 : {578} locked for r4. 4)a) No 2 at h12(2)c5 : naked single : r4c5=9=r1c6. Cage sum for h12(2) : r3c5=3. b) r4c6=2 c) Last combination for cage 22(5) at r3c6 = {12469}, {164} locked for r3 and n4. d) r12c5=h11(2)={47} locked for c5 and n2. e) 7 locked for n1 at cage 24(3) : last combination : r12c1= {35} locked for n1 and c1. f) Last combination 16(3) at r1c2 : {268} locked for r1 and n1. g) Last place for cage 24(3) : r3c2=8 : r2c3=1 h) r4c34=[61], r3c3=2, r23c4={59} locked for c4. The rest is not difficult. Ed's explanation of manu's breakthrough and Ed's one: Congratulations manu on finding a brilliant solution to this puzzle!! Love it. Worth a pic to show his key move...a hidden-cage clone. Quote: 3)a) LOL for r1234 (or for n1234) : {r5c12}={r4c34} b) LOL for c1234 (or for n1278) : {r1267c5} = {r4c34+r5c34} The following is the cracking move : c){r4c34} ={r5c12} from step 3)a), so digits at r4c34 must be different of any digit of {r12c5} since they share n4 with {r5c12} => {r4c34} = {r67c5} (from step 3)b)) = h7(2) (from step 2)e)) => {r4c34}={r5c12}=h7(2) : r5c1=6, r5c2=1 I went a more difficult way but found one interesting cell-clone move. This time from a combination of LOL and (un)available candidates. From LOL r6789: {r5c89=r6c67}. However, r5c9 cannot equal r6c6 since they do not share any candidates -> r5c9 = r6c7 and r5c8 = r6c6 This was the key move for my puzzle to get to eventually lock 1 in c5 into the h7(2) at r67c5. But manu's way is much, much better. BTW - Andrew is finally going to post a puzzle( )...so now TJK39 will be on the 1st of January. Stay tuned. Andrew's walkthrough: Ed wrote: Congratulations manu on finding a brilliant solution to this puzzle!! Love it. I agree completely! It was brilliant to combine two different LoLs in that way! I'd got each of them, and the hidden cage, but hadn't thought to put them together.Congratulations to manu for finding a short solving path. I had to work very hard to solve it. TJK 37 and TJK 38 both have the same score 1.60 (using SS v3.6.1). However this was a lot harder than TJK 37. Thanks Ed for the pics, explaining manu's breakthrough and your breakthrough, which I did find. My walkthrough is fairly long, but I found some interesting steps. Prelims a) R12C1 = {17/26/35}, no 4,8,9 b) R23C9 = {18/27/36/45}, no 9 c) R45C1 = {19/28/37/46}, no 5 d) R56C9 = {19/28/37/46}, no 5 e) R89C9 = {19/28/37/46}, no 5 f) R9C12 = {19/28/37/46}, no 5 g) 24(3) cage at R2C2 = {789} h) 9(3) cage at R2C3 = {126/135/234}, no 7,8,9 i) 20(3) cage at R4C7 = {389/479/569/578}, no 1,2 j) 8(3) cage at R6C6 = {125/134} k) 21(3) cage at R7C8 = {489/579/678}, no 1,2,3 l) 14(4) cage at R7C5 = {1238/1247/1256/1346/2345}, no 9 1. 8(3) cage at R6C6 = {125/134}, 1 locked for C6 1a. 8(3) cage at R6C6 = {125/134}, CPE no 1 in R6C8 2. Naked triple {789} in 24(3) cage at R2C2, CPE no 7,8,9 in R1C2 3. 45 rule on R1234 2 innies R4C12 = 7 = {16/34}/[25], no 7,8,9, no 2 in R4C2, clean-up: no 1,2,3 in R5C1 4. 16(3) cage at R1C2 must contain one of 7,8,9 4a. Killer triple 7,8,9 in 16(3) cage and 24(3) cage, locked for NR1C1, clean-up: no 1 in R12C1 4b. 16(3) cage = {169/268/349/358/457} (cannot be {178} which clashes with 24(3) cage at R2C2, cannot be {259/367} which clash with R12C1) 5. 45 rule on NR1C6 + NR2C6 2 innies R1C6 + R3C5 = 12 = {39/48/57}, no 1,2,6 5a. 45 rule on NR1C6 + NR2C6 2 outies R12C5 = 11 = {29/38/47/56}, no 1 6. 45 rule on C6789 1 outie R4C5 = 1 innie R1C6 -> R4C5 = {345789} 6a. 1 in NR2C6 only in R3C78, locked for R3, clean-up: no 8 in R2C9 [Note. R1C6 + R3C5 = 12 (step 5), R4C5 = R1C6 (step 6) -> R34C5 = 12 may come in useful later.] 7. 45 rule on NR6C1 + NR6C2 1 outie R5C5 = 2 innies R7C5 + R9C4 + 1 7a. Min R7C5 + R9C4 = 3 -> min R5C5 = 4 7b. Max R7C5 + R9C4 = 8, no 8 in R7C5 + R9C4 8. 45 rule on C6789 4 outies R1234C5 = 23 [Alternatively, 23(4) cage at R1C5 and R1C6 = R4C5, step 6] 8a. 45 rule on NR6C1 + NR6C2 3 outies R589C5 = 15 8b. 45 rule on C5 2 remaining innies R67C5 = 7 = {16/25/34}, no 7,8,9 9. 45 rule on NR1C6 2 innies R1C6 + R4C9 = 1 outie R2C6 + 9, IOU no 9 in R4C9 9a. Max R1C6 + R4C9 = 17 -> max R2C6 = 8 10. 45 rule on NR1C1 1 outie R3C2 = 2 innies R2C3 + R4C1 + 3 10a. Max R2C3 + R4C1 = 6, no 6 in R2C3 + R4C1, clean-up: no 1 in R4C2 (step 2), no 4 in R5C1 10b. 1 in NR1C5 only in R2C4 + R5C2, CPE no 1 in R5C4 11. 45 rule on NR6C9 1 outie R7C8 = 2 innies R6C9 + R8C7 + 3 11a. Min R6C9 + R8C7 = 3 -> min R7C8 = 6 11b. Max R6C9 + R8C7 = 6, no 6,7,8,9 in R6C9 + R8C7, clean-up: no 1,2,3,4 in R5C9 12. 45 rule on NR6C9 2 outies R5C9 + R7C8 = 1 innie R8C7 + 13 12a. Max R5C9 + R7C8 = 17 -> max R8C7 = 4 12b. Max R8C7 = 4 -> min R67C7 = 14, no 1,2,3,4 in R67C7 13. 17(3) cage at R9C6 must contain one of 1,2,3,4 13a. Killer quad 1,2,3,4 in R6C9, R8C7, R89C9 and 17(3) cage, locked for NR6C9 13b. 21(3) cage at R7C8 = {579/678}, CPE no 7 in R9C8 14. Law of Leftovers (LoL) for R6789 two outies R5C89 must exactly equal two innies R6C67, R5C9 = R6C7 = {6789} (because no 6,7,8,9 in R6C6), R6C6 = R5C8 = {12345} 15. 45 rule on R6789 2 outies R5C59 = 1 innie R6C8 + 9, IOU no 9 in R5C5 15a. Max R5C59 = 17 -> max R6C8 = 8 15b. 9 in NR5C8 only in R5C9 + R7C78, CPE no 9 in R7C9 16. 9 in C5 only in R1234C5 (step 8) = 23 = {2489/2579/3479} (cannot be {3569} which clashes with R67C5) 16a. R12C5 = 11 (step 5a) -> R12C5 = {29/47}, no 3,5,6,8 17. LoL for C1234 four outies R1267C5 must exactly equal four innies R45C34, no 8 in R1267C5 -> no 8 in R45C34 18. LoL for R1234 two outies R5C12 must exactly equal two innies R4C34, no 8 in R4C34 -> no 8 in R5C12, clean-up: no 2 in R4C1, no 5 in R4C2 (step 3) 19. 45 rule on C1234 2 outies R56C5 = 1 innie R9C4 + 8 19a. Max R56C5 = 14 -> max R9C4 = 6 20. 45 rule on C9 3 innies R147C9 = 16 = {268/358/367/457} (cannot be {169/259} because 1,2,9 only in R1C9, cannot be {178/349} which clash with the pair of 10(2) cages in C9), no 1,9 20a. 9 in C9 only in R56C9 = [91] or R89C9 = {19}, 1 locked for C9 (locking cages), clean-up: no 8 in R3C9 20b. 1 in C9 only in R689C9, locked for NR6C9 21. 45 rule on NR1C1 4 innies R2C23 + R34C1 = 21 = {1389/1479/1578/2478} (cannot be {2379} which clashes with R12C1, cannot be {3459} because R2C2 + R3C1 only contain 7,8,9) 21a. R2C23 + R34C1 = {1389/1479/2478} (cannot be {1578} because 24(3) cage at R2C2 clashes with R45C1 = [19], killer combo clash in NR1C5), no 5 21b. 3 of {1389} must be in R2C3 (cannot be 1{89}3 because 24(3) cage at R2C2 clashes with R45C1 = [37], killer combo clash in NR1C5), no 3 in R4C1, clean-up: no 4 in R4C2 (step 3), no 7 in R5C1 22. Hidden killer pair 5,6 in R12C1 and 16(3) cage at R1C2 for NR1C1, R12C1 contains one of 5,6 -> 16(3) cage must contain one of 5,6, 16(3) cage (step 4b) = {169/268/358/457} (cannot be {349} which doesn’t contain 5 or 6) 23. R4C1 = {14}, R4C12 = 7 (step 3) -> R4C12 + R5C1 = [169/436], 6 locked for NR1C5 23a. R4C12 + R5C1 = [169/436], CPE no 6 in R5C34 23b. LoL for R1234 two outies R5C12 must exactly equal two innies R4C34, when 6 is in R5C1 there must be 6 in one of R4C34 -> 6 in R4C2 or R4C34, locked for R4 [Taking step 21a a bit further] 24. R2C23 + R34C1 (step 21a) = {1479/2478} (cannot be {1389} because 7 from 24(3) cage at R2C2 and 9 from R45C1 = [19] clash with R12C5 using NR1C5, killer combo clash), no 3, 4,7 locked for NR1C1 and 24(3) cage at R2C2, no 7 in R3C3 24a. 4 in NR1C1 only in R2C3 + R4C1, CPE no 4 in R4C3 [And further still] 25. R2C23 + R34C1 (step 24) = {1479} (cannot be {2478} because R4C12 (step 3) = [43] blocks the only combination for 9(3) cage at R2C3 containing 2 in R2C3) -> R2C3 + R4C1 = {14}, locked for NR1C1, R2C2 + R3C1 = {79}, locked for NR1C1 and 24(3) cage at R2C2 -> R3C3 = 8, placed for NR1C5, clean-up: no 2 in R9C1 25a. Naked pair {14} in R2C3 + R4C1, CPE no 1 in R4C3 25b. 16(3) cage at R1C2 (step 22) = {268/358}, 8 locked for R1 25c. 1 in R1 only in R1C78, locked for NR1C6 25d. 8 in C1 only in R6789C1, locked for NR6C1 25e. Clean-up: no 4 in R1C6 + R3C5 (step 5), no 4,8 in R4C5 (step 6) 26. R12C5 (step 16a) = {29/47}, R1C6 + R3C5 (step 5) = {39/57}, R1C6 = R4C5 (step 5) -> R34C5 = {39/57} 26a. Killer pair 7,9 in R12C5 and R34C5, locked for C5 27. 9(3) cage at R2C3 = {126/135/234} 27a. R2C3 = {14} -> no 4 in R3C3 27b. 9(3) cage = {126/234} (cannot be {135} which clashes with R4C12 (step 3) = [43], killer combo clash), no 5, 2 locked for C3 27c. 1 in NR1C1 only in R2C3 -> 9(3) cage = {126} = [126] or in R4C1 -> R4C12 (step 3) = [16] (locking cages) -> 6 must be in R4C23, locked for R4 28. 15(3) cage at R2C4 = {159/249} (cannot be {357} because R4C2 = 6, R5C1 = 9 => R4C4 = 9 (LoL, step 18) blocks {357}), no 3,7, 9 locked for C4 28a. 3 in NR1C5 only in R3C3 + R45C2, CPE no 3 in R5C3 29. LoL for R1234 two outies R5C12 must exactly equal two innies R4C34 29a. No 7 in R4C34 -> no 7 in R5C2 29b. R5C12 and R4C34 cannot be [69] because R23C3 = [12] clashes with R4C2 + R5C34 = [312] -> no 9 in R5C2 30. Variable hidden killer pair 1,5 in 15(3) cage at R2C4 and R5C2 for NR1C5, R5C2 cannot contain both of 1,5 -> 15(3) cage must contain at least one of 1,5 -> 15(3) cage (step 28) = {159} (only remaining combination, cannot be {249} which doesn’t contain 1 or 5), locked for C4 31. LoL for R1234 two outies R5C12 must exactly equal two innies R4C34 31a. No 4 in R4C34 -> no 4 in R5C2 32. R12C5 = {47} (hidden pair in NR1C5), locked for C5 and 23(4) cage at R1C5, clean-up: no 5 in R1C6 + R3C5 (step 5), no 5 in R4C5 (step 6) 32a. Naked pair {39} in R34C5, locked for C5 and NR2C6 32b. 20(3) cage at R4C7 = {578} (only remaining combination), locked for R4 33. Killer pair 2,4 in R4C6 and 8(3) cage at R6C6, locked for C6 34. 1,2,4 in NR2C6 only in 22(5) cage at R3C6 = {12469} (only remaining combination), no 3,5,7 -> R3C6 = 6, R34C5 = [39], R3C3 = 2, placed for NR1C5, R1C6 = 9, placed for NR1C6, clean-up: no 3,6,7 in R2C9 35. Naked triple {159} in 15(3) cage at R2C4, 9 locked for NR1C5 -> R5C1 = 6, placed for NR1C5, R4C1 = 4, placed for NR1C1, R4C2 = 3, R24C3 = [16], R4C6 = 2, clean-up: no 2 in R12C1, no 5 in 8(3) cage at R6C6, no 4 in R6C9, no 7 in R9C1, no 4,6 in R9C2 35a. Naked pair {59} in R23C4, locked for NR1C5 -> R4C4 = 1, R5C2 = 1, clean-up: no 9 in R9C1 35b. LoL for R6789 two outies R5C89 must exactly equal two innies R6C67, no 2,5 in R5C8, no 1 in R6C6, no 6 in R6C7 36. Naked pair {35} in R12C1, locked for C1 and NR1C1, clean-up: no 7 in R9C2 36a. Naked triple {268} in 16(3) cage at R1C2, locked for R1 37. Naked triple {134} in 8(3) cage at R6C6, 1 also locked for NR5C8 37a. Naked triple {134} in 8(3) cage at R6C6, CPE no 3,4 in R6C8 38. 1 in C5 only in R67C5 (step 8b) = {16}, locked for C5 and NR6C2 38a. 2 in C5 only in R89C5, locked for NR5C8 and 14(4) cage at R7C5, no 2 in R9C4 39. 2 in C5 only in 14(4) cage at R7C5 = {1238/1256} (cannot be {2345} because R7C5 only contains 1,6) -> R7C5 = 1, R6C5 = 6, R9C4 = {36} 39a. R8C6 = 1 (hidden single in C6), clean-up: no 9 in R9C9 39b. Deleted, I did it earlier 39c. 6 in C9 only in R789C9, locked for NR6C9 40. R6C5 = 6 -> 24(4) cage at R5C5 = {3678} (only remaining combination) -> R5C5 = 8, placed for NR4C3, R67C4 = {37}, locked for C4 and NR6C2 -> R9C4 = 6, placed for NR6C1, clean-up: no 2 in R6C9, no 4 in R8C9 41. R45C2 = [31] = 4 -> R5C34 = 11 = [74/92] 41a. Naked pair {79} in R5C39, locked for R5 -> R5C6 = 5 42. R5C6 = 5, 3 in R5 only in R5C78 -> 18(4) cage at R5C5 = {2358} (only remaining combination) -> R5C7 = 2, R56C8 = [38], both placed for NR5C8, R67C6 = [34], R6C9 = 1, R5C9 = 9, placed for NR5C8, R5C34 = [74], 7 placed for NR4C3 42a. Naked pair {25} in R89C5, locked for NR5C8 42b. R6C7 = 9 -> R78C7 = 9 = [63], 3 placed for NR6C9, clean-up: no 7 in R89C9 43. 16(3) cage at R1C2 = [682], R8C4 = 8, clean-up: no 2 in R9C9 44. R67C4 = [73], R6C1 = 2, placed for NR6C1, R9C2 = 9, placed for NR6C1, R9C1 = 1 45. Naked pair {45} in R6C23, locked for NR6C2 -> R7C23 = [29] 46. R8C9 = 6 (hidden single in R8), R9C9 = 4, clean-up: no 5 in R23C9 46a. R23C9 = [27], 7 placed for NR1C6, R7C9 = 5 (hidden single in R7), placed for NR6C9, R1C9 = 3, R12C1 = [53] 46b. R1C9 = 3 -> R12C8 = 10 = [46] and the rest is naked singles, without using the nonets. |
Author: | Andrew [ Thu May 15, 2014 9:30 pm ] |
Post subject: | Texas Jigsaw Killer Archive |
Texas Jigsaw Killer 39 by Ed (31st December 2009/1st January 2010) here Puzzle Diagrams: Jigsaw nonet design: Lego Man by Cyndie Smith. Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration: Cages with cells in 3 jigsaw nonets: lilac Cages with cells in 2 jigsaw nonets: green and yellow Cages with cells in 1 jigsaw nonet: red, blue and grey Code: Select, Copy & Paste into solver: SumoCueV1=10J0=17J0+1J0=22J1+3J1+3J1=18J2+6J2=7J2=12J0+0J0+1J0+1J0=14J1+6J2+6J2+8J2=17J2+9J3+9J0=23J0+20J1+13J1=18J1+23J2+17J2+17J4=22J3=18J3+20J5+20J5+13J1+23J5+23J5=19J4=26J4+27J3+28J3+28J3=7J5+39J1+39J5+34J4+34J4+35J4+27J3=9J3+46J3=7J5=12J5=12J5=5J4+51J4+35J4+27J6=19J6=11J6+48J6+49J7+50J8=17J8=12J8+35J8+55J6+55J6+56J6=16J7+66J7+66J7+60J8+61J8+61J8=10J6+72J6+56J7=16J7+75J7+75J7+60J7=9J8+79J8 Solution: +-------+-------+-------+ Quote: Ed: Many thanks to Andrew for starting this thread for me. Happy New Year to everyone! As has become the norm with these puzzles, Texas Jigsaw Killer 39 (TJK39) has a really short way to crack it. But I(Ed) know that SudokuSolver can't do at least one of the tricks I used so there must be at least one other way to solve this one. Thanks to Børge for supplying the images. Love his images now having the row and column numbering! SSscore: 1.66 manu: Nice puzzle from our best jigsaw Killer. John Kramer would not have made a more frightening one : thanks Ed ! Ed: Thanks! My Apprentice passed the test. You SAW 4 from r3c9 in a really neat way! Andrew (in 2013): I really enjoyed this one, especially after the long struggle with TJK 38. My solving path was very similar to manu's, including the step shown in Ed's pic. It's a bit longer because I didn't spot manu's step 2b. manu's walkthrough: Nice puzzle from our best jigsaw Killer. John Kramer would not have made a more frightening one : thanks Ed ! Walkthrough TJK 39 Jigsaw nonets : prelims (sudocue) n1 at r1c1 n2 at r1c4 n3 at r1c7 n4 at r3c1 n5 at r4c3 n6 at r3c9 n7 at r7c1 n8 at r7c5 n9 at r7c6 1)a) Innies-outies for n1 : r3c3=6+r3c1 = r3c3=(789), r3c1=(123) b) Innies-outies for n4 : r7c1=4+r3c1 : r7c1=(567) c) Innies-outies for n6 : r7c9=5+r3c9 : r3c9=(1234), r7c9=(6789) d) Innies-outies for n3 : r3c7=r3c9+3 : r3c7=(4567) 2)a) Innies for r9 : r9c37=h10(2). b) Using cage h10(2), innie for n8 : r7c5=3, cage sum r6c5=9 3)a) 1 locked for n6 at r3c9+5(2)={14/23} : r3c9 <> 4 ! b) step 1)d) => r3c7<>7 c) step 1)c) => r7c9<>9 4)a) 3 locked for n2 and r3 at r3c46. b) r3c1<>3 =>(step 1)a) r3c3<>9 and =>(step 1)b) r7c1<>7 c) r3c9<>3 => (step 1)d) r3c7 <> 6 and => (step 1)c) r7c9 <> 8. 5)a) Naked pair {12} at r3c19 locked for r3 : r3c1+r3c9=3. b) Steps 1)b+1)c : r7c1+r7c9=9+r3c1+r3c9=9+3=12 : only combination : r7c19=[57] c) Step 1)b => r3c1= 1, r3c9=2. d) Step 1)a => r3c3=7, step 1)d) => r3c7=5 : it's cracked ! 6)a) Last combination : 17(3)n3={269}, {69} locked for n3. b) 7(2)n3={34} locked for n3. c) LOL for n123 : r45c5=r3c19={12} locked for c5 and n2. d) Innie for n2 : r3c4+r3c6+r5c5=h9(2) = {234}, since it must contain 3(step 4)a), and {135} blocked by r3c17=[15] . r5c5=2, r3c46={34} locked for r3. e) r4c5=1, r23c5=[58/76]. 7)a) 5(2)n6={14} locked for n6 and r6. b) 26(4)={5678} (last combo), {568} locked for c9 and n6. c) 12(2) at r6c6 : [39/84] d) Killer pair {34} locked for c6 at r3c6+12(2) : r5c6=1, r5c4=4 8)a) Innies-outies for n9 : r9c7=r7c6=(49). b) r9c37=h10(2)=[19/64] c) Innies-outies for n7 : r9c3=r7c4=(16) d) 7(2) at r6c4 : [61] The rest is easy Ed's explanation of manu's breakthrough and Ed's one: manu wrote: John Kramer would not have made a more frightening one : ! Thanks! My Apprentice passed the test. You SAW 4 from r3c9 in a really neat way! Worth a pic. manu's walkthrough Quote: 3)a) 1 locked for n6 at r3c9+5(2)={14/23} : r3c9 <> 4 ! This looks similar to one aspect of the "Locking/Blocking Cages" technique (post in techniques forum coming) but involves just one cage and one cell. So, is "Locking Cage-cell". Nice.I couldn't get rid of that 4 but used "45" on disjoint nonets 1 & 3 to lock 2 in r3c19. This led to the breakthrough in r7. Since 2 locked at r3c19 -> r7c1 = 6 or r7c9 = 7 but not both. Andrew's walkthrough: I really enjoyed this one, especially after the long struggle with TJK 38. My solving path was very similar to manu's, including the step shown in Ed's pic. It's a bit longer because I didn't spot manu's step 2b. Prelims a) 10(2) cage at R1C1 = {19/28/37/46}, no 5 b) 7(2) cage at R1C9 = {16/25/34}, no 7,8,9 c) R6C23 = {18/27/36/45}, no 9 d) R67C4 = {16/25/34}, no 7,8,9 e) R67C5 = {39/48/57}, no 1,2,6 f) R67C6 = {39/48/57}, no 1,2,6 g) R6C78 = {14/23} h) R9C12 = {19/28/37/46}, no 5 i) R9C89 = {18/27/36/45}, no 9 j) 22(3) cage at R1C4 = {589/679} k) 19(3) cage at R4C8 = {289/379/469/478/568}, no 1 l) 7(3) cage at R5C4 = {124} m) 19(3) cage at R7C2 = {289/379/469/478/568}, no 1 n) 11(3) cage at R7C3 = {128/137/146/236/245}, no 9 o) 26(4) cage at R4C9 = {2789/3689/4589/4679/5678}, no 1 Steps resulting from Prelims 1a. 22(3) cage at R1C4 = {589/679}, 9 locked for R1 and NR1C4, clean-up: no 1 in R2C2 1b. 7(3) cage at R5C4 = {124}, locked for R5 2. 45 rule on NR1C4 3 innies R3C46 + R5C5 = 9 = {126/135/234}, no 7,8 3. 45 rule on NR3C1 1 outie R7C1 = 1 innie R3C1 + 4, R3C1 = {12345}, R7C1 = {56789} 4. 45 rule on NR3C9 1 outie R7C9 = 1 innie R3C9 + 5, R3C1 = {1234}, R7C9 = {6789} 5. 45 rule on C12 1 outie R5C3 = 2 innies R16C2 + 1 5a. Max R16C2 = 8, no 8 in R16C2, clean-up: no 1 in R6C3 5b. Min R16C2 = 3 -> no 3 in R5C3 6. 1 in NR3C9 only in R3C9 or R6C78 = {14} -> no 4 in R3C9 (locking-out cages), clean-up: no 9 in R7C9 (step 4) 7. 45 rule on NR1C7 1 innie R3C7 = 1 outie R3C9 + 3, R3C9 = {123} -> R3C7 = {456} 8. 45 rule on NR1C7 3 innies R2C9 + R3C78 = 20 = {479/569/578} (cannot be {389} because R3C7 only contains 4,5,6), no 1,2,3 8a. 4 of {479} must be in R3C7 -> no 4 in R2C9 + R3C8 9. 45 rule on NR1C1 1 innie R3C3 = 1 outie R3C1 + 6, R3C1 = {123}, R3C3 = {789}, clean-up: R7C1 = {567} (step 3) 10. Law of Leftovers (LoL) for R123 two outies R45C5 must exactly equal two innies R3C19, R3C19 = {123} -> R4C5 = {123}, R5C5 = {12} 10a. Naked triple {124} in 7(3) cage at R5C4, 4 locked for NR4C4, clean-up: no 3 in R7C4, no 8 in R7C5, no 8 in R7C6 11. 14(3) cage at R2C5 = {158/167/248} (cannot be {257/356} which clash with 22(3) cage at R1C4, cannot be {347} which clashes with R67C5), no 3 11a. Naked pair {12} in R45C5, locked for C5 and NR1C4 11b. 3 in NR1C4 only in R3C46, locked for R3, clean-up: no 9 in R3C3 (step 9), no 6 in R3C7 (step 7), no 7 in R7C1 (step 3), no 8 in R7C9 (step 4) 11c. Naked pair {12} in R3C19, locked for R3 11d. Killer pair 1,2 in R3C9 and R6C78, locked for NR3C9 12. R2C9 + R3C78 (step 8) = {479/569/578} 12a. R3C7 = {45} -> no 5 in R2C9 + R3C8 13. 12(3) cage at R2C1 = {129/138/147/156/237/246} (cannot be {345} because R3C1 only contains 1,2) 13a. 12(3) cage = {129/138/156/237/246} (cannot be {147} which clashes with R3C13 = [17], step 9, killer combo blocker using NR1C1) 13b. 7,8,9 of {129/138/237} must be in R3C2 -> no 7,8,9 in R2C1 14. 45 rule on NR3C1 3(2+1) outies R2C1 + R3C2 + R7C1 = 16 14a. Max R26C1 = 11 -> min R3C2 = 5 14b. R2C1 + R3C2 + R7C1 cannot be [565] -> no 5 in R2C1 15. 45 rule on NR3C9 3(2+1) outies R2C9 + R3C8 + R7C9 = 22 15a. R27C9 cannot total 14 (cannot be [77] and [86] clashes with R3C8 = 8) -> no 8 in R3C8 16. 26(4) cage at R4C9 = {4679/5678} (cannot be {3689} which clashes with R6C78 = {23} because R37C9 = [16], step 4, cannot be {4589} because R7C9 only contains 6,7), no 3, 6,7 locked for C9, clean-up: no 1 in R2C8, no 2,3 in R9C8 [Alternatively consider combinations for R6C78 = {14/23} R6C78 = {14} => R3C9 = 2, R7C9 = 7 (step 4) => 26(4) cage cannot be {3689} or R6C78 = {23}, locked for NR3C9 …] 17. 45 rule on R9 2 innies R9C37 = 10 = [19]/{28/37/46}, no 5, no 1 in R9C7 [I ought to have spotted this after step 11; then analysing the 26(4) cage at R4C9 would have been simpler than in step 16 …] 18. R3C19 = [12] (cannot be [21] because R7C19 cannot be [66] using steps 3 and 4), 1 placed for NR3C1, 2 placed for NR3C9, R3C3 = 7 (step 9), placed for NR1C1, R3C7 = 5 (step 7), placed for NR1C7, R7C1 = 5 (step 3), placed for NR7C1, R7C9 = 7 (step 4), placed for NR6C6 [More formally R7C1 = R3C1 + 4 (step 3), R7C9 = R3C9 + 5 (step 4) -> R3C1 cannot be 1 more than R3C9 because R7C19 cannot be equal …] [manu found R3C19 = {12} = 3 -> R7C19 = 12 (using steps 3 and 4) = [57] … which is a better way to get this result.] 18a. Clean-up: no 3 in R1C1, no 3,9 in R2C2, no 2 in R2C8, no 2 in R6C2, no 8 in R6C3, no 2 in R6C4, no 5,7 in R6C5, no 5,7 in R6C6, no 3 in R6C78, no 9 in R9C2 [Cracked, the rest is straightforward.] 19. Naked pair {14} in R6C78, locked for R6 and NR3C9, clean-up: no 5 in R6C23, no 6 in R7C4 19a. 2 in R6 only in R6C13, locked for NR3C1 20. R7C9 = 7 -> 26(4) cage at R4C9 = {5678} (only remaining combination), 5,6,8 locked for C9 and NR3C9 -> R2C9 = 9, R3C8 = 6, placed for NR1C7, clean-up: no 1 in R1C9, no 1,4 in R9C8, no 3 in R9C9 20a. Naked pair {34} in 7(2) cage at R1C9, locked for NR1C7 20b. 1 in C9 only in R89C9, locked for NR7C6 21. Naked pair {34} in R3C46, locked for NR1C4 -> R3C5 = 8, placed for NR1C4, R3C2 = 9, R2C1 = 2 (cage sum), placed for NR1C1, clean-up: no 8 in 10(2) cage at R1C1, no 5 in 22(3) cage at R1C4, no 4 in R7C5, no 8 in R9C2 21a. Naked pair {46} in 10(2) cage at R1C1, locked for NR1C1 22. Naked triple {679} in 22(3) cage at R1C4, locked for R1 and NR1C4 -> R2C5 = 5, R4C5 = 1 (cage sum), R5C5 = 2 22a. Naked pair {39} in R67C5, locked for C5 22b. 4 in C5 only in R89C5, locked for NR7C5 23. 45 rule on NR7C1 1 remaining innie R7C4 = 1 outie R9C3 = {12}, clean-up: no 3 in R6C4 24. 45 rule on NR7C6 1 remaining innie R7C6 = 1 outie R9C7 = {39}, clean-up: no 8 in R6C6 24a. Naked pair {39} in R7C56, locked for R7 24b. Naked pair {39} in R67C6, locked for C6 24c. Naked pair {39} in R6C56, locked for R6 and NR4C3, clean-up: no 6 in R6C23 24d. R6C23 = [72], 7 placed for NR3C1, R9C3 = 1, R7C4 = 1 (step 23), R6C4 = 6, R5C46 = [41], R3C46 = [34], R2C34 = [38], R1C23 = [15], 7(2) cage at R1C9 = [34], 10(2) cage at R1C1 = [46], R2C67 = [71], R6C1 = 8, placed for NR3C1, R6C9 = 5, 22(3) cage at R1C4 = [976], R6C78 = [41], R9C9 = 4, R9C8 = 5, R9C5 = 6, R8C5 = 4, clean-up: no 3,9 in R9C1, no 2 in R9C2 25. R9C3 = 1 -> R78C3 = 10 = [46] -> R4C3 = 8, R4C4 = 5 (cage sum) 26. R9C7 = 9 (hidden single in R9), R7C6 = 9 (step 24), placed for NR7C6 26a. R8C9 = 1 -> R78C8 = 11 = [83], both placed for NR7C6 and the rest is naked singles, without using the nonets. |
Author: | Andrew [ Thu May 22, 2014 2:26 am ] |
Post subject: | Texas Jigsaw Killer Archive |
Texas Jigsaw Killer 40 by Ed (January 2010) here Puzzle Diagrams: [edit: original image gone so used one of Børge's. Thanks!] Børge's image with udosuk Style Killer Cages and Ruud TJK#33 inspiration: Cages with cells in 4 jigsaw nonets: pink There were 5 further images in the original post, only differing from the images in this archive entry by the choice of pastel colour. Code: Select, Copy & Paste into solver: SumoCueV1=36J0+0J0+0J0=15J1+3J1=15J1+5J1=13J2+7J2=10J0+9J0+0J0=10J1+3J1=9J1+14J1=10J2+16J2=37J0+18J0+0J3+12J3+12J4=16J1+23J2=28J2+25J2+18J0+0J3+0J3=11J3=17J4+23J4+23J5=5J2+25J2+18J3=9J3+30J3+30J4+31J4=22J4+41J5+34J5+25J5+18J6+37J6=26J3+47J4+31J4+41J5=33J5+51J5+25J7+18J6+18J6+47J6+47J8=13J4+58J5+51J5+25J7+25J7=9J6+63J6=10J8+65J8=14J8+58J8+51J7=15J7+70J7=13J6+72J6=9J8+74J8+67J8+67J8+51J7+51J7+51J7 Solution: +-------+-------+-------+ Quote: Ed: I had a lot of trouble with this puzzle so it must be at the upper end of my ability. Had to do it 5 times to get it properly. Fortunately, there are many interesting moves available so very worthy of the big 4-oh. I know manu will love it! I really enjoyed making it for you. Mike (mhparker): Thanks, Ed, for a great TJK! This one was a real pleasure to solve, since - as Ed said - there were lots of interesting moves available. I'm glad that Ed told me about this TJK, because it would have been a travesty of justice for no-one to have written a walkthrough for it! It will be interesting to see whether Ed's solving tricks were different than mine. Ed: Thanks very much for your walkthrough Mike. Love your style! I'm really glad you included the long version of the WT since it shows some of the really interesting clone moves available with this cage pattern. I missed your step 10 so had to use an alternative way to crack the puzzle (different again to Mike's really neat and powerful alternative). However, I also used your step 4 so that is the really key one. [edit: actually, Mike found a way so that it's not needed. See here]. Interesting that you called it Nishio. Andrew (in 2013): Solving this puzzle was interesting for what I spotted but then found that I didn’t need to use. My solving path was very different from Mike's. It was a bit more like Ed's, in the sense that I used the same 45 as his step 7, but I used it is a different way; not the clever way he used it. Mike's walkthrough: Thanks, Ed, for a great TJK! This one was a real pleasure to solve, since - as Ed said - there were lots of interesting moves available. I'm glad that Ed told me about this TJK, because it would have been a travesty of justice for no-one to have written a walkthrough for it! It will be interesting to see whether Ed's solving tricks were different than mine. Texas Jigsaw Killer 40 Walkthrough Nonet layout: 111222233 111222233 114452333 144455633 444555666 774556669 777856699 778888999 778888999 Prelims: a) 36(7) at R1C1 = {1236789/1245789/1345689/2345679} (no eliminations); 9 locked b) 15(2) at R1C6 and R8C8 = {69/78} (no 1..5) c) 13(2) at R1C8 and R9C1 = {49/58/67} (no 1..3) d) 10(2) at R2C1 and R8C3 = {19/28/37/46} (no 5) e) 10(3) at R2C4, R2C8 = {127/136/145/235} (no 8,9) f) 9(2) at R2C6, R5C2, R8C1 and R9C3 = {18/27/36/45} (no 9) g) 37(7) at R3C1 = {1246789/1345789/2345689} (no eliminations); 4,8,9 locked h) 28(7) at R3C8 = {1234567} (no 8,9); 1..7 locked i) 11(3) at R4C4 = {128/137/146/236/245} (no 9) j) 5(2) at R4C8 = {14/23} (no 5..9) k) 22(3) at R5C6 = {589/679} (no 1..4); 9 locked -> no 9 in R7C6 (CPE) l) 26(4) at R6C3 = {2789/3689/4589/4679/5678} (no 1) m) 33(7) at R6C7 = {1234689/1235679/1245678} (no eliminations); 1,2,6 locked 1. 15(2) at R1C6 (prelim b) = {(6/7)..} 1a. -> {67} combo blocked for 13(2) at R1C8 (prelim c) = {49/58} (no 6,7) 1b. 15(2) at R1C6 and 13(2) at R1C8 form killer pair (KP) on {89} in R1 1c. -> no 8,9 elsewhere in R1 2. Innies N2: R2C4+R3C6 = 6(2) = {15/24} (no 3,6..9) 2a. -> {45} combo blocked for 9(2) at R2C6 (prelim f) = {18/27/36} (no 4,5) 2b. {45} in N2 locked in 15(3) and h6(2) at R2C4+R3C6, which must contain 1 of {45} 2c. -> 15(3) at R1C4 must contain exactly 1 of {45} = {159/249/348/357} (no 6) (Note: {258} blocked by 6(2) at R2C4+R3C6) 2d. {89} in 15(3) only available in R2C5 2e. -> R2C5 = {357}+{89} = {35789} (no 1,2,4) 3. 5 of R2 now locked in innies R2: R2C345 = 16(3) = {259/358/457} (no 1,6) 3a. cleanup: no 5 in R3C6 (step 2) 4. Nishio: R3C7 sees all of R1C789 4a. -> if R3C7 = 9, then 9 of R1 would be forced into R1C6 4b. but this would leave nowhere to place the 9 in 22(3) at R5C6 (prelim k) 4c. -> no 9 in R3C7 5. Law of Leftovers (LoL) R12: R3C126+R4C1 = R12C89 5a. 9 of N3 locked in R12C89 5b. -> 9 locked in R3C12+R4C1 for N1 and 37(7) 5c. cleanup: no 1 in R2C12 == The next part of the strategy is to remove the 9 from R2C5 in order to constrain it to the == 10(2) cage at R2C8. I found a long (but more traditional) and a short way of doing this. == I'll start with the long way first, then describe the shortcut as an appendix. >>>>> Start of long way of removing the 9 at R2C5 >>>>> 6. 36(7) at R1C1 (prelim a) and 37(7) at R3C1 (prelim g) form grouped X-Wing on 9 within R34 6a. -> no 9 elsewhere in R34 (i.e., no 9 in R4C567) 7. Innies C89: R6C8+R9C89 = 19(3) = {289/379/469/478/568} (no 1) (Note: no duplicates allowed because all 3 innies belong to 33(7) cage) 7a. max. R9C89 = 15 (because {79/89} blocked by 15(2) at R8C8) 7b. -> min. R6C8 = 4 (no 2,3) 7c. 1 of 33(7) (prelim m) locked in split 14(4) at R6789C7 = {1238/1247/1256/1346} (no 9) 7d. -> 1 locked for C7 7e. cleanup: no 8 in R2C6 8. LoL C89: R5C89+R6C8 = R389C7 8a. no 9 in outies at R389C7 -> no 9 in innies at R5C89+R6C8 8b. -> no 9 in R6C8 8c. R6C8 = R3C7 (cannot equal either of R89C7 because they share the same cage) 8d. -> no 2,3 in R3C7 8e. R5C89 = R89C7 8f. -> no 8 in R89C7 9. 9 in N6 locked in R5C7+R6C6 9a. -> no 9 in R5C6 10. Common Peer Elimination (CPE): R6C4 sees all candidate positions for 9 in R7 10a. -> no 9 in R6C4 11. 9 of N5 locked in R567C5 for C5 (Note: there are other moves involving eliminations on 9 available here, e.g., 9 in C4 locked in R78C4 for N8. Also, there's a C6789 innie/outie difference cage 1(2) at R7C5+R9C6 that would remove the 9 from R7C5 and lock the 9 of C5 into 17(3) at R4C5.) <<<<< End of long way of removing the 9 at R2C5 <<<<< 12. 9 in R2 locked in R2C89 12a. -> 10(2) at R2C8 = {19}, locked for R2 and N3 12b. cleanup: no 4 in R1C89, no 8 in R2C7, no 4 in R5C8 13. LoL R12 (see step 5): R12C89 = {1589} 13a. -> R3C126+R4C1 = {1589} 13b. -> R3C6 = 1, R3C12+R4C1 = {589}, locked for N1 and 37(7) 13c. -> R2C4 = 5 (step 2) 13d. cleanup: no 2 in R2C12, no 4 in R9C3 14. Hidden single (HS) in R2 at R2C5 = 8 14a. -> R2C3 = 3 (h16(3) cage sum, step 3) 14b. cleanup: no 7 in R1C67, no 7 in R2C12, no 6 in R2C67, no 7 in R8C4, no 6 in R9C4 14c. extended cleanup (last nonet digits): R1C123 = {127} (no 4,6), R1C45 = {34} (no 2,7) 15. Split 5(2) at R3C45 = {23} (last combo), locked for R3 16. Innie/Outie difference (I/O diff.), C1234: R1C4 = R3C5 16a. -> R1C4 = 3, R3C5 = 3 16b. -> R1C5 = 4, R3C4 = 2 16c. cleanup: no 7 in R6C2, no 7,8 in R8C3, no 6,7 in R9C3 17. Hidden pair (HP) in N3 at R4C89 = {23}, locked for R4 17a. -> 5(2) at R4C8 (prelim j) = {23}, locked for C8 17b. extended cleanup (last nonet digits): R3C789 = {467} (no 5,8) (Note: ignoring the fact that they are also locked for R4 here, as this goes beyond the scope of a cleanup) 18. R1C123 (= {127}) = 10 18a. -> Split cage at R3C3+R4C23 = 23(3) = {689}, locked for N4 18b. cleanup: no 1,3 in R6C2 19. 11(3) at R4C4 (prelim i) = {146} (last combo) 19a. -> R5C4 = 6, R4C4+R5C3 = {14}, locked for N4 19b. cleanup: no 5,8 in R6C2, no 4 in R8C3 20. 17(3) at R4C5 = {179} (last combo), locked for C5 and N5 21. HS in N5 at R7C5 = 2 22. NP at R89C5 = {56}, locked for N8 22a. -> R9C6 = 3 (cage sum) 22b. cleanup: no 4 in R89C4 23. Innies N8: R7C4+R8C6 = 12(2) = {48} (last combo) 23a. -> no 4,8 in R7C6 and R8C4 23b. cleanup: no 2 in R8C3 All singles and cage sums to finish now. **************** Appendix: Short way of eliminating the 9 at R2C5: 6. 1 in R2 locked in 9(2) at R2C6 and 10(2) at R2C8 6a. if 1 in 10(2), then R2C89 = {19} 6b. if 1 in 9(2), then R2C67 = {18} -> 15(2) at R1C6 = {69} 6c. -> 9 locked in R1C67+R2C89 6d. -> no 9 in R2C5 (common peer) Technically, this move can be considered to be a grouped XY-chain with 5 links: (9,1)r2c89=(1,8)r2c67-(8=9)r1c67 Here, the strong links are denoted by a '=', the weak link by a '-' and the direct links by a ','. Note that a similar logic could have been applied directly before the nishio step (step 4) above: (9,1)r2c1289=(1,8)r2c67-(8=9)r1c67 -> 9 locked in R1289C2+R1C67 -> no 9 in R2C5 (common peer) This works because both constituent 10(2) cages have a direct link on 1 and 9, a property that is therefore inherited by the combined 20(4) at R2C1289. Ed's alternative way to crack this puzzle: Thanks very much for your walkthrough Mike. Love your style! I'm really glad you included the long version of the WT since it shows some of the really interesting clone moves available with this cage pattern. I missed your step 10 so had to use an alternative way to crack the puzzle (different again to Mike's really neat and powerful alternative). However, I also used your step 4 so that is the really key one. [edit: actually, Mike found a way so that it's not needed. See here]. Interesting that you called it Nishio. I have had TJK41 ready for a while so will post it on 1st April. Perhaps I'll just do these bi-monthly. Feel free to do one Mike! Alternative way to crack TJK40 This is how I removed the 9 from r2c5. From Mike's step 5. 6. 9 in n3 only in 13(2)={49} or 10(2)={19} 6a. -> {46} blocked from the 10(2) (Locking-out Cages) 6b. 10(2) = {19/28/37}(no 4,6) Now for a Cloned CCC! 7. "45" on r1: 1 outie r2c5 + 2 = 3 innies r1c123 7a. min. 3 innies = 6 -> min. r2c5 = 4 7b. NOTE: no cell at r1c123 can equal r2c5 since if one did, the other 2 cells would have to sum to the IOD of 2 which is impossible 7c. -> the digit at r2c5 must be cloned at one of r1c89 a 13(2) cage (this cloning eliminates 7 from r2c5 but this is not the important bit) 7d. -> the 15(3) at r1c4 cannot contain 2 in r1c45 since it would leave a 13(2) split cage at one of r1c45 and with r2c5, but this would clash with the 13(2) at r1c8 (CCC) 7e. ->no 2 in r1c45 8. 2 in r1 only in n1: locked for n1 and 36(7) 8a. no 8 in 10(2) at r2c1 8b. 10(2) = {37/46} = [4/7..] 9. h16(3) at r2c345 = {259/358}(no 4,7) ({457} is blocked by step 8b) 10. 4 in r2 only in 10(2) at r2c1 = {46}: both locked for r2 & n1 10a. no 3 in 9(2) at r2c6 11. 3 in n2 only in 15(3) at r1c4 = 3{48/57}(no 9) 11. 3 locked for r1 On from here. Andrew's walkthrough: Solving this puzzle was interesting for what I spotted but then found that I didn’t need to use. My solving path was very different from Mike's. It was a bit more like Ed's, in the sense that I used the same 45 as his step 7, but I used it is a different way; not the clever way he used it. Here is my walkthrough for TJK 40 Prelims a) R1C67 = {69/78} b) R1C89 = {49/58/67}, no 1,2,3 c) R2C12 = {19/28/37/46}, no 5 d) R1C67 = {18/27/36/45}, no 9 e) R1C89 = {19/28/37/46}, no 5 f) R45C8 = {14/23} g) R56C2 = {18/27/36/45}, no 9 h) R8C12 = {18/27/36/45}, no 9 i) R8C34 = {19/28/37/46}, no 5 j) R8C89 = {69/78} k) R9C12 = {49/58/67}, no 1,2,3 l) R9C34 = {18/27/36/45}, no 9 m) 10(3) cage at R2C4 = {127/136/145/235}, no 8,9 n) 11(3) cage at R4C4 = {128/137/146/236/245}, no 9 o) 22(3) cage at R5C6 = {589/679} p) 26(4) cage at R6C3 = {2789/3689/4589/4679/5678}, no 1 q) 28(7) cage at R3C8 = {1234567}, no 8,9 1. R1C89 = {49/58} (cannot be {67} which clashes with R1C67), no 6,7 1a. Killer pair 8,9 in R1C67 and R1C89, locked for R1 2. 45 rule on NR1C4 2 innies R2C4 + R3C6 = 6 = {15/24} 2a. R2C67 = {18/27/36} (cannot be {45} which clashes with R2C4 + R3C6), no 4,5 3. 45 rule on NR1C4 2 outies R3C45 = 1 innie R3C6 + 4, IOU no 4 in R3C45 4. 45 rule on NR7C4 2 innies R7C4 + R8C6 = 12 = {39/48/57}, no 1,2,6 5. 45 rule on NR7C4 2 outies R7C56 = 1 innie R7C4 + 1, IOU no 1 in R7C56 5a. 13(3) cage at R7C5 = {238/247/256/346}, no 9, clean-up: no 3 in R7C4 (step 3) 6. 45 rule on R8 3 innies R8C567 = 11 = {128/137/146/236/245}, no 9 6a. 8 of {128} must be in R8C6 -> no 8 in R8C57 7. 45 rule on C89 3 innies R6C8 + R9C89 = 19 = {289/379/469/478/568}, no 1 7a. 2,3,5 of {289/379/568} must be in R9C89 (R9C89 cannot be {89/79/68} which clash with R8C89), no 2,3,5 in R6C8 7b. 45 rule on C89 4 outies R6789C7 = 14 = {1238/1247/1256/1346} (cannot be {2345} which clashes with R6C8 + R9C89 or, if preferred, 33(7) cage must contain1), no 9, 1 locked for C7, clean-up: no 8 in R2C6 8. 45 rule on C1234 1 outie R3C5 = 1 innie R1C4, no 4 in R1C4 9. 45 rule on C6789 1 innie R9C6 = 1 outie R7C5 + 1, no 1,2 in R9C6 [Just spotted 5 in R2 only in R2C345] 10. 45 rule on R2 3 innies R2C345 = 16 = {259/358/457}, no 1,6, clean-up: no 5 in R3C6 (step 2) 11. 10(3) cage at R2C4 = {127/145/235} (cannot be {136} because R2C4 only contains 2,4,5), no 6, clean-up: no 6 in R1C4 (step 8) 12. 45 rule on R12 3 outies R3C3 + R4C23 = 1 innie R2C4 + 18 12a. Min R2C4 = 2 -> min R3C3 + R4C23 = 20, no 1,2 in R3C3 + R4C23 13. Law of Leftovers (LoL) for C123 two outies R34C4 must exactly equal two innies R89C3, no 9 in R34C4 -> no 9 in R8C3, clean-up: no 1 in R8C4 14. LoL for C789 two outies R67C6 must exactly equal two innies R12C7, no 4,5 in R12C7 -> no 4,5 in R67C6 15. 45 rule on R1 3 innies R1C123 = 1 outie R2C5 + 2 15a. Min R1C123 = 6 -> min R2C5 = 4 15b. R2C345 (step 10) = {259/358/457} 15c. 3 of {358} must be in R2C3, no 8 in R2C3 16. 3 in NR1C4 only in 15(3) cage at R1C4 = {348/357} or in R2C67 = {36} -> 15(3) cage = {159/249/258/348/357} (cannot be {168/267/456}, locking-out cages), no 6 16a. 15(3) cage = {159/249/348/357} (cannot be {258} which clashes with R2C4 + R3C6) [With hindsight, 15(3) cage at R1C4 = {159/249/348/357} (cannot be {168/267} which clash with R1C67, cannot be {258/456} which clash with R2C4 + R3C6), no 6 is simpler.] 16b. 4 of {249/348} must be in R1C5 -> no 2 in R1C5, no 4 in R2C5 17. R1C67 = {69/78}, R1C89 = {49/58} -> combined cage R1C6789 = {69}{58}/{78}{49} 17a. 15(3) cage at R1C4 (step 16a) = {159/348/357} (cannot be {249} which clashes with combined cage R1C6789), no 2, clean-up: no 2 in R3C5 (step 8) 18. 2 in R1 only in R1C123, locked for NR1C1, clean-up: no 8 in R2C12 18a. 36(7) cage = {1236789/1245789/2345679} must contain 7 19. 15(3) cage at R1C4 (step 17a) = {159/348/357}, R1C4 = R3C5 (step 8) -> R123C5 = {159/348/357} 19a. 17(3) cage at R4C5 = {179/269/278/368/467} (cannot be {359/458} which clash with R123C5), no 5 19b. 45 rule on C6789 3 outies R789C5 = 13 = {148/157/238/247/256/346} (cannot be {139} which clashes with R123C5), no 9 20. 2 in R1 only in R1C123 20a. Hidden killer pair 1,3 in R1C123 and 15(3) cage at R1C4 for R1, 15(3) cage contains one of 1,3 -> R1C123 must contain one of 1,3 20b. R1C123 = R2C5 + 2 (step 15) 20c. R2C5 = {5789} -> R1C123 = 7,9,10,11 = {124/126/127} (cannot be {234/235} which clash with 15(3) cage = {35}7/{34}8), cannot be {236} because R1C123+R2C5 = {236}9 clashes with R2C12, killer combo clash, other combinations don’t contain 2 or one of 1,3), no 3,5, 1 locked for R1 and NR1C1, clean-up: no 9 in R2C12, no 1 in R3C5 (step 8) 20d. 1 in NR1C4 only in R23C6, locked for C6 [I omitted to say that step 20c eliminates 9 from R2C5; however the next step does that.] 21. 15(3) cage at R1C4 (step 17a) = {348/357}, no 9, 3 locked for NR1C4, clean-up: no 6 in R2C67 21a. LoL for C789 two outies R67C6 must exactly equal two innies R12C7, no 3 in R12C7 -> no 3 in R7C6 22. R1C67 = {69} (hidden pair in NR1C4), locked for R1, clean-up: no 4 in R1C89 22a. Naked pair {58} in R1C89, locked for R1 and NR1C8, clean-up: no 2 in R2C89, no 5 in R3C5 (step 8) 22b. Caged X-Wing for 9 in R1C67 and 22(3) cage at R5C6, no other 9 in C67, clean-up: no 8 in R7C5 (step 9) 23. 5 in NR1C4 only in R2C45, locked for R2 23a. R2C345 (step 10) = {259/358} (cannot be {457} which clashes with R2C12), no 4,7, clean-up: no 2 in R3C6 (step 2) 24. Killer pair 4,7 in R1C123 and R2C12, locked for NR1C1 24a. 5,8 in NR1C1 only in R3C12 + R4C1, locked for 37(7) cage at R3C1, no 5,8 in R56C1 + R7C12 24b. 37(7) cage contains 5 so must contain 3 = {1345789/2345689} 25. 10(3) cage at R2C4 (step 11) = {127/235}, 2 locked for C4, clean-up: no 8 in R8C3, no 7 in R9C3 25a. R3C5 = {37} -> no 3,7 in R3C4 26. 1,2 in R1 only in 36(7) cage at R1C1 (step 18a) = {1236789/1245789}, 8 locked for NR3C3, clean-up: no 1 in R6C2 26a. 36(7) cage = {1236789/1245789}, CPE no 9 in R6C4 27. 1 in NR3C3 only in R34C4 + R5C123, CPE no 1 in R5C4 28. LoL for R789 three outies R6C129 must exactly equal three innies R7C567, no 9 in R7C567 -> no 9 in R6C1 [At this stage I spotted some interesting forcing chains starting from the combinations of R45C8, using caged X-wings for C89, in the case for R45C8 = {14} with one caged X-wing leading to a second caged X-wing within the same path of the forcing chain. But then I spotted the much simpler …, which had been available since step 22b, but I’d been doing steps which were more obvious to me at the time] 29. 9 in NR1C8 only in R2C89 = {19}, locked for R2 and NR1C8 -> R2C3 = 3, placed for NR1C1, clean-up: no 7 in R2C12, no 8 in R2C7, no 4 in R5C8, no 7 in R8C4, no 6 in R9C4 29a. Naked pair {27} in R2C67, locked for R2 and NR1C4 -> R1C45 = [34], 4 placed for NR1C4, R2C45 = [58], R3C6 = 1, R3C4 = 2, placed for NR3C3, R3C5 = 3 (cage sum), placed for NR3C5, clean-up: no 7 in R6C2, no 7 in R8C3, no 4,6 in R9C3, no 4,5 in R9C6 (step 9) 30. R3C12 + R4C1 = {589} (hidden triple in NR1C1), locked for 37(7) cage at R3C1, no 9 in R5C1 + R7C12 31. Naked triple {127} in R1C123, locked for 36(7) cage at R1C1, no 7 in R3C3 + R4C23 31a. 36(7) cage at R1C1 (step 26a) = {1236789} (only remaining combination), no 4,5 31b. Naked triple {689} in R3C3 + R4C23, locked for NR3C3, clean-up: no 3 in R6C2 32. 11(3) cage at R4C4 = {146} (only remaining combination) -> R5C4 = 6, placed for NR3C5, R4C4 + R5C3 = {14}, locked for NR3C3, clean-up: no 5,8 in R6C2, no 4 in R8C3, no 7 in R9C6 (step 9) 32a. 3 in NR3C3 only in R5C12, locked for R5, clean-up: no 2 in R4C8 33. 17(3) cage at R4C5 (step 19a) = {179} (only remaining combination), locked for C5 and NR3C5, clean-up: no 8 in R9C6 (step 9) 34. 14(3) cage at R8C5 = {356} (only remaining combination) -> R9C6 = 3, R89C5 = {56}, locked for C5 and NR7C4 -> R7C5 = 2, placed for NR3C5, clean-up: no 4 in R8C4, no 4 in R9C4 34a. Killer pair 8,9 in R8C4 and R8C89, locked for R8, clean-up: no 1 in R8C12 35. R7C5 = 2 -> R78C6 = 11 = [74], 7 placed for NR4C7, 4 placed for NR7C4, R2C67 = [27], clean-up: no 5 in R8C12 35a. Killer pair 6,7 in R8C12 and R8C89, locked for R8 -> R89C5 = [56], clean-up: no 7 in R9C12 36. Naked pair {58} in R45C6, locked for C6 and NR3C5 -> R6C4 = 4, R4C4 = 1, R5C3 = 4 37. R9C4 = 7 (hidden single in C4), R9C3 = 2, R8C3 = 1, R8C4 = 9, clean-up: no 6 in R8C89 37a. Naked pair {78} in R8C89, locked for R8 and NR6C9, clean-up: no 2 in R8C12 37b. Naked pair {36} in R8C12, locked for R8 and NR6C1 -> R8C7 = 2, placed for NR6C9, R6C2 = 2, R5C2 = 7, R5C1 = 3 38. Naked pair {14} in R7C12, locked for R7 and NR6C1 -> R6C1 = 7, clean-up: no 9 in R9C12 38a. Naked pair {58} in R9C12, locked for R9 and NR6C1 -> R7C3 = 9 39. 22(3) cage at R5C6 = {589} (only remaining combination) -> R6C6 = 9, R5C67 = {58}, locked for R5 39a. 17(3) cage at R4C5 = [791] 40. Naked triple {356} in R6C9 + R7C89, locked for 28(7) cage at R3C8, no 3,6 in R3C89 + R4C9 40a. Naked pair {47} in R3C89, locked for NR1C8 -> R3C7 = 6, R4C8 = 3, R5C8 = 2 41. R3C67 = [16] = 7 -> R4C67 = 9 = [54] and the rest is naked singles, without using the nonets. How Andrew made the key elimination: Since Mike and Ed have shown that eliminating 9 from R2C5 is one of the key steps. Here is a clearer version of how I did that 2. 45 rule on NR1C4 2 innies R2C4 + R3C6 = 6 = {15/24} 16. (simplified) 15(3) cage at R1C4 = {159/249/348/357} (cannot be {168/267} which clash with R1C67, cannot be {258/456} which clash with R2C4 + R3C6), no 6 16a. 8,9 only in R2C5 -> R2C5 = {35789} 17. R1C67 = {69/78}, R1C89 = {49/58} -> combined cage R1C6789 = {69}{58}/{78}{49} 17a. 15(3) cage at R1C4 (step 16) = {159/348/357} (cannot be {249} which clashes with combined cage R1C6789), no 2 17b. 2 in R1 only in R1C123 (2 locked for NR1C1, but this isn't necessary for the key step below) 15 and 20 combined 45 rule on R1 3 innies R1C123 = 1 outie R2C5 + 2 Min R1C123 = 6 -> no 3 in R2C5 Hidden killer pair 1,3 in R1C123 and 15(3) cage for R1, 15(3) cage contains one of 1,3 -> R1C123 must contain one of 1,3 and 2 (cannot be {123} because min R1C123 = 7) R1C123 + R2C5 cannot be 11 + 9 = {236} + 9 which clashes with R2C12 My step 20c (in the full walkthrough above) did more analysis than that, also locking 1 in R1C123. |
Author: | Andrew [ Wed May 28, 2014 3:18 am ] |
Post subject: | Texas Jigsaw Killer Archive |
Texas Jigsaw Killer 41 by Ed (April 2010) here Puzzle Diagrams: Jigsaw nonet design: Cross by Andrew Smith. Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration: Cages with cells in 3 jigsaw nonets: pink There were 5 further images in the original post, only differing from the images in this archive entry by the choice of pastel colour. Code: Select, Copy & Paste into solver: SumoCueV1=16J0+0J1=31J1+2J1+2J1+2J1=12J2=13J2+7J3+0J0=11J0=7J1+11J1+2J1+6J2+6J2=18J3+7J3+0J4+10J0=15J0=9J1=19J2=15J2+16J3+16J3=14J3=5J4=26J4+20J0+21J0+22J2+23J2=9J3+16J3+26J5+27J4+28J4+28J4+21J0+22J0+23J2+33J3=12J5=22J5=17J4+28J4=20J6+47J6=23J7=8J7+50J5+43J5+44J5+45J4+45J6+47J6+49J6+49J8+49J7+49J7+44J5+44J5=31J6+45J6+47J6+63J8=19J8+67J8=22J7+69J7=11J5+63J6+63J8+63J8+63J8+67J8+69J8+69J7+71J7+71J7 Solution: +-------+-------+-------+ Quote: Ed: This is not a practical joke, just a really hard Texas Jigsaw Killer (TJK). Found a way to make big inroads early but there must be more conventional ways to do it. Many thanks to Børge for making the pics for me. Mike (mhparker): Wow, that was a difficult one! You certainly got me working hard there, Ed! Thanks for the puzzle, which proved to be much more interesting than it looked at first sight (TJK18 feeling again... ). Ed wrote: ... but there must be more conventional ways to do it. Maybe. But as you know, I'm not exactly the most conventional of solvers , so we'll have to wait for someone else (or a software solver) to do it "by the book". Here's the WT. Found a couple of really interesting "inroads" (as Ed referred to them). I wonder whether there the same ones that he used? Ed: Wow Mike! Step 8!! We both picked on exactly the same area to get into this one. I couldn't believe how many of the same elements we both used (I only missed ). So, here's my alternate step 8. Could only stretch it out to 8k. [edit: went a bit too far with original ALT step] Conventional walkthrough welcome! Andrew (in 2013): An interesting puzzle, once one found a way in. Loved Ed’s step 8. I found another way in, without needing that step. Must admit I didn't work through Mike's step 8, which looked extremely complicated. Ed wrote: Conventional walkthrough welcome! Maybe this is it? I think the main difference from Mike's and Ed's solving paths is that they used LoL for C89; I used LoL for C789.The SSv3.6.1 score of 1.80 looks far too high. Maybe SS couldn't find my step 10. Mike's step 4? Mike's walkthrough: Wow, that was a difficult one! You certainly got me working hard there, Ed! Thanks for the puzzle, which proved to be much more interesting than it looked at first sight (TJK18 feeling again... ). Ed wrote: ... but there must be more conventional ways to do it. Maybe. But as you know, I'm not exactly the most conventional of solvers , so we'll have to wait for someone else (or a software solver) to do it "by the book". Here's the WT. Found a couple of really interesting "inroads" (as Ed referred to them). I wonder whether there the same ones that he used? Texas Jigsaw Killer 41 Walkthrough Nonet Layout: 122222334 112223344 511233444 551133446 555113466 557788666 577798866 777999886 799999888 Prelims a) 11(2) at R2C2 = {29/38/47/56} (no 1) b) 7(2) at R2C3 = {16/25/34} (no 7..9) c) 15(2) at R3C3 = {69/78} (no 1..5) d) 9(3) at R3C4 = {126/135/234} (no 7..9) e) 19(3) at R3C5 and R8C5 = {289/379/469/478/568} (no 1) f) 14(2) at R3C9 = {59/68} (no 1..4,7) g) 5(2) at R4C1 = {14/23} (no 5..9) h) 26(4) at R4C2 = {2789/3689/4589/4679/5678} (no 1) i) 9(2) at R4C7 = {18/27/36/45} (no 9) j) 12(2) at R5C8 = {39/48/57} (no 1,2,6) k) 8(2) at R6C6 = {17/26/35} (no 4,8,9) l) 11(3) at R8C9 = {128/137/146/236/245} (no 9) 1. 1 in N5 locked in R34567 for C1 2. 1 in N1 locked in R45C4 for C4 2a. 9(3) at R3C4 (prelim d) = {1..} = {126/135} (no 4) 2b. cleanup: no 6 in R2C3 3. Innies N2: R1C2+R3C4 = 7(2) = [16/25/43/52] (no 3,6..9 in R1C2) 4. Outies N1234: R3C1+R4C9 = 9(2) = [18/36/45] (no 2,7,9; no 5,6,8 in R3C1) 4a. cleanup: no 5 in R3C9 5. Innie/outie difference (IOD) N123: R3C1 = R1C8 5a. -> R1C8 = {134} 6. IOD N3: R5C5 = R1C8 + 1 6a. -> R5C5 = {245} 6b. 19(3) at R3C5 (prelim e) = {(2/4/5)..} = {289/469/478/568} (no 3) 6c. can only contain 1 of {245}, which must go in R5C5 6d. -> no 2,4,5 in R34C5 7. Innies N6: R4C9+R6C7+R8C9 = 11(3) = {128/146/236/245} (no 7) (note: {137} blocked because none of these digits in R4C9) 7a. only 1 of 5,6,8, which must go in R4C9 7b. -> no 5,6,8 in R6C7+R8C9 7c. cleanup: no 1,2,3 in R6C6 Now for what's probably the most complicated move I've ever made in a walkthrough... 8a. Law of Leftovers (LoL) C89: R3456C7 (outies) = R189C8+R9C9 (innies) 8b. R3456C7 (being all peers of each other) cannot contain any repeats 8c. -> R189C8+R9C9 cannot contain any repeats either 8d. IOD C89: R3C7 = R8C8 8e. -> R3C7 maps to R8C8 8f. The remaining three outies R456C7 must map to R19C8+R9C9 8g. if R6C7 = R1C8, the same digit would be forced into R9C9**, which is impossible (see step 8c) (**Reason: R12C9 could not contain the digit because they are peers of R1C8 (same cage), R45678C9 could not contain the digit because they are peers of R6C7, and R3C9 could not contain the digit because it has no candidates in common with R6C7) 8h. -> R6C7 must map to one of R9C89 8i. -> 11(3) at R8C9 and 11(3) at R4C9+R6C7+R8C9 (step 7) (which both share the cell R8C9) must contain the same combination! 8j. -> R4C9 = R9C8 (the only non-peer of R4C9 in 11(3) at R8C9) 8k. -> R9C8 = {568} 8l. -> R6C7 = R9C9 8m. -> R9C9 = {123} 8n. -> the remaining two outies from step 8a, R45C7 (= 9(2)), must map to R19C8 8o. -> R19C8 must also sum to 9 8p. Outies C9: R179C8 = 15(3) 8q. -> R7C8 = 6 (from outie cage split using R19C8 = 9(2) from step 8o) 8r. -> R45C7 must contain 1 of {58} (step 8n) 8s. -> 9(2) at R45C7 = {18/45} (no 2,3,6,7) 8t. cleanup: no 8 in R3C9, no 6 in R3C7 (step 8e), no 3 in R3C1 (step 4), no 3 in R1C8 (step 5), no 4 in R5C5 (step 6) Grid state after step 8: Code: .-----------------------.-----------------------------------------------.-----------.-----------------------. | 23456789 1245 | 123456789 23456789 123456789 123456789 | 123456789 | 14 123456789 | | .-----------+-----------------------. .-----------' :-----------. | | 23456789 | 23456789 | 12345 23456 | 123456789 | 123456789 123456789 | 12345789 | 123456789 | | | :-----------.-----------+-----------+-----------.-----------' :-----------: | 14 | 23456789 | 6789 | 2356 | 6789 | 123456789 | 12345789 12345789 | 69 | :-----------+-----------: | | | :-----------. | | | 1234 | 23456789 | 6789 | 12356 | 6789 | 123456789 | 1458 | 12345789 | 58 | | | '-----------: | | | :-----------+-----------: | 1234 | 23456789 23456789 | 12356 | 25 | 123456789 | 1458 | 345789 | 12345789 | :-----------: .-----------'-----------+-----------+-----------'-----------: | | | 123456789 | 23456789 | 123456789 23456789 | 123456789 | 567 123 | 345789 | 12345789 | | '-----------: .-----------' '-----------------------+-----------' | | 12345789 12345789 | 12345789 | 2345789 12345789 12345789 12345789 | 6 12345789 | :-----------. | :-----------.-----------------------.-----------'-----------.-----------: | 23456789 | 123456789 | 123456789 | 23456789 | 23456789 23456789 | 123456789 12345789 | 1234 | | '-----------'-----------' | .-----------' .-----------' | | 23456789 123456789 123456789 23456789 | 23456789 | 123456789 123456789 | 58 123 | '-----------------------------------------------'-----------'-----------------------'-----------------------' 9. R45C1 (prelim g) = {23}, locked for C1 and N5 (Note: {14} blocked by R3C1) 10. R4C9+R6C7+R8C9 (step 7) and 11(3) at R8C9 (step 8i) = {128/245} (no 3) 10a. 2 locked in R89C9 for C9 10b. cleanup: no 5 in R6C6 11. 19(3) at R3C5 (step 6b) = {289/568} (no 7) 11a. 8 locked in R34C5 for C5 and N3 12. 8 in N2 locked in R1C346 for R1 13. Innies R89: R8C23 = 7(2) = {16/25/34} (no 7..9) 13a. -> R78C2 cannot sum to 7 (combo crossover clash (CCC)) 13b. -> R67C1 (remaining two cells of 17(4) at R6C1) cannot sum to 10 13c. -> R3C1 (remaining innie cell in N5) cannot sum to 4 (= 45 - 10 - 5 - 26) 13d. -> no 4 in R3C1 14. Naked single (NS) at R3C1 = 1 14a. -> R4C9 = 8 (step 4), R1C8 = 1 (step 5), R5C5 = 2 (step 6) 14b. -> R3C9 = 6, R45C1 = [23], R9C8 = 8 (step 8j), R34C5 = [89] (step 11) 14c. -> R34C3 = [96] (prelim c, last permutation), R45C7 = [18] (step 8n) 14d. -> R6C67 = [62] 14e. -> R9C9 = 2 (step 8l) 14f. -> R8C9 = 1 (cage sum) 14g. cleanup: no 5 in R23C2, no 3 in R2C2, no 4 in R56C8, no 9 in R6C8, no 9 in R8C8 (step 8e) 15. Hidden single (HS) in C4 at R5C4 = 1 15a. -> split 8(2) at R34C4 = {35} (last combo), locked for C4 15b. cleanup: no 2,4 in R2C3, no 5 in R1C2 (step 3) 16. 4 in N1 locked in R12C1+R23C2 16a. -> no 4 in R1C2 (CPE) 17. NS at R1C2 = 2 17a. -> R3C4 = 5 (step 3) 17b. -> R4C4 = 3 17c. cleanup: no 8 in R2C2, no 5 in R8C8 (step 8e) 18. 15(3) at R3C6 = {357} (last combo) 18a. -> R3C6 = 3, R45C6 = {57}, locked for C6 and N3 18b. cleanup: no 3 in R8C8 (step 8e) 19. Naked pair (NP) at R2C47 = {46}, locked for R2 All singles and cage sums to end. Ed's alternative ending: Wow Mike! Step 8!! We both picked on exactly the same area to get into this one. I couldn't believe how many of the same elements we both used (I only missed ). So, here's my alternate step 8. Could only stretch it out to 8k. [edit: went a bit too far with original ALT step] Alt. step 8 & alt ending 8. "45" on c89: 1 outie r3c7 = 1 innie r8c8 8a. -> r1c8 "sees" all of n4 directly through c8, the 13(3) cage and it sees r3c7 indirectly since r8c8 = r3c7 EXCEPT r3c9, r45c7 8b. since r1c8 cannot equal r3c9 (no common candidates) -> r1c8 must be cloned in one cell of 9(2) at r45c7 8c. -> 9(2) must have 1,3,4 = {18/36/45}(no 2,7) 8d. "45" on n4: 2 outies r1c8 + r4c9 = 9 8e. since this outie cage and the clone celled cage (step 8b) have the same total -> r4c9 equals the other cell of 9(2) at r45c7 8f. since r4c9 sees r4c7 -> r4c9 = r5c7 = (568) (Clone CCC), r4c7 = (134) 8g. "45" on n34: 2 outies r4c9 + r5c5 = 10 8h. since r4c9 = r5c7 -> r5c57 = 10 = [28/46](no 5) 8i. -> no 5 in r4c9 -> no 4 in r1c8 (outies n4 = 9) 8j. no 4 in r4c7 8k. 14(2) at r34c9 = {68}: both locked for c9 Added from here 8l. no 3 in R3C1 (step 4) 9. 5(2)r4c1 = {23}, locked for c1 and n5 ({14} blocked by r3c1) 10. 19(3)r3c5 must have 2,4 = {289/469/478} ie, must have 6 or 8 in r34c5 11. 6 & 8 in r34: 14(2)r3c9 has 2 of; r34c5 has 1 of (step 10); 15(2)r3c3 has 1 of: -> both 6 & 8 locked for r34 11a. no 3,5 in r2c2 12. 9(3)r3c4, {126} must be [216] but this clashes with [1/6] in 9(2) at r4c7 12a. 9(3) = {135}: all locked for c4 and no 3 or 5 in r3c2 12b. no 2,4 in r2c3 12c. no 6,8 in r2c2 13. 3 in n1 only in r45c4 -> no 3 in r3c4 13a. r3c4 = 5 13b. no 2 in r2c4 14. 1 innie n2: r1c2 = 2 Cracked now. Conventional walkthrough welcome! Andrew's walkthrough: An interesting puzzle, once one found a way in. Loved Ed’s step 8. I found another way in, without needing that step. Must admit I didn't work through Mike's step 8, which looked extremely complicated. Ed wrote: Conventional walkthrough welcome! Maybe this is it? I think the main difference from Mike's and Ed's solving paths is that they used LoL for C89; I used LoL for C789.The SSv3.6.1 score of 1.80 looks far too high. Maybe SS couldn't find my step 10. Mike's step 4? Here is my walkthrough for TJK 41 My walkthrough has been simplified while checking it, before posting the archive entry for TJK 41. Prelims a) R23C2 = {29/38/47/56}, no 1 b) R2C34 = {16/25/34}, no 7,8,9 c) R34C3 = {69/78} d) R34C9 = {59/68} e) R45C1 = {14/23} f) R45C7 = {18/27/36/45}, no 9 g) R56C8 = {39/48/57}, no 1,2,6 h) R6C67 = {17/26/35}, no 4,8,9 i) 9(3) cage at R3C4 = {126/135/234}, no 7,8,9 j) 19(3) cage at R3C5 = {289/379/469/478/568}, no 1 k) 19(3) cage at R8C5 = {289/379/469/478/568}, no 1 l) 11(3) cage at R8C9 = {128/137/146/236/245}, no 9 m) 26(4) cage at R4C2 = {2789/3689/4589/4679/5678}, no 1 1. 1 in NR3C1 only in R34567C1, locked for C1 1a. 1 in NR1C1 only in R45C4, locked for C4, clean-up: no 6 in R2C3 1b. 9(3) cage at R3C4 contains 1 = {126/135}, no 4 2. 45 rule on R12 2 outies R3C12 = 1 innie R2C8 2a. Min R3C12 = 3 -> min R2C8 = 3 2b. Max R3C12 = 9, no 8,9 in R3C1, no 9 in R3C2, clean-up: no 2 in R2C2 3. 45 rule on R89 2 innies R8C23 = 7 = {16/25/34}, no 7,8,9 4. 45 rule on C1234 3(2+1) innies R1C34 + R7C4 = 23 4a. Max R1C34 = 17 -> min R7C4 = 6 4b. Max R17C4 = 17 -> min R1C3 = 6 4c. Max R1C3 + R7C4 = 18 -> min R1C4 = 5 5. 45 rule on NR1C2 2 innies R1C2 + R3C4 = 7 = [16/25/43/52], R1C2 = {1245} 6. 45 rule on NR1C9 1 innie R3C9 = 1 outie R1C8 + 5 -> R3C9 = {689}, R1C8 = {134}, clean-up: no 9 in R4C9 7. 45 rule on NR1C7 1 outie R5C5 = 1 innie R1C8 + 1 -> R5C5 = {245} 8. 45 rule on NR4C9 3 innies R4C9 + R6C7 + R8C9 = 11 = {128/146/236/245} (cannot be {137} because R4C9 only contains 5,6,8), no 7, clean-up: no 1 in R6C6 8a. R4C9 = {568} -> no 5,6,8 in R6C7 + R8C9, clean-up: no 2,3 in R6C6 9. Law of Leftovers (LoL) for C789 three outies R6C56 + R7C6 must exactly equal three innies R1C78 + R2C7 9a. R6C6 = {567} -> R12C7 must contain at least one of 5,6,7 9b. 12(3) cage at R1C7 = {147/156/237/246/345} (cannot be {129/138} which don’t contain any of 5,6,7), no 8,9 9c. LoL for C789 no 8,9 in R1C78 + R2C7 -> no 8,9 in R6C5 + R7C6 10. 45 rule on NR1C1 + NR1C2 + NR1C7 + NR1C9 1 innie R3C9 = 1 outie R3C1 + 5 -> R3C1 = {134} 11. 45 rule on NR3C1 2 outies R78C2 = 1 innie R3C1 + 3 11a. Max R3C1 = 4 -> max R78C2 = 7, no 7,8,9 in R7C2 11b. R8C23 = 7 (step 3) -> max R78C2 = 6 (cannot be 7 which clashes with R8C23, CCC), no 6 in R78C2, clean-up: no 1 in R8C3 (step 3) 11c. Max R78C2 = 6 -> max R3C1 = 3, clean-up: no 9 in R3C9 (step 10), no 4 in R1C8 (step 6), no 5 in R4C9, no 5 in R5C5 (step 7) 11d. Killer pair 1,3 in R3C1 and R45C1, locked for C1 and NR3C1 11e. Naked pair {68} in R34C9, locked for C9 11f. Naked pair {68} in R34C9, CPE no 6,8 in R4C78 using NR1C9, clean-up: no 1,3 in R5C7 12. 19(3) cage at R3C5 = {289/469/478} (cannot be {379/568} because R5C5 only contains 2,4), no 3,5 12a. R5C5 = {24} -> no 2,4 in R34C5 13. 13(3) cage at R1C8 = {139/157} (cannot be {247} because R1C8 only contains 1,3), no 2,4 13a. 13(3) cage = {139/157}, CPE no 1 in R34C8 using NR1C9 14. 19(3) cage at R3C5 (step 12) = {289/469/478} 14a. 19(3) cage at R8C5 = {289/379/469/478/568} 14b. 2,3,5 of {289/379/568} must be in R89C5 (R89C5 cannot be {89/79/68} which clash with 19(3) cage at R3C5), no 2,3,5 in R8C6 15. R34C3 contains one of 6,8, 19(3) cage at R3C5 contains one of 6,8 in R34, naked pair {68} in R34C9 -> double caged X-Wing for 6,8 in R34C3, 19(3) cage and R34C9, no other 6,8 in R34, clean-up: no 1 in R1C2 (step 5), no 3,5 in R2C2 16. 9(3) cage at R3C4 (step 1b) = {126/135} 16a. 2 of {126} must be in R3C4 -> no 2 in R45C4 17. 45 rule on C89 1 outie R3C7 = 1 innie R8C8, no 6,8 in R8C8 18. Deleted. Unnecessary after I found steps 19 and 20. This was analysis of 22(4) cage at R5C9 looking at interactions with R4C9 + R6C7 + R8C9 and with 13(3) cage at R1C8. [I should have spotted this a lot earlier, and the next step after step 15. However they are much more powerful now …] 19. 16(4) cage at R1C1 must contain one of 6,7,8,9 in R12C1 -> killer quad 6,7,8,9 in 16(4) cage, R23C2 and R34C3, locked for NR1 19a. 9(3) cage at R3C4 (step 1b) = {135} (only remaining combination), locked for C4, clean-up: no 5 in R1C2 (step 5), no 2,4 in R2C3 20. 3 in NR1C1 only in R3C2 + R45C4, CPE no 3 in R3C4 -> R3C4 = 5, R1C2 = 2 (step 5), both placed for NR1C2, naked pair {13} in R45C4, locked for NR1C1, clean-up: no 6,8,9 in R2C2, no 5 in R8C3 (step 3) [Cracked. The rest is fairly straightforward.] 21. Naked pair {47} in R23C2, locked for C2 and NR1C1 -> R5C5 = 2, R1C8 = 1 (step 7), placed for NR1C7, R3C9 = 6 (step 6), placed for NR1C9, R4C9 = 8, placed for NR4C9, R3C1 = 1 (step 10) 21a. R4C7 = 1 (hidden single in NR1C9), R5C7 = 8, placed for NR1C9, R45C4 = [31] 21b. R1C2 = 2, R3C1 = 1 -> R12C1 = 13 = {58}, locked for C1 and NR1C1 -> R34C3 = [96] 21c. R5C5 = 2 -> R34C5 = 17 = [89], 9 placed for NR1C7, R4C2 = 5 21d. Clean-ups: no 4 in R45C1, no 4 in R56C8, no 7 in R6C6, no 1 in R8C2, no 2,3 in R8C3 (both step 3) 22. R78C2 = [13], R8C3 = 4, all placed for NR6C3 23. 26(4) cage at R4C2 = {5678} (only remaining combination) -> R5C3 = 7, R56C2 = [68], 6,7 placed for NR3C1, R1C3 = 8, R12C1 = [58], R9C2 = 9, placed for NR7C5, clean-up: no 5 in R6C8 24. R45C1 = [23], R89C1 = {67}, locked for NR7C3 and 31(6) cage at R8C1, no 6,7 in R89C4 24a. Naked pair {25} in R67C3, locked for C3 and 20(4) cage at R6C3 -> R6C4 = 9, R7C4 = 8, R89C4 = [24], both placed for NR7C5, R2C4 = 6, placed for NR1C2, R2C3 = 1, R9C3 = 3, placed for NR7C5, R1C4 = 7 24b. Naked pair {34} in R12C5, locked for C5 and 31(5) cage at R1C3 -> R1C6 = 9, R1C9 = 3, placed for NR1C9, R2C9 = 9 (cage sum), R12C5 = [43] 24c. R1C7 = 6, R2C67 = 6 = {24}, locked for R2 and NR1C7 24d. 15(3) cage at R3C6 = [375], R5C8 = 9, R6C8 = 3 and the rest is naked singles, without using the nonets. |
Author: | Andrew [ Tue Oct 21, 2014 3:18 am ] |
Post subject: | Texas Jigsaw Killer Archive |
Jigsaw Killer HARD (Texas Jigsaw #42 HARD) by h3lix (Dan) (June 2010) here The links to the original puzzle diagrams no longer work, so they were removed from the puzzle thread. Børge's images with udosuk Style Killer Cages:
Code: Select, Copy & Paste into solver: SumoCueV1=0J0=0J0=0J0=0J1=0J1=0J2=34J2+6J2+6J2=14J0=0J0=7J0=15J0=0J1=14J1+6J2+6J2+6J2+9J3=0J3+11J0+12J0=0J1+14J1=15J2+24J2+24J4+9J3=0J3=34J5+29J1=20J1=24J1+32J5=0J4=0J4=0J3=0J3+29J5+29J5+31J5+32J5+32J5=0J4=0J4=0J3=0J3+29J5+29J6+31J6+32J6+32J5=0J4=21J4=21J3+54J7+54J7=4J6=0J6=7J8=12J8=0J4+53J4=21J7+63J7+63J7+57J6=0J6+59J8+60J8=0J8+53J8+63J7+63J7+63J7=0J7=0J6=0J6=0J8=0J8=0J8 Note. This code string doesn't work for SudokuSolver. Solution: +-------+-------+-------+ Quote: Dan (h3lix): Here's a Jigsaw killer! This one comes in two difficulties, the first is SS 0.97 Børge: I took the liberty adding row and column headers since Ed absolutely fancies them, and hence are far more likely to try and solve your Zero Jigsaw Killers. What is the difference between a Jigsaw Killer and a Texas Jigsaw Killer? Dan: Nothing as far as I know, the latter was the name Ruud came up with when he was making these. I perhaps could have named it TJK 40-something, but I hadn't presumed I could. Børge: If you study the Other Variants forum, you can see that manu posted A new jigsaw killer, which Para and Ed suggested should be renamed to TJK#36, which is was. Perhaps your Jigsaw Zero Killer should be TJK#42 or TJK#43 with a v1 and a v2. Ed already has a new TJK ready, currently under the codename TJK#42. I know since I have made the pics @Ed: If Dan's Jigsaw Killer is included in the TJK series, I can easily rename my pics for your new TJK and/or his Jigsaw Killer and do the full set of pics for Dan's Jigsaw Killer. Normally I would have done the full set of pics right away, but it is late here and I am tired since I have been out high speed driving all day to collect some pick up only goods I won on eBay. Ed: The Insane is a really great puzzle. Definitely worthy of the prestige of a Texas Jigsaw Killer . So, if you don't mind h3lix, I'd like to christen it as a part of the TJK series. I'll post my #43 on the 1st of July. Just to note again that the SS score should usually be low for zero killers since there aren't as many cages to get non-essential solving steps from. I found a way to get a placement as step 1 but am holding that back for a Really Insane version of this puzzle. Still haven't solved it. Dan: I think I may know what early placements you're talking about. This isn't the first time I've spent at least 5 minutes trying to find them again might it be...: LOL: R456C7 = R178C6 => R145678C6 = 24 Innie on C6, R9C6 = 7 repeat on C4: R1C4=7 Naked single in C5: R5C5=7 Andrew (in 2013): Nice puzzles Dan! They are definitely worthy of being called TJKs. I found them harder than I ought to have done because I missed Dan's shortcut. After seeing Dan's shortcut, I decided to re-work my walkthrough, also using some LoLs which I didn't use the first time, since it removes my hardest steps and gives a much simpler solving path. Andrew's original walkthrough: Nice puzzles Dan! They are definitely worthy of being called TJKs. I found them harder than I ought to have done because I missed Dan's shortcut. Prelims a) R23C3 = {16/25/34}, no 7,8,9 b) R23C4 = {69/78} c) R23C6 = {59/68} d) R78C4 = {13} e) R78C6 = {16/25/34}, no 7,8,9 f) R78C7 = {39/48/57}, no 1,2,6 g) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2 h) 21(3) cage at R6C9 = {489/579/678}, no 1,2,3 i) 21(3) cage at R7C1 = {489/579/678}, no 1,2,3 j) 21(6) cage at R8C1 = {123456}, no 7,8,9 Steps resulting from Prelims 1a. Naked pair {13} in R78C4, locked for C4 and NR6C4 1b. 21(6) cage at R8C1 = {123456}, locked for NR7C2 1c. 1 in C5 only in R123C5, locked for NR1C4 2. 21(3) cage at R7C1 = {489/579/678} 2a. 4,5,6 only in R7C1 -> R7C1 = {456} 3. 45 rule on NR1C6 3 innies R1C6 + R3C78 = 11 = {128/137/146/236/245}, no 9 3a. 45 rule on NR1C6 1 outie R3C9 = 1 innie R1C6 + 4, R1C6 = {12345}, R3C9 = {56789} [I haven’t been using Law of Leftovers for TJKs with low SSscores. However in this case it’s very useful. I think this puzzle would be very hard to solve without using LoL. I later noticed Ed’s comment in the TJK42 thread “Just to note again that the SS score should usually be low for zero killers since there aren't as many cages to get non-essential solving steps from.”, which implies that TJK42 is harder than its SSscore.] 4. Law of Leftovers (LoL) for C123 three outies R239C4 must exactly equal three innies R456C3, R239C4 only contain 6,7,8,9 -> R456C3 = {6789} 5. 34(6) cage at R4C3 = {245689} (only remaining combination) -> R456C3 = {689}, locked for C3 and NR4C3, R456C4 = {245}, locked for C4, clean-up: no 1 in R23C3 [With hindsight I realise that I’d forgotten to do LoL for C123 in the opposite direction after eliminating 7 from the 34(6) cage.] [When posting my walkthrough, I checked through the other messages in the TJK 42 thread and found that I’d missed making full use of LoL for C123 and C789. LoL for C123 R456C3 = R239C4 -> R234569C4 = 34, 45 rule on C4 -> R1C4 = 7, placed for NR1C4 LoL for C789 R456C7 = R178C6 -> R145678C6 = 24, 45 rule on C6 -> R9C6 = 7, placed for NR6C4 R5C5 = 7 (hidden single in C5).] 6. R7C3 = 7, placed for NR7C2, R7C12 = 14 = [59/68], clean-up: no 5 in R8C7 6a. Killer pair 8,9 in R23C4 and R9C4, locked for C4 7. LoL for R789 three outies R6C456 must exactly equal three innies R7C189, no 1,3 in R6C456 -> no 1,3 in R7C8, no 7 in R7C189 -> no 7 in R6C56 8. LoL for R123 three outies R4C456 must exactly equal three innies R3C129, no 1 in R4C456 -> no 1 in R3C12 9. 24(6) cage at R4C6 = {123459/123468/123567} 9a. Killer pair 6,9 in R23C6 and 24(6) cage, locked for C6, clean-up: no 1 in R78C6 10. R7C4 = 1 (hidden single in R7), R8C4 = 3, clean-up: no 4 in R7C6, no 9 in R7C7 10a. 21(6) cage at R8C1 = {123456}, 3 locked for R9 11. Grouped X-Wing for 3 in 24(6) cage at R4C6 and R7C67, no other 3 in C67 12. 24(6) cage at R4C6 = {123459/123468/123567} 12a. Consider placement for 3 in R7C67 3 in R7C6 => R78C6 = [34], R78C7 = {57}, locked for C7 => 24(6) cage = {123459/123468} (cannot be {123567} which clashes with R23C6) or 3 in R7C7 => R78C6 = {25}, locked for C6, R23C6 = {68}, locked for C6 => 24(6) cage = {123459} -> 24(6) cage = {123459/123468}, no 7 13. R5C5 = 7 (hidden single in NR4C3), R46C5 = 13 = {49/58}, no 3,6 14. R1C4 = 7 (hidden single in NR1C4), clean-up: no 8 in R23C4 14a. Naked pair {69} in R23C4, locked for C4 and NR1C1 -> R9C4 = 8, R7C2 = 9, R7C1 = 5 (cage sum), placed for NR3C1, clean-up: no 2 in R8C6, no 7 in R8C7 15. R78C6 = [25] (cannot be [34] which clashes with R78C7), both placed for NR7C6, clean-up: no 9 in R23C6 15a. Naked pair {68} in R23C6, locked for C6 and NR1C4 15b. Caged X-Wing for 6 in R23C4 and R23C6, no other 6 in R23 [Cracked. The rest is fairly straightforward.] 16. R7C7 = 3 (hidden single in R7), R8C7 = 9, placed for NR7C6 16a. R9C5 = 9 (hidden single in R9), placed for NR6C4, R6C6 = 4, placed for NR6C4, R1C6 = 1, placed for NR1C6, R3C9 = 5 (step 3a), placed for NR3C9, R45C6 = [93], R9C6 = 7, clean-up: no 2 in R2C3 16b. Naked triple {146}, locked for R9 and NR7C6 16c. Naked triple {235} in R9C123, locked for NR7C2 17. R3C5 = 1 (hidden single in R3), R8C3 = 1 (hidden single in C3), R8C5 = 2 (hidden single in R8), placed for NR6C4, R6C4 = 5, R6C5 = 8, R4C5 = 5 (cage sum), R7C5 = 6 17a. Naked pair {12} in R46C7, locked for C7 and NR4C3 -> R5C4 = 4, R4C4 = 2, R456C7 = [152] 17b. Naked pair {48} in R7C89, locked for NR3C9 17c. 4 in C3 only in R123C3, locked for NR1C1 18. R3C9 = 5 -> R3C78 = [73/82] 18a. 7,8 in C7 only in R123C7, locked for NR1C6 19. 21(3) cage at R6C9 = {489/678} 19a. 6,9 only in R6C9 -> R6C9 = {69} 19b. Naked pair {69} in R6C39, locked for R6 20. 2 in NR3C9 only in R5C89, locked for R5 20a. 2 in NR3C1 only in R3C12, locked for R3 -> R3C8 = 3, placed for NR1C6, R3C7 = 7 (step 18), R3C3 = 4, R2C3 = 3, placed for NR1C1, R12C5 = [34], R2C7 = 8, R23C6 = [68], R23C4 = [96], R2C9 = 2, R2C8 = 5, R3C12 = [92] 21. R3C1 = 9 -> R24C1 = 5 = [14], R8C1 = 6, R5C1 = 8, R1C123 = [285], R9C123 = [352], R2C2 = 7, R6C1 = 7, R6C8 = 1, R456C2 = [613], R4C8 = 7, R78C8 = [48], R78C9 = [87], R6C9 = 6 (cage sum) and the rest is naked singles, without using the nonets. Andrew's modified walkthrough: After seeing Dan's shortcut, I decided to re-work my walkthrough, also using some LoLs which I didn't use the first time, since it removes my hardest steps and gives a much simpler solving path. Prelims a) R23C3 = {16/25/34}, no 7,8,9 b) R23C4 = {69/78} c) R23C6 = {59/68} d) R78C4 = {13} e) R78C6 = {16/25/34}, no 7,8,9 f) R78C7 = {39/48/57}, no 1,2,6 g) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2 h) 21(3) cage at R6C9 = {489/579/678}, no 1,2,3 i) 21(3) cage at R7C1 = {489/579/678}, no 1,2,3 j) 21(6) cage at R8C1 = {123456}, no 7,8,9 Steps resulting from Prelims 1a. Naked pair {13} in R78C4, locked for C4 and NR6C4 1b. 21(6) cage at R8C1 = {123456}, locked for NR7C2 1c. 1 in C5 only in R123C5, locked for NR1C4 2. 21(3) cage at R7C1 = {489/579/678} 2a. 4,5,6 only in R7C1 -> R7C1 = {456} 3. 45 rule on NR1C6 3 innies R1C6 + R3C78 = 11 = {128/137/146/236/245}, no 9 3a. 45 rule on NR1C6 1 outie R3C9 = 1 innie R1C6 + 4, R1C6 = {12345}, R3C9 = {56789} [I haven’t been using Law of Leftovers for TJKs with low SSscores. However in this case it’s very useful. I think this puzzle would be very hard to solve without using LoL. I later noticed Ed’s comment in the TJK42 thread “Just to note again that the SS score should usually be low for zero killers since there aren't as many cages to get non-essential solving steps from.”, which implies that TJK42 is harder than its SSscore.] 4. Law of Leftovers (LoL) for C123 three outies R239C4 must exactly equal three innies R456C3, R239C4 only contain 6,7,8,9 -> R456C3 = {6789} 5. 34(6) cage at R4C3 = {245689} (only remaining combination) -> R456C3 = {689}, locked for C3 and NR4C3, R456C4 = {245}, locked for C4, clean-up: no 1 in R23C3 5a. R7C3 = 7, placed for NR7C2, R7C12 = 14 = [59/68], clean-up: no 5 in R8C7 6. Law of Leftovers (LoL) for C123 three outies R239C4 must exactly equal three innies R456C3, R456C3 = {689}, no 7 -> R23C4 = {69}, locked for C4 and NR1C1, R9C4 = 8, placed for NR7C2, R1C4 = 7, placed for NR1C4, R7C2 = 9, R7C1 = 5 (cage sum), placed for NR3C1, clean-up: no 2 in R8C6, no 3,7 in R8C7 6a. R78C6 = {16}/[25] (cannot be {34} which clashes with R78C7) 7. LoL for C789 three outies R178C6 must exactly equal three innies R456C7, no 7 in R178C6 -> no 7 in R456C7, no 6 in R456C7 -> no 6 in R78C6, clean-up: no 1 in R78C6 7a. R78C6 = [25], both placed for NR7C6, clean-up: no 9 in R23C6 7b. LoL for C789, R78C6 = [25] -> R456C7 must contain both of 2,5, locked for C7 and NR3C3 -> R5C4 = 4, placed for NR4C3 7c. 5 in NR7C2 only in R9C23, locked for R9 7d. 5 in NR6C4 only in R6C45, locked for R6 8. Naked pair {68} in R23C6, locked for C6 and NR1C4 [Taking step 7 further using Dan’s shortcut …] 9. R178C6 = R456C7 -> R145678C6 = 24 9a. 45 rule on C6 1 remaining innie R9C6 = 7, placed for NR6C4 10. R5C5 = 7 (hidden single in C5), R46C5 = 13 = {49}/[58], no 3,6 10a. R6C4 = 5 (hidden single in R6), R4C4 = 2, placed for NR1C4 11. LoL for R789 three outies R6C456 must exactly equal three innies R7C189, no 9 in R7C189 -> R6C56 = [84], 4 placed for NR6C4, R7C5 = 6, R7C89 = {48} 11a. R6C5 = 8 -> R4C5 = 5 (cage sum) 11b. Naked pair {48} in R7C89, locked for R7 and NR3C9 -> R7C7 = 3, R8C7 = 9, both placed for NR7C6, R89C5 = [29] 11c. R456C7 = [152], R45C6 = [93] 12. LoL for R123 three outies R4C456 must exactly equal three innies R3C129, R4C456 = [259] -> R3C129 = [925], 2 placed for NR3C1, R34C4 = [96], R34C6 = [68], clean-up: no 2,5 in R2C4 12a. R3C9 = 5 -> R3C78 = 10 = [73], both placed for NR1C6, R1C6 = 1, placed for NR1C6, R23C3 = [34], both placed for NR1C1, R3C5 = 1, R8C3 = 1, R78C4 = [13] 12b. Naked triple {258} in R1C123, locked for R1 and NR1 12c. R3C1 = 9 -> R24C1 = 5 = [14], R8C12 = [64], R5C1 = 8, R1C123 = [285], R9C123 = [352], R6C1 = 7 13. Naked pair {69} in R6C39, locked for R6 -> R6C8 = 1, placed for NR3C9, R6C2 = 3, R2C2 = 7, R4C2 = 6, R4C8 = 7, R78C8 = [48], R78C9 = [87], R6C9 = 6 (cage sum) and the rest is naked singles, without using the nonets. |
Author: | Andrew [ Tue Oct 21, 2014 3:35 am ] |
Post subject: | Texas Jigsaw Killer Archive |
Jigsaw Killer INSANE (Texas Jigsaw #42 INSANE) by h3lix (Dan) (June 2010) here The links to the original puzzle diagrams no longer work, so they were removed from the puzzle thread. Børge's images with udosuk Style Killer Cages:
Code: Select, Copy & Paste into solver: SumoCueV1=0J0=0J0=0J0=0J1=0J1=0J2=34J2+6J2+6J2=14J0=0J0=7J0=15J0=0J1=14J1+6J2+6J2+6J2+9J3=0J3+11J0+12J0=0J1+14J1=0J2=0J2=0J4+9J3=0J3=34J5+29J1=20J1=24J1+32J5=0J4=0J4=0J3=0J3+29J5+29J5+31J5+32J5+32J5=0J4=0J4=0J3=0J3+29J5+29J6+31J6+32J6+32J5=0J4=21J4=0J3=0J7=0J7=4J6=0J6=7J8=12J8=0J4+53J4=21J7+63J7+63J7+57J6=0J6+59J8+60J8=0J8+53J8+63J7+63J7+63J7=0J7=0J6=0J6=0J8=0J8=0J8 Note. This code string doesn't work for SudokuSolver. Solution: +-------+-------+-------+ Quote: Dan (h3lix): Here's a Jigsaw killer! This one comes in two difficulties, ... and the other is 1.12 (Archive Note) For general comments in the TJK42 thread, see the previous archive entry for TJK42 HARD. Ed: The Insane is a really great puzzle. Definitely worthy of the prestige of a Texas Jigsaw Killer . I found a way to get a placement as step 1 but am holding that back for a Really Insane version of this puzzle. Still haven't solved it. Andrew (in 2013): TJK 42 Insane wasn't much harder than TJK 42 Hard, but it took longer to finish because two cages had been removed. As with TJK 42 Hard, I missed some LoLs and Dan's shortcut when I first solved TJK 42 Insane. I also re-worked my walkthrough for TJK 42 Insane, using LoLs I missed (or didn’t use) first time and Dan’s shortcut. This took out the more complicated steps in my original walkthrough, but this time the solving path was as long. It seems that one either has to use Dan's shortcut or use a more complicated step (step 11 in my original walkthrough or Ed's cracker step) to eliminate 7 from 24(6) cage at R4C6. Ed's walkthrough: The Insane is a really great puzzle. Definitely worthy of the prestige of a Texas Jigsaw Killer . So, if you don't mind h3lix, I'd like to christen it as a part of the TJK series. I'll post my #43 on the 1st of July. Just to note again that the SS score should usually be low for zero killers since there aren't as many cages to get non-essential solving steps from. I found a way to get a placement as step 1 but am holding that back for a Really Insane version of this puzzle. Still haven't solved it. Walkthrough for Texas Jigsaw Killer 42 Insane 19 steps Prelims n1 = r1c1 n2=r1c4 n3 = r1c6 n4 = r3c1 n5 = r3c9 n6 = r4c3 n7 = r6c4 n8 = r7c2 n9 = r7c6 i. 7(2)r2c3: no 7,8,9 ii. 15(2)r2c4 = {69/78} iii. 14(2)r2c6 = {59/68} iv. 20(3)r4c5: no 1,2 v. 21(3)r6c9: no 1,2,3 vi. 4(2)r7c4 = {13} vii. 7(2)r7c6: no 7,8,9 viii. 12(2)r7c7: no 1,2,6 ix. 21(6)r8c1: no 7,8,9 1. hidden triple 7,8,9 in n8 in r7c23 + r9c4 1a. each cell = (789) 2. naked pair 1,3 at r78c4: both locked for c4 and n7 3. LoL c123: 3 outies r239c4 = 3 innies r456c3 3a. 3 outies from (6..9) -> 3 innies from (6..9) 4. 34(6)r4c3 = {245689} only (no 7) 5. naked triple {689} in r456c3: all locked for c3, 34(6) and n6 5a. no 1 in 7(2)r2c3 6. LoL c123 (step 3) -> no 7 in r239c4 6a. 15(2)r2c4 = {69}: both locked for c4 and n1 7. r7c3 = 7, r9c4 = 8, r7c2 = 9 7a. no 3,5 in r8c7 8. hidden single 7 for c4 in r1c4 9. 7 in n1 only in r2c12: 7 locked for r2 10. "45" on n3: 3 innies r1c6 + r3c78 = 11 10a. must have 7 for n3 = {137} only: all locked for n3 10b. 7 locked for r3 11. LoL on c789: 3 outies r178c6 = 3 innies r456c7 11a. 3 outies: no 7 -> no 7 in r456c7 11b. 3 innies: no 6 -> no 6 in r78c6 11c. no 1 in r78c6 12. LoL on r89: 4 outies r7c2367 = 4 innies r8c45 & r9c56 12a. outies must have 9 & 7 -> innies must have 9&7: both locked for n7 12b. no 1 or 6 in outies -> no 1 or 6 in innies 12c. r4c4 = 3, r7c4 = 1 12d. no 4 in r7c6 13. from Lol r89 (step 12): innies must have 3 -> outies must have 3 13a. 3 must be in r7c67: locked for r7 and n9 13b. 7(2)r7c6 = [34] or 12(2)r7c7 = [39] -> {48} blocked from 12(2)r7c7 (no 4,8) (Locking-out Cages) 14. from LoL r89 (step 12): no 4 in outies -> no 4 in innies The cracker. 15. no 7 in r5c6. Like this. 15a. 24(6)r4c6 = {123459/123468/123567} = [4/7..but not both] 15b. 4 in c7 is in 24(6)r4c6 -> no 7 (step 15a) 15c. or 4 is in r8c6: and from LoL c789 (step 11) -> 4 in r456c7 in 24(6)r4c6 -> no 7 (step 15a) 16. r5c5 = 7 (hsingle n6) 16a. r9c6 = 7 (hsingle c6) 17. 9 in n7 only in r89c5: 9 locked for c5 18. 20(3)r4c7 = {578} only: 5 & 8 locked for c5 19. r89c5 = {29}: 2 locked for c5 & n7 19a. and 2 locked for LoL r89 (step 12) -> outies must have 2 -> r7c6 = 2 on from there. Andrew's original walkthrough: TJK 42 Insane wasn't much harder than TJK 42 Hard, but it took longer to finish because two cages had been removed. As with TJK 42 Hard, I missed some LoLs and Dan's shortcut when I first solved TJK 42 Insane. I’ve started by using steps from my walkthrough for TJK 42 Hard, omitting the ones relating to the two cages which have been removed. Prelims a) R23C3 = {16/25/34}, no 7,8,9 b) R23C4 = {69/78} c) R23C6 = {59/68} d) R78C4 = {13} e) R78C6 = {16/25/34}, no 7,8,9 f) R78C7 = {39/48/57}, no 1,2,6 g) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2 h) 21(3) cage at R6C9 = {489/579/678}, no 1,2,3 i) 21(6) cage at R8C1 = {123456}, no 7,8,9 Steps resulting from Prelims 1a. Naked pair {13} in R78C4, locked for C4 and NR6C4 1b. 21(6) cage at R8C1 = {123456}, locked for NR7C2 1c. 1 in C5 only in R123C5, locked for NR1C4 2. 45 rule on NR1C6 3 innies R1C6 + R3C78 = 11 = {128/137/146/236/245}, no 9 3. Law of Leftovers (LoL) for C123 three outies R239C4 must exactly equal three innies R456C3, R239C4 only contain 6,7,8,9 -> R456C3 = {6789} 4. 34(6) cage at R4C3 = {245689} (only remaining combination) -> R456C3 = {689}, locked for C3 and NR4C3, R456C4 = {245}, locked for C4, clean-up: no 1 in R23C3 [With hindsight I realise that I’d forgotten to do LoL for C123 in the opposite direction after eliminating 7 from the 34(6) cage. I’ll remember when I try Ed’s Really Insane variant; but I might not be able to finish it.] [When posting my walkthrough, I checked through the other messages in the TJK 42 thread and found that I’d missed making full use of LoL for C123 and C789. LoL for C123 R456C3 = R239C4 -> R234569C4 = 34, 45 rule on C4 -> R1C4 = 7, placed for NR1C4 LoL for C789 R456C7 = R178C6 -> R145678C6 = 24, 45 rule on C6 -> R9C6 = 7, placed for NR6C4 R5C5 = 7 (hidden single in C5.] 5. R7C3 = 7, placed for NR7C2, clean-up: no 5 in R8C7 5a. Killer pair 8,9 in R23C4 and R9C4, locked for C4 6. LoL for R789 three outies R6C456 must exactly equal three innies R7C189, no 1,3 in R6C456 -> no 1,3 in R7C18, no 7 in R7C189 -> no 7 in R6C56 7. LoL for R123 three outies R4C456 must exactly equal three innies R3C129, no 1 in R4C456 -> no 1 in R3C129 8. 24(6) cage at R4C6 = {123459/123468/123567} 8a. Killer pair 6,9 in R23C6 and 24(6) cage, locked for C6, clean-up: no 1 in R78C6 9. R7C4 = 1 (hidden single in R7), R8C4 = 3, clean-up: no 4 in R7C6, no 9 in R7C7 9a. 21(6) cage at R8C1 = {123456}, 3 locked for R9 10. Grouped X-Wing for 3 in 24(6) cage at R4C6 and R7C67, no other 3 in C67 11. 24(6) cage at R4C6 = {123459/123468/123567} 11a. Consider placement for 3 in R7C67 3 in R7C6 => R78C6 = [34], R78C7 = {57}, locked for C7 => 24(6) cage = {123459/123468} (cannot be {123567} which clashes with R23C6) or 3 in R7C7 => R78C6 = {25}, locked for C6, R23C6 = {68}, locked for C6 => 24(6) cage = {123459} -> 24(6) cage = {123459/123468}, no 7 11b. Killer pair 8,9 in R23C6 and 24(6) cage, locked for C6 12. R5C5 = 7 (hidden single in NR4C3), R46C5 = 13 = {49/58}, no 3,6 12a. 3 in C5 only in R123C5, locked for NR1C4 13. R1C4 = 7 (hidden single in NR1C4), clean-up: no 8 in R23C4 13a. Naked pair {69} in R23C4, locked for C4 and NR1C1 -> R9C4 = 8, placed for NR7C2, R7C2 = 9 13b. R9C6 = 7 (hidden single in C6) 14. LoL for R89 four outies R7C2367 must exactly equal four innies R8C45 + R9C56, no 6 in R7C2367 -> no 6 in R89C5, R7C2 = 9 -> R89C5 must contain 9, locked for C5 and NR6C4 14a. R46C5 (step 12) = {58} (only remaining combination), locked for C5 14b. LoL for R89, no 5 in R8C45 + R9C56 -> no 5 in R7C67, clean-up: no 2 in R8C6, no 7 in R8C7 14c. 5 in NR6C4 only in R6C456, locked for R6 15. R78C6 = [25] (cannot be [34] which clashes with R78C7), both placed for NR7C6, clean-up: no 9 in R23C6 15a. Naked pair {68} in R23C6, locked for C6 and NR1C4 -> R6C6 = 4, placed for NR6C4, R1C6 = 1, placed for NR1C6, R45C6 = [93], R46C5 = [58], R7C5 = 6 15b. X-Wing for 6 in R23C4 and R23C6, no other 6 in R23 16. R7C7 = 3 (hidden single in R7), R8C7 = 9, R8C5 = 2, placed for NR6C4, R6C4 = 5, R9C5 = 9 16a. Naked triple {146} in R9C789, locked for R9 and NR7C6 16b. R8C3 = 1 (hidden single in C3) 16c. 4 in C3 only in R123C3, locked for NR1C1 17. Naked pair {12} in R46C7, locked for C7 and NR4C3 -> R5C7 = 5, R5C4 = 4, R4C4 = 2, R46C7 = [12] 18. 7,8 in C7 only in R123C7, locked for NR1C6 18a. R2C12 = {17} (hidden pair in NR1C1), locked for R2 18b. R3C5 = 1 (hidden single in C5), R3C7 = 7 (hidden single in C7) 18c. R1C6 + R3C78 = 11 (step 2), R1C6 = 1, R3C7 = 7 -> R3C8 = 3, placed for NR1C6, clean-up: no 4 in R2C3 18d. R4C9 = 3 (hidden single in C9) 19. 9 in R1 only in R1C89, locked for NR1C6 19a. R2C4 = 9 (hidden single in R2), R3C4 = 6, R23C6 = [68] 19b. R2C7 = 8 (hidden single in R2) 20. 7 in C9 only in 21(3) cage at R6C9 = {579/678}, no 4 20a. 6,9 only in R6C9 -> R6C9 = {69} 20b. Naked pair {69} in R6C39, locked for R6 20c. R8C9 = 7 (hidden single in C9), R8C8 = 8 21. 14(3) cage at R2C1 = {149/158} (other combinations blocked) -> R2C1 = 1, R2C2 = 7, R34C1 = [58/94] 22. R4C8 = 7 (hidden single in R4), R6C8 = 1, R6C12 = [73] 23. 4 in R4 only in R4C12, locked for NR3C1 23a. R34C1 (step 21) = [94] (cannot be [58] which clashes with R7C1), R8C12 = [64] 24. R45C2 = [61] (hidden pair in C2), R4C3 = 8 25. R7C8 = 4 (hidden single in R7), placed for NR3C9, R9C78 = [46], R1C7 = 6 26. R3C3 = 4 (hidden single in R3), R2C3 = 3, R12C5 = [34] 27. Naked pair {25} in R23C9, locked for C9 -> R7C9 = 8, R6C9 = 6 (cage sum) and the rest is naked singles, without using the nonets. Andrew's modified walkthrough: I also re-worked my walkthrough for TJK 42 Insane, using LoLs I missed (or didn’t use) first time and Dan’s shortcut. This took out the more complicated steps in my original walkthrough, but this time the solving path was as long. It seems that one either has to use Dan's shortcut or use a more complicated step (step 11 in my original walkthrough or Ed's cracker step) to eliminate 7 from 24(6) cage at R4C6. Prelims a) R23C3 = {16/25/34}, no 7,8,9 b) R23C4 = {69/78} c) R23C6 = {59/68} d) R78C4 = {13} e) R78C6 = {16/25/34}, no 7,8,9 f) R78C7 = {39/48/57}, no 1,2,6 g) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2 h) 21(3) cage at R6C9 = {489/579/678}, no 1,2,3 i) 21(3) cage at R7C1 = {489/579/678}, no 1,2,3 j) 21(6) cage at R8C1 = {123456}, no 7,8,9 Steps resulting from Prelims 1a. Naked pair {13} in R78C4, locked for C4 and NR6C4 1b. 21(6) cage at R8C1 = {123456}, locked for NR7C2 1c. 1 in C5 only in R123C5, locked for NR1C4 2. 45 rule on NR1C6 3 innies R1C6 + R3C78 = 11 = {128/137/146/236/245}, no 9 3. Law of Leftovers (LoL) for C123 3three outies R239C4 must exactly equal three innies R456C3, R239C4 only contain 6,7,8,9 -> R456C3 = {6789} 4. 34(6) cage at R4C3 = {245689} (only remaining combination) -> R456C3 = {689}, locked for C3 and NR4C3, R456C4 = {245}, locked for C4, clean-up: no 1 in R23C3 5. R7C3 = 7, placed for NR7C2, clean-up: no 5 in R8C7 6. LoL for C123 three outies R239C4 must exactly equal three innies R456C3, R456C3 = {689}, no 7 -> R23C4 = {69}, locked for C4 and NR1C1, R9C4 = 8, placed for NR7C2, R1C4 = 7, placed for NR1C4, R7C2 = 9, clean-up: no 3 in R8C7 7. LoL for R789 three outies R6C456 must exactly equal three innies R7C189, no 1,3 in R6C456 -> no 1,3 in R7C18, no 7,9 in R7C189 -> no 7,9 in R6C56 8. LoL for C789 three outies R178C6 must exactly equal three innies R456C7, no 7 in R178C6 -> no 7 in R456C7, no 6,8 in R456C7 -> no 6,8 in R178C6, clean-up: no 1 in R78C6 [Taking step 8 further using Dan’s shortcut …] 9. R178C6 = R456C7 -> R145678C6 = 24 9a. 45 rule on C6 1 remaining innie R9C6 = 7, placed for NR6C4 10. R5C5 = 7 (hidden single in C5), R46C5 = 13 = {58}/[94], no 3,6 11. LoL for R123 three outies R4C456 must exactly equal three innies R3C129, no 1,7 in R4C456 -> no 1,7 in R3C129 12. R7C4 = 1 (hidden single in R7), R8C4 = 3, clean-up: no 4 in R7C6 12a. 21(6) cage at R8C1 = {123456}, 3 locked for R9 13. Grouped X-Wing for 3 in 24(6) cage at R4C6 and R7C67, no other 3 in C67 14. LoL for R89 four outies R7C2367 must exactly equal four innies R8C45 + R9C56, no 6 in R7C2367 -> no 6 in R89C5, R7C2 = 9 -> R89C5 must contain 9, locked for C5 14a. R46C5 (step 10) = {58} (only remaining combination), locked for C5 14b. LoL for R89, no 5 in R8C45 + R9C56 -> no 5 in R7C67, clean-up: no 2 in R8C6, no 7 in R8C7 14c. 5 in NR6C4 only in R6C456, locked for R6 15. R78C6 = [25] (cannot be [34] which clashes with R78C7), both placed for NR7C6, clean-up: no 9 in R23C6 15a. Naked pair {68} in R23C6, locked for C6 and NR1C4 -> R6C6 = 4, placed for NR6C4, R1C6 = 1, placed for NR1C6, R45C6 = [93], R46C5 = [58], R7C5 = 6 15b. X-Wing for 6 in R23C4 and R23C6, no other 6 in R23 16. R7C7 = 3 (hidden single in R7), R8C7 = 9, R8C5 = 2, placed for NR6C4, R6C4 = 5, R9C5 = 9 16a. Naked triple {146} in R9C789, locked for R9 and NR7C6 16b. R8C3 = 1 (hidden single in C3) 16c. 4 in C3 only in R123C3, locked for NR1C1 17. Naked pair {12} in R46C7, locked for C7 and NR4C3 -> R5C7 = 5, R5C4 = 4, R4C4 = 2, R46C7 = [12] 18. 7,8 in C7 only in R123C7, locked for NR1C6 18a. R2C12 = {17} (hidden pair in NR1C1), locked for R2 18b. R3C5 = 1 (hidden single in C5), R3C7 = 7 (hidden single in C7) 18c. R1C6 + R3C78 = 11 (step 2), R1C6 = 1, R3C7 = 7 -> R3C8 = 3, placed for NR1C6, clean-up: no 4 in R2C3 18d. R4C9 = 3 (hidden single in C9) 19. 9 in R1 only in R1C89, locked for NR1C6 19a. R2C4 = 9 (hidden single in R2), R3C4 = 6, R23C6 = [68] 19b. R2C7 = 8 (hidden single in R2) 20. 7 in C9 only in 21(3) cage at R6C9 = {579/678}, no 4 20a. 6,9 only in R6C9 -> R6C9 = {69} 20b. Naked pair {69} in R6C39, locked for R6 20c. R8C9 = 7 (hidden single in C9), R8C8 = 8 21. 14(3) cage at R2C1 = {149/158} (other combinations blocked) -> R2C1 = 1, R2C2 = 7, R34C1 = [58/94] 22. R4C8 = 7 (hidden single in R4), R6C8 = 1, R6C12 = [73] 23. 4 in R4 only in R4C12, locked for NR3C1 23a. R34C1 (step 21) = [94] (cannot be [58] which clashes with R7C1), R8C12 = [64] 24. R45C2 = [61] (hidden pair in C2), R4C3 = 8 25. R7C8 = 4 (hidden single in R7), placed for NR3C9, R9C78 = [46], R1C7 = 6 26. R3C3 = 4 (hidden single in R3), R2C3 = 3, R12C5 = [34] 27. Naked pair {25} in R23C9, locked for C9 -> R7C9 = 8, R6C9 = 6 (cage sum) and the rest is naked singles, without using the nonets. |
Author: | Andrew [ Tue Oct 21, 2014 3:47 am ] |
Post subject: | Texas Jigsaw Killer Archive |
Texas Jigsaw Killer 42 Really Insane by Ed (June 2010) here Puzzle Diagram: Code: Select, Copy & Paste into solver: SumoCueV1=0J0=0J0=0J0=0J1=0J1=0J2=34J2+6J2+6J2=14J0=0J0=7J0=15J0=0J1=14J1+6J2+6J2+6J2+9J3=0J3+11J0+12J0=0J1+14J1=0J2=0J2=0J4+9J3=0J3=34J5+29J1=20J1=24J1+32J5=0J4=0J4=0J3=0J3+29J5+29J5+31J5+32J5+32J5=0J4=0J4=0J3=0J3+29J5+29J6+31J6+32J6+32J5=0J4=21J4=0J3=0J7=0J7=4J6=0J6=7J8=12J8=0J4+53J4=0J7=0J7=0J7+57J6=0J6+59J8+60J8=0J8+53J8=10J7+72J7+72J7=0J7=0J6=0J6=0J8=0J8=0J8 Note. This code string doesn't work for SudokuSolver. Solution: +-------+-------+-------+ Quote: Dan (h3lix): I think I may know what early placements you're talking about. (Archive Note) See the archive entry for TJK42 HARD. Ed: Correct! And you expressed it better than I did. Still 3 or so decent moves (but look simple once you see them) to crack it from there. Good luck! SS has to use Bingo but JSudoku doesn't have any problems. I really enjoy jigsaw killers. Andrew (in 2013): Ed's Really Insane version is a lot harder than the Insane version, because the triple 7,8,9 in NR7C2 has been taken away. It’s amazing how so many 7s get placed before any other numbers. Ed wrote: SS has to use Bingo but JSudoku doesn't have any problems. JSudoku, which I've never used, has a reputation for being good at using "fishes" (similar to forcing chains).Andrew's walkthrough: Ed's Really Insane version is a lot harder than the Insane version, because the triple 7,8,9 in NR7C2 has been taken away. It’s amazing how so many 7s get placed before any other numbers. Ed wrote: SS has to use Bingo but JSudoku doesn't have any problems. JSudoku, which I've never used, has a reputation for being good at using "fishes" (similar to forcing chains).Prelims a) R23C3 = {16/25/34}, no 7,8,9 b) R23C4 = {69/78} c) R23C6 = {59/68} d) R78C4 = {13} e) R78C6 = {16/25/34}, no 7,8,9 f) R78C7 = {39/48/57}, no 1,2,6 g) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2 h) 21(3) cage at R6C9 = {489/579/678}, no 1,2,3 i) 10(3) cage at R9C1 = {127/136/145/235}, no 8,9 Steps resulting from Prelims 1a. Naked pair {13} in R78C4, locked for C4 and NR6C4 1b. 1 in C5 only in R123C5, locked for NR1C4 2. 45 rule on NR1C6 3 innies R1C6 + R3C78 = 11 = {128/137/146/236/245}, no 9 3. Law of Leftovers (LoL) for C123 three outies R239C4 must exactly equal three innies R456C3, no 1,3 in R239C4 -> no 1,3 in R456C3 4. 34(6) cage at R4C3 = {245689} (only remaining combination), no 7 5. LoL for C123 three outies R239C4 must exactly equal three innies R456C3, no 7 in R456C3 -> no 7 in R239C4, clean-up: no 8 in R23C4 5a. Naked pair {69} in R23C4, locked for C4 and NR1C1, clean-up: no 1 in R23C3 5b. 34(6) cage at R4C3 = {245689}, 6,9 locked for C3 and NR4C3 6. R1C4 = 7 (hidden single in C4), placed for NR1C4 6a. 7 in NR1C1 only in R2C12, locked for R2 6b. 7 in NR1C6 only in R3C78, locked for R3 6c. 7 in C3 only in R789C3, locked for NR7C2 7. 7 in R3C78 -> R1C6 + R3C78 (step 2) = {137} (only remaining combination), locked for NR1C6 8. 24(6) cage at R4C6 = {123459/123468/123567} 8a. Killer pair 6,9 in R23C6 and 24(6) cage, locked for C6, clean-up: no 1 in R78C6 9. LoL for R123 three outies R4C456 must exactly equal three innies R3C129, no 1 in R4C456 -> no 1 in R3C129 10. LoL for R789 three outies R6C456 must exactly equal three innies R7C189, no 1,3 in R6C456 -> no 1,3 in R7C18 11. LoL for C789 three outies R178C6 must exactly equal three innies R456C7, no 7,8 in R178C6 -> no 7,8 in R456C7 11a. 7 in NR4C3 only in R5C56, locked for R5 12. Hidden killer triple 7,8,9 in R23C6, 24(6) cage at R4C6 and R9C6 for C6, R23C6 contains one of 8,9, 24(6) cage contains one of 7,8,9 -> R9C6 = {78} 13. 24(6) cage at R4C6 = {123459/123468/123567} 13a. Consider combinations for R78C6 = {25/34} R78C6 = {25}, locked for C6 => R23C6 = {68}, locked for C6 => 24(6) cage = {123459} or R78C6 = {34}, locked for NR7C6 => R78C7 = {57}, locked for C7 => 24(6) cage = {123459/123468} (cannot be {123567} which clashes with R23C6) -> 24(6) cage = {123459/123468}, no 7 [Alternatively Dan’s shortcut gives the same result … LoL for C789 three outies R178C6 must exactly equal three innies R456C7 -> R145678C6 = 24 45 rule on C6 1 remaining innie R9C6 = 7] 14. R9C6 = 7 (hidden single in C6), placed for NR6C4 14a. R5C5 = 7 (hidden single in C5), R46C5 = 13 = {49/58}, no 3,6 14b. 3 in C5 only in R123C5, locked for NR1C4 15. LoL for R789 three outies R6C456 must exactly equal three innies R7C189, no 7 in R6C456 -> no 7 in R7C189 16. LoL for R123 three outies R4C456 must exactly equal three innies R3C129, no 3 in R4C456 -> no 3 in R3C129 17. R78C6 = {25/34}, R78C7 = {39/48/57} -> combined cage R78C67 = {25}{39}/{25}{48}/{34}{57}, 5 locked for NR7C6 [Taking step 13 a little further] 18. 24(6) cage at R4C6 (step 13a) = {123459/123468} 18a. Consider combinations for R78C6 = {25/34} R78C6 = {25}, locked for C6 => R23C6 = {68}, locked for C6 => 24(6) cage = {123459}, 5 locked for C7 or R78C6 = {34}, locked for NR7C6 => R78C7 = {57}, locked for C7 -> 5 in R45678C7, locked for C7 19. LoL for R12 four outies R3C3478 must exactly equal four innies R1C45 + R2C56, no 8 in R3C3478 -> no 8 in R1C5 + R2C56, clean-up: no 6 in R3C6 [Alternatively 8 in NR1C1 and NR1C6 only in R1C123 + R2C12 + 34(6) cage at R1C7, locked for R12] [I was finding it hard to make further progress until I spotted …] 20. 24(6) cage at R4C6 (step 13a) = {123459/123468} 20a. Consider placement for 1,3 R5C6 = {13} => naked pair {13} in R15C6, locked for C6 => R78C6 = {25} => R78C7 = {39/48} => R3C7 = 7 (hidden single in C7) or both of 1,3 in R456C7, locked for C7 => R3C7 = 7 -> R3C7 = 7, clean-up: no 5 in R78C7 20b. R7C3 = 7 (hidden single in R7) 21. R78C6 = {25} (only remaining combination, cannot be {34} which clashes with R78C7), locked for C6 and NR7C6, clean-up: no 9 in R23C6 [Alternatively 5 in NR7C6 only in R78C6 = {25} …] 21a. R23C6 = [68], placed for NR1C4, R23C4 = [96], clean-up: no 5 in R6C5 (step 14a) 21b. Naked pair {49} in R46C6, locked for 24(6) cage at R4C6, no 4 in R5C6 + R456C7 21c. 24(6) cage at R4C6 (step 13a) = {123459} (only remaining combination), 2 locked for C7 [At last I’ve placed some other numbers than 7s …] 22. 45 rule on NR4C3 6(3+3) outies R46C456 = 33, R46C5 = 13 (step 14a), R46C6 = {49} = 13 -> R46C4 = 7 = {25}, locked for C4 and 34(6) cage at R4C3, no 2,5 in R456C3 23. R78C7 = {39} (only remaining combination, cannot be {48} which clashes with R2C7), locked for C7 and NR7C6 23a. Naked triple {125} in R456C7, locked for C7 and 24(6) cage at R4C6 -> R5C6 = 3, R1C6 = 1, R3C8 = 3, clean-up: no 4 in R2C3 23b. R3C5 = 1 (hidden single in R3) 24. R9C5 = 9 (hidden single in R9), placed for NR6C4 -> R6C6 = 4, placed for NR6C4, R4C6 = 9, R6C5 = 8, R4C5 = 5 (cage sum), R46C4 = [25], 2 placed for NR1C4, R456C7 = [152] 25. LoL for R123 three outies R4C456 must exactly equal three innies R3C129, R4C456 = [259] -> R3C129 = {259}, locked for R3 -> R3C3 = 4, R2C3 = 3, both placed for NR1C1, R12C5 = [34], R2C7 = 8 25a. Naked pair {25} in R2C89, locked for R2 and NR1C6 26. Naked triple {689} in R456C3, locked for C3 and 34(6) cage at R4C3 -> R5C4 = 4, R9C4 = 8, placed for NR7C2 27. Naked triple {146} in R9C789, locked for R9 and NR7C6 27a. Naked triple {235} in 10(3) cage at R9C1, locked for NR7C2 -> R8C3 = 1, R78C4 = [13], R78C7 = [39] 28. Naked pair {46} in R8C12, locked for R8 and NR7C2 -> R7C2 = 9, R78C5 = [62], R78C5 = [25] 29. 21(3) cage at R6C9 = {489/579/678} 29a. 6,9 only in R6C9 -> R6C9 = {69} 29b. Naked pair {69} in R6C39, locked for R6 [Just spotted] 30. R4C9 = 3 (hidden single in NR3C9) 30a. 7 in NR3C9 only in R46C8, locked for C8 -> R8C8 = 8, R8C9 = 7 30b. 21(3) cage at R6C9 = {579/678} (cannot be {489} which doesn’t contain 7), no 4 31. 14(3) cage at R2C1 = {149/158} (other combinations blocked) -> R2C1 = 1, R34C1 = [58/94], R2C2 = 7 32. R6C1 = 7 (hidden single in C1), R6C8 = 1, R6C2 = 3 32a. R5C2 = 1 (hidden single in NR3C1) 32b. Naked pair {25} in R39C2, locked for C2 -> R1C2 = 8 33. R4C8 = 7 (hidden single in R4), R7C8 = 4 (hidden single in NR3C9) 34. R34C1 (step 31) = [94] (cannot be [58] which clashes with R7C1) 35. Naked pair {25} in R23C9, locked for C9 -> R7C9 = 8, R6C9 = 6 (cage sum) and the rest is naked singles, without using the nonets. In this case Dan's shortcut only affected one step, so I've included it as a note. |
Author: | Andrew [ Tue Oct 21, 2014 10:37 pm ] |
Post subject: | Texas Jigsaw Killer Archive |
Texas Jigsaw Killer 43 by Ed (July 2010) here Puzzle Diagrams: Many thanks to Børge for making the pics for me. More Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration: Cages with cells in 3 jigsaw nonets: pink Code: Select, Copy & Paste into solver: SumoCueV1=6J0=27J0=19J0+2J1=28J1+4J1=19J1=10J1+7J2+0J3+1J0+1J0+2J1+2J1+4J1+6J2+6J1=12J2=15J3+18J3+1J0+1J0+4J4+4J4+6J2=10J2+17J2+18J3=16J3+28J0=5J0+30J4=17J4=10J2+25J2=8J2=15J3+28J3=10J3=6J4+39J4+32J4+33J4=15J5+35J5+36J6=12J6+38J3=12J6+48J6+48J4+43J5+43J5=16J5=5J6+46J6=20J6=25J6+57J7=31J7+59J7+53J5+53J5+54J8+56J8+56J8+57J6=17J7+67J7+59J7+59J5=8J5=11J8+72J8+56J8+57J8+57J8+67J8+67J7+59J7+71J7 Solution: +-------+-------+-------+ Quote: Ed: This is a bit late, having computer problems. This puzzle is very straightforward compared to the last few of mine. But didn't seem trivial. I'll try and ramp it up again for my next one. SSscore: 1.32 manu: No trivial yes ! There are so many paths to explore that it takes time to find good ones. Thanks Ed for a great and rich puzzle. Andrew (in 2013): Thanks Ed for an enjoyable TJK! manu's step 2 was definitely a good one! An easy start, then it took me some time to find the breakthrough in step 14. Looks like I solved this one without using LoL; it's some time since I solved this puzzle, so I can't remember whether I was looking for it - maybe I wasn't as the SSv3.6.1 score is 1.20. manu's walkthrough: Ed wrote: This puzzle is very straightforward compared to the last few of mine. But didn't seem trivial. No trivial yes ! There are so many paths to explore that it takes time to find good ones. Thanks Ed for a great and rich puzzle. WALKTHROUGH TJK #43 WALKTHROUGH Nonets : 1 1 1 2 2 2 2 2 3 4 1 1 2 2 2 3 2 3 4 4 1 1 5 5 3 3 3 4 4 1 1 5 5 3 3 3 4 4 4 5 5 5 5 6 6 7 7 4 7 7 5 6 6 6 7 7 7 7 8 8 8 6 6 9 9 9 7 8 8 8 6 6 9 9 9 9 9 9 6 6 6 Prelims : remove non valid candidates from cage sums. 1)a) {89} locked for N5 and C6 at R45C6. b) At C1 : 6(2)+5(2) = 11(4) = {1235} => {15} locked for C1 at R12C1 => {23} locked for C1 at R78C1. 2)Innies outies for C12345 : R1C5 + R3C5 + R8C5 = 21 + R6C6. a) Min R1C5 + R3C5 + R8C5 = 22 : R138C5 = (56789). b) Max R6C6 = 3 3)a) Outies for C1 : R3C2 + R9C2 = h7(2) : No 7, 8, 9. Clean up : R9C1 <> 4. b) 4 locked for C1 and N4 at 15(3) => R3C2 <> 4 => (step 3)a) 11(2) at R9C1 <> [83] c) 11(2) at R9C1 = [65/74/92], h7(2) at C2 = [25/34/52] (contains 5 or one of (34).). So 12(2) + h 7(2) at C2 contains 5, locked for C2. 4)L.O.L for N 6789 : R6C3 <>5 and R6C6 <> 5 => R5C89 <> 5 => 5 locked for R5 at R5C45. 5)a) At N5 : 6(2)={15} locked for N5 and R5. b) From Step 2), R1C5 + R3C5 + R8C5 = 23/24 = {6/7}89 => {89} locked for C at R1C5 + R8C5, and R3C5=(67). 6)From step 4 (L.O.L) , R5C89 <> 1 => R6C3 <>1 : 10(2) at R5C3 = {28/37}. In particular, R6C3=(2378) 7)Combos for 15(3) at R3C1 (using digit 4 locking at from step 3)b ) : {29/56}4 , since {348} block all combos of 10(2) at R5C3. => 8 locked at 15(2) for C1 : {78} locked for C1. => R9C12=[65/92], h7(2) at C2 = {25} locked for C2. 8)Outies for R123 : R4C18=h11(2) = [47/92]. => Killer pair {24} locked at h11(2) + 5(2) for R4. 9)From step 4), R5C89=R6C36=(2378) => Naked quad {2378} locked for R5 at R5C1389. Cracked ! 10)a) R5C6=9, R4C6=8. b) Hidden singles for R5 : R5C7=4(=>R4C7=6) and R5C2=6. c) R4C5=(23) => 5(2)={23} locked for R4. => Naked pair {23} locked for N5 at R4C5 + R6C6 => Naked pair {67} at R3C56 locked for R3, and the rest of cage 28(5). d) Last combo for 16(3) at R4C2 : {169} with {19} locked at R4C23 for R4. e) Last combo : 12(2) at C9 : {48} locked for C9 and N3. And so on : the rest is easier Andrew's walkthrough: Thanks Ed for an enjoyable TJK! manu wrote: There are so many paths to explore that it takes time to find good ones. manu's step 2 was definitely a good one!An easy start, then it took me some time to find the breakthrough in step 14. Looks like I solved this one without using LoL; it's some time since I solved this puzzle, so I can't remember whether I was looking for it - maybe I wasn't as the SSv3.6.1 score is 1.20. Prelims a) R12C1 = {15/24} b) R1C89 = {19/28/37/46}, no 5 c) R23C9 = {39/48/57}, no 1,2,6 d) R34C8 = {19/28/37/46}, no 5 d) R4C45 = {14/23} e) R45C6 = {89} f) R45C7 = {19/28/37/46}, no 5 g) R45C9 = {17/26/35}, no 4,8,9 h) R56C1 = {69/78} i) R56C3 = {19/28/37/46}, no 5 j) R5C45 = {15/24} k) R67C2 = {39/48/57}, no 1,2,6 l) R78C1 = {14/23} m) R89C9 = {17/26/35}, no 4,8,9 n) R9C12 = {29/38/47/56}, no 1 1. Naked pair {89} in R45C6, locked for C6 and NR3C5, clean-up: no 1,2 in R4C7 2. R12C1 = {15} (cannot be {24} which clashes with R78C1), locked for C1, clean-up: no 4 in R78C1, no 6 in R9C2 2a. Naked pair {23} in R78C1, locked for C1, clean-up: no 8,9 in R9C2 2b. Naked pair {15} in R12C1, CPE no 1,5 in R2C23 3. 45 rule on C1 2 outies R39C2 = 7 = {25/34}, no 1,6,7,8,9, clean-up: no 4 in R9C1 4. 4 in C1 only in R34C1, locked for NR2C1, clean-up: no 6 in R56C3, no 3 in R9C2 (step 3), no 8 in R9C1 4a. 15(3) cage at R3C1 contains 4 = {249/348/456}, no 7 5. R23C9 = {39/48} (cannot be {57} which clashes with the pair of 8(2) cages in C9), no 5,7 6. 45 rule on C9 2 outies R17C8 = 9 = {18/27/36}/[45], no 9, no 4 in R7C8, clean-up: no 1 in R1C9 7. 45 rule on R123 2 outies R4C18 = 11 = [47/83/92], clean-up: R3C8 = {378} 7a. R17C8 (step 6) = {18/36}/[45] (cannot be {27} which clashes with R34C8), no 2,7, clean-up: no 3,8 in R1C9 7b. Killer pair 3,8 in R23C9 and R34C8, locked for NR2C7, clean-up: no 2,7 in R5C7, no 5 in R5C9 8. 45 rule on R789 2 outies R6C29 = 10 = [37/46/73/82/91], clean-up: no 7 in R7C2 9. 45 rule on C123 1 outie R3C4 = 1 innie R1C3 + 2, no 8,9 in R1C3, no 1,2 in R3C4 10. 45 rule on C789 1 outie R7C6 = 1 innie R9C7 + 4, R7C6 = {567}, R9C7 = {123} 11. R39C2 (step 3) = {25}/[34], R67C2 = {39/48}/[75] -> combined cage R39C2 + R67C2 = {25}{39}/{25}{48}/[34][75], 5 locked for C2 12. Hidden killer pair 4,8 in R17C9 and R23C9 for C9, R23C9 contains both or neither of 4,8 -> R17C9 must contain both or neither of 4,8, no 8 in R1C9 -> no 4 in R7C9 12a. 4 in C9 only in R123C9, locked for NR1C9, clean-up: no 6 in R5C7 [If I’d spotted step 14 earlier, step 12 wouldn’t have been needed – which would have been a pity.] 13. 28(5) cage at R1C5 must contain at least one of 8,9 -> R1C5 = {89} 13a. 28(5) cage = {15679/24679/25678/34579/34678}, CPE no 7 in R6C6 13b. 1 of {15679} must be in R123C6 (R123C6 cannot be {567} which clashes with R7C6), no 1 in R3C5 13c. 7 in NR3C5 only in R3C56, locked for R3 and 28(5) cage, no 7 in R12C6, clean-up: no 5 in R1C3 (step 9), no 3 in R4C8 13d. 6 in NR3C5 only in R3C56 + R6C6, CPE no 6 in R12C6 14. The two 8(2) cages in C9 + R6C9 must contain 3, locked for C9, clean-up: no 9 in R23C9 14a. Naked pair {48} in R23C9, locked for C9 and NR1C9 -> R3C8 = 3, R4C8 = 7, placed for NR1C9, clean-up: no 1 in R1C3 (step 9), no 6 in R1C8, no 3 in R5C7, no 1 in R5C9, no 6 in R7C8 (step 6), no 4 in R9C2 (step 3), no 7 in R9C1 14b. Naked pair {25} in R39C2, locked for C2, clean-up: no 7 in R6C2 [Cracked. The rest is fairly straightforward.] 15. R56C1 = {78} (only remaining combination, cannot be {69} which clashes with R9C1), locked for C1 15a. Naked pair {78} in R56C1, CPE no 7,8 in R6C3, clean-up: no 2,3 in R5C3 16. Killer pair 1,4 in R5C45 and R5C7, locked for R5, clean-up: no 9 in R6C3 17. Naked triple {789} in R5C136, locked for R5, clean-up: no 1 in R4C9 18. 16(3) cage at R4C2 = {169/268/349/358} (cannot be {259} because 2,5 only in R4C3) 18a. R5C2 = {36} -> no 3,6 in R4C23 19. 3 in R4 only in R4C45 = {23}, locked for R4, clean-up: no 6 in R5C9 20. 1 in R4 only in 16(3) cage at R4C2 (step 18) = {169} (only remaining combination) -> R5C2 = 6, placed for NR2C1, R34C1 = {49}, locked for NR2C1 -> R4C2 = 1, placed for NR2C1, R2C1 = 5, placed for NR2C1, R1C1 = 1, placed for NR1C1, R3C2 = 2, placed for NR2C1, R4C3 = 9, placed for NR1C1, R34C1 = [94], R45C6 = [89], R4C7 = 6, placed for NR1C9, R5C7 = 4, placed for NR3C5, R4C9 = 5, placed for NR1C9, R5C9 = 3, placed for NR5C8, R3C7 = 1, R6C3 = 3, R5C3 = 7, R5C1 = 8, R6C1 = 7 placed for NR6C1, clean-up: no 4 in R1C8, no 9 in R1C9, no 2 in R5C45, no 9 in R7C2, no 5 in R7C6 (step 10) 20a. Naked pair {15} in R5C45, locked for R5 and NR3C5 -> R5C8 = 2 [Some other clean-ups missed; they aren’t important.] 21. R1C8 = 8, placed for NR1C4, R1C9 = 2, placed for NR1C9, R2C7 = 9, R1C5 = 9, R7C8 = 1 (step 6) -> R67C9 = 15 = [69], all placed for NR5C8, R6C6 = 2, placed for NR3C5, R4C5 = 3, R4C4 = 2, placed for NR1C1 22. Naked pair {45} in R68C8, locked for C8 and NR5C8 -> R2C8 = 6, R1C7 = 3 (cage sum), both placed for NR1C4, R6C7 = 8, R6C8 = 5 (cage sum), R8C8 = 4, R9C7 = 2, placed for NR7C5 22a. Naked pair {57} in R78C7, locked for NR7C5 -> R7C6 = 6, placed for NR7C5, R3C56 = [67] 23. R6C6 = 2 -> R6C45 = 10 = [91], 1 placed for NR6C1, R6C2 = 4, R7C2 = 8, both placed for NR6C1 24. Naked pair {48} in R2C39, locked for R2 -> R2C6 = 1, R1C6 = 5 (cage sum) and the rest is naked singles, without using the nonets. |
Page 6 of 7 | All times are UTC |
Powered by phpBB® Forum Software © phpBB Group https://www.phpbb.com/ |