Ruud: If you have trouble solving the V1... Andrew: I felt that it wasn't much lighter than A48 with the exception that it finished smoothly without needing a breakthrough
Walkthrough by Andrew:
Congratulations to the tag team on the Hevvie! =D>
I must have a look at your moves when I've got time.
mhparker wrote:
What's the situation with the Lite version? Is anybody planning on writing a walkthrough for it?
I've been doing it while the Hevvie was in progress. I felt that it wasn't much lighter than A48 with the exception that it finished smoothly without needing a breakthrough.
Here is my walkthrough
Para. Thanks for your comments and corrections. I must remember not to refer to naked pairs as killer pairs.
1. R1C34 = {79}, locked for R1
2. R12C5 = {12}, locked for C1 and N2
3. R1C67 = [34/43/52/61], no 8, no 5,6 in R1C7
4. R23C4 = {36/45}, no 7,8,9
5. R23C6 = {69/78}, no 3,4,5
6. R5C12 = {89}, locked for R5 and N4
7. R5C89 = {17/26/35}, no 4
8. R78C4 = {16/25/34}, no 7,8,9
9. R78C6 = {16/25/34}, no 7,8,9
10. R89C5 = {49/58/67}, no 3
11. R9C34 = {69/78}
12. R9C67 = {16/25/34}, no 7,8,9
13. 19(3) cage in N36 = {289/378/469/478/568}, no 1
14. 9(3) cage in N47 = {126/135/234}, no 7,8,9
15. R678C9 = {289/378/469/478/568}, no 1
16. 17(5) cage in N9 = 123{47/56}, no 8,9, 1,2,3 locked for N9, clean-up: no 4,5,6 in R9C6
17. 45 rule on C9 3 innies R159C9 = 10 = {127/136/145/235}, no 8
18. 45 rule on C123 3 innies R159C3 = 19 = {289/378/469/478} (cannot be {568} because no 5,6,8 in R1C3), no 1,5,6,7 in R5C3, no 7,9 in R9C3, clean-up: no 6,8 in R9C4
22. 4,8 locked in 17(4) cage in N45 (steps 21 and 20) = {2348}, no 1,5,6, 2,3 locked for C4 and N5, clean-up: no 6 in R23C4, no 4,5 in R78C4
23. 1 in N5 locked in R456C6, locked for C6 and 21(4) cage -> no 1 in R5C7, clean-up: no 6 in R78C6, no 6 in R9C7
24. Naked pair {45} in R23C4, locked for N2, clean-up: no 2,3 in R1C7
25. Naked pair {16} in R78C4, locked for N8, clean-up: no 7 in R89C5
26. Killer pair 2/3 in R78C6 and R9C6 for C6 and N8
27. R1C67 = [61] (naked singles) -> R12C5 = [21], clean-up: no 9 in R23C6
28. Naked pair {78} in R23C6, locked for C6 and N2
29. R1C34 = [79], R3C5 = 3, R9C34 = [87] (naked singles), clean-up: no 5 in R8C5
30. 9 in C6 locked in R46C6, locked for N5
31. 45 rule on C789 2 outies R19C6 – 2 = 1 innie R5C7, min R19C6 = 8 -> min R5C7 = 6 31a. 21(4) cage in N56 = 19{47/56}
32. Killer triple 5/6/7 in R5C5, R5C7 and R5C89 for R5 -> R5C6 = 1, clean-up: no 7 in R5C89
33. R34567C5 = 367{49/58} 33a. 8,9 only in R7C5 -> R7C5 = {89}
34. R159C9 (step 17) = {136/145/235} 34a. 1 only in R9C9 -> no 4,6 in R9C9
35. 45 rule on C1 3 innies R159C1 = 16 = [385/394/493/583/592], no 8 in R1C1, no 1,6,9 in R9C9
36. 45 rule on N7 3 outies R6C123 = 9 = {126/135} = 1{26/35}, no 7, 1 locked for R6 and N4
37. 7 in N4 locked in R4C12, locked for R4 37a. 45 rule on N1 3 outies R4C123 = 15 = 7{26/35}
38. R4C9 = 1 (hidden single in R4) 38a. R23C9 = 15 = {69/78}, no 2,3,4,5
39. 45 rule on N3 1 remaining innie R3C8 = 2, clean-up: no 6 in R5C9 39a. R4C78 = 17 = {89}, locked for R4 and N6
40. R6C4 = 8, R6C6 = 9 (hidden singles in R6)
41. R159C9 (step 34) = {235}, locked for C9
42. 4 in C9 locked in R678C9 = 4{69/78}
43. 45 rule in N1 1 outie R4C1 – 1 = 1 innie R3C2, no 8,9 in R3C2, no 3 in R4C1
44. 45 rule on N7 1 outie R6C1 = 1 innie R7C2, no 4 in R7C2 44a. R6C1 and R7C2 cannot contain any candidates that aren’t in R123C3; in this case in R23C3 since R1C3 = 7 which isn’t in R6C1/R7C2
45. 4 in R4 locked in R4C56, locked for N5
46. 45 rule on N9 1 innie R7C8 – 2 = 2 outies R6C9 + R9C6, min R6C9 + R9C6 = 6 -> min R7C8 = 8, max R6C9 + R9C6 = 7 -> R6C9 = 4
47. 17(3) cage in N69 = [269/278/359/368/539/638], no 7 in R6C7
48. Naked pair {89} in R47C8, locked for C8
49. Naked pair {89} in R7C58, locked for R7, clean-up: no 6,7 in R8C9
50. R1C2 = 8 (hidden single in R1) -> R5C12 = [89]
51. R9C5 = 9 (hidden single in R9) -> R7C58 = [89], R4C78 = [98], R8C5 = 4, R8C9 = 8, R7C9 = 7, clean-up: no 3 in R78C6
54. 17(3) cage in N69 (step 47) = [26/35/53]9 -> no 6 in R6C7, no 7 in R6C8
55. R5C7 = 7 (hidden single in N6) -> R2C8 = 7 (hidden single in N3) -> R23C6 = [87] -> R1C8 = 4, R3C7 = 8 (hidden singles in N3), R6C5 = 7 (hidden single in N5) [Para pointed out that I had missed R7C1 = 4 (hidden single in N7). This would have simplified step 59.]
56. 6 in C7 locked in R78C7, locked for N9
57. R9C2 = 6, R9C8 = 1 (hidden singles in R9), clean-up: no 6 in R6C1 (step 44)
58. 6 in C1 locked in R234C1 = 6{29/47}, no 1,3,5
59. 1 in C1 locked in R678C1 = 1{29/47}, no 3,5, clean-up: no 3,5 in R7C2 (step 44) 59a. 9 only in R8C1 -> no 2 in R8C1
60. R7C1 = 4 (hidden single in R7) -> R68C1 = [17] (step 59), R7C2 = 1 (step 44) 60a. R6C23 = [26]/{35}, no 2 in R6C3
61. R4C2 = 7 (hidden single in R4) 61a. R3C2 + R4C3 = 7 = [43/52], no 5,6 in R4C3
62. R234C1 (step 58) = {269}, locked for C1
and the rest is naked singles and cage sums
Last edited by Ed on Sat Dec 27, 2008 10:31 pm, edited 1 time in total.
Para: There's a part in the middle where i was just looking for something to break open this puzzle. Took a few steps but it finally cracked rcbroughton: I agree with Para, a bit more straightforward than that 48Heavie we've been struggling with CathyW: A good, challenging puzzle - helping me improve combination analysis! sudokuEd: Andrew has set another new standard in his walk-throughs by adding comment about other's W-Ts
Walkthrough by Para:
Hi
Ok finished this one. There's a part in the middle where i was just looking for something to break open this puzzle. Took a few steps but it finally cracked. But i think the step that helped me was there a while already.
Walk-through Assassin 49
1. R12C1 = {19/28/37/46}: no 5
2. R12C5 and R12C9 = {16/25/34}: no 7,8,9
3. R23C3 and R23C7 = {59/68}: no 1,2,3,4,7
4. 11(3) in R3C8 = {128/137/146/236/245}: no 9
5. 13(4) in R4C3 = {1237/1246/1345}: no 8,9; 1 locked in 13(4) cage: R5C12: no 1
6. 23(3) in R6C8 = {689}: {689} locked in 23(3) cage: R89C8: no 6,8 or 9 7. R78C3, R89C1 and R89C5 = {29/38/47/56}: no 1
8. R78C7 = {39/48/57}: no 1,2,6
9. R89C9 = {17/26/35}: no 4,8,9
10. 45 on R12: 2 innies: R2C37 = {58} -->> locked for R2 10a. Clean up: R3C37 = {69} -->> locked for R3 10b. Clean up: R1C1: no 2; R1C59: no 2
13. R89C9 = {26} -->> locked for C9 and N9 13a. Naked Pair {89} in R7C89 -->> locked for R7, N9 and 23(3) cage in R6C8 13b. R6C8 = 6 13c. R12C9 = {34} -->> locked for C9 and N3
14. Clean up: R12C1: no 1; R9C1: no 4; R9C5: no 3,4
15. {134} locked in R8C8+R9C78 in 22(5) in R8C6 15a. 22(5) = {13459/13468} 15b. R89C6 = {59}/[68] 15c. R89C5: no {56}: clashes with R89C6
16. 9 in N3 locked for 27(5) cage in R1C6 -->> R12C6: no 9
17. 9 in N2 locked for C4
18. 21(4) in R4C9 needs 1 of {89} and 2 of {157} in R456C9 -->> 21(4) = {1479/1578} 18a. R5C8 = {14578} 18b. 1 and 7 locked in 21(4) cage for N6 (nowhere else in N6)
19. 21(4) in R4C9 needs 3 of {2349} in R456C7 -->> 21(4) = {2379/2469/3459} 19a. R5C6 = {567} 19b. 9 locked in 21(4) cage in R456C7 -->> locked for C7 and N6 19c. Hidden Single: R7C9 = 9; R7C8 = 8
20. 21(4) in R4C9 = {1578} -->> locked for N6
21. 11(3) in R3C8 = [254]/{17}[3] -->> R3C8: no 5, R4C8: no 2 21a. 2 in N6 locked for C7 21b. R1C7 = 1 21c. Clean up: R2C5: no 6 21d. 1 in N9 locked for C8
23. {159} locked in 27(5) in R1C6 -->> 27(5) = 1{2789/4679} -->> R12C6 = {46}/[82] 23a. R89C6 = {59}: [68] clashes with R12C6 -->> {59} locked for C6 and N8 23b. Clean up : R89C5 = [38/47] 23c. R12C5: no {34}: clashes with R8C5
24. 16(3) in R4C5 = {169/259}: 9 locked in N5 in 16(3) and {349} clashes with R8C5 24a. 45 on C5: 2 innies: R37C5 = 11 = {47} : locked for C5 24b. R89C5 = [38]; R89C8 = [13]
25. 15(3) in R3C1 needs 2 of {13478} in R3C12 -->> 15(3) = {168/348/357} -->> R4C2 = {3568}
26. 14(3) in R6C2 needs 2 of {12467} in R7C12 -->> 14(3) = {[9]14/167/[8]24/[5]27}: [3]{47} would clash with R7C5 -->> R6C2 = {15789}
27. 22(5) needs 3 of {12467} in R7C456 and one of {47} in R7C5: 22(5) = {12478/13468/13567/23467} 27a. 22(5) needs at least one of {67} in R7C456 -->> 14(3) in R6C2 can’t have both {67} in R7C12: 14(3) = {[9]14/[7]{16}/[8]24/[5]27}: R6C2: no 1
28. 13(4) in R4C3 = {1237/1246} -->> 2 locked in 13(4) cage: R5C12: no 2
29. 9 in N2 locked in 26(5) in R12C4 -->> 26(5) = {12689/13589/13679/14579/23489/23589/24569} 29a. 26(5): no combinations with {15} allowed: 26(5) uses 5: R1C4 = 5 -->> R12C5 = [61] -->> no room for 1 in 26(5) 29b. 26(5) = {12689/13679/23489/23579/24569}
30. R7C4: no 4: sees all 4’s in N5
31. Can’t have both {48} in R3C456: clashes with R12C6 -->> R3C12 at least needs one of {48} 31a. 15(3) = {18[6]/{348}: no 5,7; 8 locked in 15(3) -->> R1C2: no 8 31b. 7 in R3 locked for N2 31c. 7 in R3 locked in 23(5) in R3C4 -->> 23(5) = {12578/13478/14567/23567} 31d. 23(5) needs 3 of {13478} in R3C456 -->> 23(5): no {23567}
Finally found what I was looking for: 32. 2 in R1 locked in 26(5) in R1C2: R2C24: no 2 -->> 26(5) = {12689/23489/23579/24569} 32a. 26(5) needs one of {58}, 5 and 8 only in R1C4 -->> R1C4 = {58} 32b. 2 in R1 locked for N1 32c. Clean up: R1C1: no 8 32d. 8 in N1 locked for R3 32e. 8 in N1 locked for 15(3) in R3C1: R4C2: no 8
33. Killer Pair {26} in R12C5 + R12C6 locked for N2
3. from 2a. 11(2)n7 can't be [56] as it blocks 14(2)n1 3a. cleanup from 2 - 12(2)n9 can't be [39]
4. outies of r89 - r7c37=8 can only be [35] 4a. 11(2)n7=[38] 4b. 12(2)n9=[57] 4c. 14(2)n1=[59] 4d. 14(2)n3=[86]
5. cleanup 5a no 4 r9c1, 5b no 3,4 r9c5 5c 8(2)n9={62} locked for c9 and n9 5d no 1 10(2)n1 5e. no 1,5 r9c1 5f. 7(2)n3={34} locked for n3 and c9
6. 23(3)n69 = 6{89} - {89} locked for r7 and n9
7. 45 on c5 - r37c5=11 - r3c5={47}/[56]
8. 45 on c9 - innies - outies = 9 - no 9 at r5c8
9. 45 on c1 - innies = outies+1 - no 1 at r5c2
10. 45 on n1 - outies total 20 - max r12c4=17 - so no 1,2 at r4c2
11. 45 on n9 - outies r89c6 total 14 - no 1,2,3,4,7 ={59}/[68]
12. 11(3)n36=[218]/[173]/[713]/[254] - no 5 at r3c8, no 1,2,5,7 at r4c8
13. 11(2)n8 ={29}/[38] - other combos blocked by 7(2)n2 and/or r37c5=11(2) 13a. 4 locked in 7(2)n2 and r37c5 for c5
14. 13(4)n45={1237}/{1246} - no 5,7 at r5c4 14a. must use {12} - no 1,2 at r5c1 and no 2 at r5c2
15. 21(4)n6={1389}/{1479}/{1578} - no 2, 9 at r5c8 and 1 locked for n6
16. 21(4)n56 ={2379}/{2469}/{3459} - r5c6=5/6/7 only 16a. must use 9 locked in r456c7 for c7 and n6
17. from 15 - 21(4)n6={1578} - locked for n6
18. 45 on n34 - outies = 31, but r89c6=14, r125c6 total 17 18a. -> r1c6={4/6/7/8/9} 18b. -> r2c6={1/2/3/4/6/7}
19. 45 on r89 - innies total 20 19a. only combo in r1289c8 is {79}{13} - locked for c8, {79} locked for n3 an 27(5), {13} locked for n9 cleanup 19b. r9c7=4 19c. 11(3)n36 = [254] 19d. r1c7=1 19e. r5c8=5 19f. 23(3)n69=[689] 19g. r5c6=7
20. 27(2)n23 - no 3 at r2c6 20a. r12c6={46}/[82] 20b. r89c6={59} - locked for n8 and c6
21. 11{2}n8=[38] 21a. r89c8=[13] 21b. 9 locked in 16(3)n5 for n5 and c5 21c. 7(2)n2=[52]/[61]
22. {12569} locked in 7(2) & 16(3)c5 - remove 6 from r7c5
23. 14(3)n47=9{14}/{167}/8{42}/5{27}/3{47} - no combo with 2,4 in r6c2
24. 15(3)n14={18}6/{34}8/{37}5 - no 3,7,9 at r4c2
25. 2,6 locked in 7(2) and r12c6 in n2 - nowhere else in n2
26. 45 on n1 - outies = 20 - r4c2=5/6/8 - r12c4=12,14,15 26a. -> no 4,7 r1c3 26b. -> no 1 r2c3
27. 2 locked in n2 c56 for r2 27a. cleanup no 8 r1c1
28. 45 on r7 - outies r6c246=16={178}/[952]/{358} - no 2 at r6c4
29. 45 on r3 - outies r4c246=15={168}/{258} - no 3 29a r4c246 - 8 locked for r4
30, 45 on n7 - outies total 14 30a. r89c4 can only equal 13,11,9,7,6,5 - no possible 6 at r9c4
31. 26(5)n12 combos: {12689} - ok {24569} - ok {13679}/{14579} - blocked by {79} r12c8 {14678} - {46}[817] blocked by r1c6 {67}[814] blocked by 10(2)n1 {23489} - blocked by 10(2)n1 or 7(2)n3 {23678} - blocked by 10(2)n1 {24578} - [825]{74} - blocked by 7(2)n2 {34568} - blocked by 10(2)n1 {23579} - ok but 9 locked at r2c4 31a. no 7 at r2c3
32. 7 now locked in c456 for r3 32a. cleanup 15(3)n14 - no 5 32b. from step 26 r12c4=[59]/{39}/[84] - no 3 at r2c4
33. 23(5)n25 - {348}{26} blocked by r3c12 {12578}/{14567} - must put 5 at r4c4 {13478} - ok 33a. no 2,6 at r4c4
34. 11(2)n9 - can't use [47] because of 10(2)n1
35. 15(3)n14 - must use 8 - removes 8 from r1c2 35a. 8 now locked in r3c12 for n1 - locked for r3 and for 15(3)={18}6 35b. {18} locked in r3c12 for r3 and n1 35c. from step 31 {12689}/{24569}/{23579} - 9 locked in r2c4
I'll take a look at this V2 some time . . . I love a challenge.
Rgds Richard
Walkthrough by CathyW:
As promised, here's my walkthrough - steps in the order I did them including a few (possibly) redundant outies. Not sure without doing it again if it would have made much difference if my step 26 had been done earlier:
Edit: Typo corrections and some clarifications, especially of last step before it falls out. Note I have assumed obvious inclusions and exclusions from cage sums e.g. 23(3) must be {689}, no 5 in 10(2).
1. Innies r12 -> r2c37 = 13 –> only option is {58} due to 14(2) cages. 5, 8 not elsewhere in r2.
2. Outies r12 -> r3c37 = 15 = {69}. 6, 9 not elsewhere in r3.
3. Clean up odd combinations from steps 1 and 2: r1c159 <> 2.
4. Innies r89 -> r8c37 = 15 -> 69/78/87
5. Outies r89 -> r7c37 = 8 -> must be {35}, not elsewhere in r7 -> r8c3 = 6/8, r8c7 = 7/9.
6. If 11(2) in N7/c3 = {56}, no options left for 14(2) in N3/c3 -> r7c3 = 3, r8c3 = 8, r7c7 = 5, r8c7 = 7 -> r2c3 = 5, r3c3 = 9, r2c7 = 8, r3c7 = 6.
7. Clean up odd combinations from placements: 10(2) in N1 <> 1 7(2) in N3 <> 1 8(2) in N9 = {26} -> 2,6 not elsewhere in N9/c9 -> r6c8 = 6 -> 7(2) in N3 = {34} -> 3,4 not elsewhere in N3/c9 -> 89 naked pair in N9 -> not elsewhere in N9/r7. r9c1 <> 4 r9c5 <>3,4
8. 22(5) in N8/9: within N9 = {134} -> r89c6 = 14 = 59/95/68
9. Innies c5 -> r37c5 = 11 = 47/74/56 If r37c5 = {47}, 7(2) in r12c5 = {16/25} If r37c5 = 56, 7(2) in r12c5 = {34} -> 4 not in 16(3) or 11(2) of c5 -> r9c5 <> 7.
10. Since 7(2) in r12c9 = {34}, 7(2) in r12c5 cannot also be {34} as this would lead to two solutions for the puzzle -> 7(2) in r12c5 = {16/25} -> split 11(2) in r37c5 = {47}, not elsewhere in c5, 11(2) in r89c5 cannot be {56}.
11. 11(2) in r89c5 = {29/38}, split 14(2) in r89c6 = {59/68} -> 8, 9 not elsewhere in N8.
12. Combination options for 11(3) in r3c89 + r4c8: {128/137/245} -> r3c8 <> 5, r4c8 cannot have 1257 -> r3c8 = 127, r4c8 = 348.
21. 9 locked to r12c4 -> not elsewhere in c4 -> both 26(5) in N1/2 and complex 20(3) must have 9. Options for complex cage 20(3) in r12c4+r4c2 = {389/479/569}. 2 locked to r1c23 within 26(5) -> 26(5) must have 2 and 9 -> options 12689/23489/23579/24569.
22. 14(3) in r6c2 + r7c12: Combination options {149/167/248/257}. {347} not possible due to r7c5 = 4/7 -> r6c2 <> 3, analysis of remaining options -> r6c2 <> 2, 4
23. 10(2) in r12c1 = {37/46} -> 11(2) in r89c1 can’t be {47} -> within r8, 4 locked to 23(5) cage -> combination options {12479/13469/14567/23459}
32. Combination options for 26(5) in r1c234+r2c24: r1c2=2 / {1689/3489/3579/4569} If 1689 -> r2c2 = 1, r1c4 = 8, r2c4 = 9, r1c3 = 6 If 3489 -> r2c2 = 3, r1c4 = 8, r2c4 = 9, r1c3 = 4 If 3579 -> r2c2 = 3, r1c4 = 5, r2c4 = 9, r1c3 = 7 If 4569 -> r2c2 = 4/6, r1c4 = 5, r2c4 = 9, r1c3 = 4/6 -> r2c4 = 9 -> r2c8 = 7, r1c8 = 9 -> remaining options for complex 20(3): r1c4 = 5, r4c2 = 6 ... The puzzle falls out from here.
A good, challenging puzzle - helping me improve combination analysis!
Edit: Just had a scan of Richard's walkthrough - looks like mostly the same moves though some in a different order. Para seems to have taken a more varied route.
Walkthrough by Andrew:
I only managed to finish Assassin 49 yesterday and then worked through the 3 posted walkthroughs which all contained some interesting moves and were quite a bit different from the way that I eventually solved it.
Most of my difficulties were my own fault. First I had a couple of flawed moves based on incorrect mental arithmetic. Then after fixing that I got stuck because I'd forgotten that 9 was locked in R12C4 for the 26(5) cage. After starting again to reach that position it came out fairly easily. Each time I restarted I spotted some moves earlier than I'd previously seen them, and moved them to the earlier position, so I no longer have a couple of "crossover" moves that were originally in the walkthrough. My final logic flaw is mentioned in the walkthrough.
CathyW wrote:
Just had a scan of Richard's walkthrough - looks like mostly the same moves though some in a different order.
One thing Cathy had, which I don't remember in Richard's walkthrough, was the use of a UR step to eliminate {34} from R12C5.
Here is my walkthrough, modified as a result of several restarts.
Thanks Para for the comments and typo correction.
1. R12C1 = {19/28/37/46}, no 5
2. R12C5 = {16/25/34}, no 7,8,9
3. R12C9 = {16/25/34}, no 7,8,9
4. R23C3 = {59/68}
5. R23C7 = {59/68}
6. R78C3 = {29/38/47/56}, no 1
7. R78C7 = {39/48/57}, no 1,2,6
8. R89C1 = {29/38/47/56}, no 1
9. R89C5 = {29/38/47/56}, no 1
10. R89C9 = {17/26/35}, no 4,8,9
11. 11(3) cage in N36 = {128/137/146/236/245}, no 9
12. 23(3) cage in N69 = {689}, no 6,8,9 in R89C8
13. 13(4) cage in N45 = 1{237/246/345}, no 8,9, no 1 in R5C12
14. 45 rule on R12 2 innies R2C37 = 13 = {58}, locked for R2, clean-up: no 2 in R1C1, no 2 in R1C5, no 2 in R1C9, no 5,8 in R3C37 14a. Naked pair {69} in R3C37, locked for R3
16. 45 rule on C5 2 innies R37C5 = 11 = [29/56]/{38/47}, no 1, no 2,5 in R7C5
17. 45 rule on R89 2 outies R7C37 = 8 = {35}, locked for R7, clean-up: no 8 in R3C5, no 7 in R8C3, no 8 in R8C7
18. R23C3 = [59] ([86] clashes with R8C3) -> R78C3 = [38], R23C7 = [86], R78C7 = [57], clean-up: no 1 in R12C1, no 1 in R12C9, no 1,3 in R89C9, no 4 in R9C1, no 3,4 in R9C5
19. Naked pair {26} in R89C9, locked for C9 and N9, clean-up: no 5 in R1C9
20. Naked pair {34} in R12C9, locked for C9 and N3
21. Naked pair {89} in R7C89, locked for R7, N9 and 23(3) cage -> R6C8 = 6, clean-up: no 2,3 in R3C5 (step 16)
22. 22(5) cage in N89 naked triple {134} in R8C8 + R9C78 -> R89C6 = 14 = {59}/[68]
23. 13(4) cage in N45 (step 13) = 1{237/246} (cannot be {1345} because 3,5 only in R5C4) = 12{37/46}, no 5, no 2 in R5C12 23a. 3 only in R5C4 -> no 7 in R5C4
24. 45 rule on C9 2 innies R37C9 – 9 = 1 outie R5C8, max R37C9 = 16 -> max R5C8 = 7 Para wrote “You can also eliminate 2,3 from R5C8 with this move. Doesn't complicate the solving process though.”
Yes, I must admit that I only looked at the max and min cases with the latter not helping at this time. With early multiple innies/outies there are usually too many candidates for anything more to be helpful. In this case it is already down to 3 candidates in R3C1 and 2 candidates in R7C1. Fortunately missing the elimination of 2,3 didn’t matter in this case; the 3 goes in step 29 and the 2 in step 31. I must look more carefully at cases like this.
25. 45 rule on C6789 4 innies R3467C6 = 14, no 9
26. 21(4) cage in N56 max R456C7 = 16 -> min R5C6 = 5 26a. 45 rule on N6 1 outie R5C6 – 3 = 1 remaining innie R4C8 -> R4C8 = {2345}, no 9 in R5C6 26b. Max R5C6 = 8 -> min R456C7 = 13 -> must contain 9, locked for C7 and N6
27. R7C8 = 8, R7C9 = 9 (hidden singles in C8 and C9)
28. 11(3) cage in N36 = {137/245} 28a. 4 only in R4C8 -> no 2,5 in R4C8 28b. 2 only in R3C8 -> no 5 in R3C8 28c. R4C8 = {34} -> R5C6 = {67} (step 26a)
29. Naked triple {134} in R489C8, locked for C8 29a. 1 in C8 locked in R89C8, locked for N9
30. 11(3) cage in N36 = {137/245} 30a. 1 only in R3C9 -> no 7 in R3C9
31. 7,8 in C9 locked in R456C9 -> 21(4) cage in N6 = {1578}, locked for N6 -> R5C8 = 5 31a.1 locked in R456C9 for C9 -> R3C9 = 5, R34C8 = [24] (step 30) , R5C6 = 7 (step 26a), clean-up: no 6 in R7C5
32. R1C7 = 1 (naked single), clean-up: no 6 in R2C5
33. R9C7 = 4 (hidden single in N9)
34. Naked pair {47} in R37C5, locked for C5, clean-up: no 3 in R12C5
35. R89C5 = {29}/[38] (cannot be {56} which clashes with R1C5), no 5,6
36. Naked pair {79} in R12C8, locked for 27(5) cage in N23 36a.R12C6 = 10 = {46}/[82], no 3,5, no 2 in R1C6
37. 9 in C6 locked in R89C6 = {59}, locked for C6 and N8, clean-up: no 2 in R89C5 = [38] -> R89C8 = [13] 37a. R3467C6 = 13{28/46}
38. 9 in C5 locked in R456C5, locked for N5 38a. R456C5 = 9{16/25}
39. 14(3) cage in N47 = {149/167/248/257} (cannot be {158/239/356} because 3,5,8,9 only in R6C2, cannot be {347} because {47} in R7C12 clashes with R7C5), no 3 39a. 5,8,9 only in R6C2 -> no 2,4 in R6C2
40. 15(3) cage in N14 = {168/348/357} (cannot be {159/249/258/267/456} because 2,5,6,9 only in R4C2), no 2,9 40a. 5 only in R4C2 -> no 7 in R4C2 Para wrote “Also 6 only in R4C2 -> no 1 in R4C2 You get this in step 46 with the 45-test on N1.”
Thanks. Don’t know why I missed that one.
41. 23(5) cage in N25 ={12578/13478/14567/23468/23567} (cannot be {13568} which doesn’t contain 4,7 for R3C5)
42. 22(5) cage in N58 = {12478/13468/13567/23467} (cannot be {12568} which doesn’t contain 4,7 in R7C5, cannot be {23458} because 3,5,8 only in R6C46)
43. 45 rule on R123 3 remaining outies R4C246 = 15 = {168/258}, no 3 = 8{16/25}, 8 locked for R4
44. 45 rule on R789 3 remaining outies R6C246 = 16 = {178/259/349/358/457} 44a. 7 only in R6C2 -> no 1 in R6C2 44b. 9 only in R6C2 and only other 5 in R6C4 -> no 2 in R6C4
45. 23(5) cage in N78 with 1 locked in R9C234 = 1{2479/2569/4567}
46. 45 rule on N1 3 outies R12C4 + R4C2 = 20 (doubles possible), no 1 46a. Max R4C2 = 8 -> min R12C4 = 12, no 2
47. 45 rule on N7 3 outies R6C2 + R89C4 = 14 47a. no 6 in R9C4 (no {17/26/35/44} in R6C2 + R8C4) Para wrote “You should add no {44} to 47a, that could also be possible. ”
Good point! It’s in there now. I usually remember to look for “doubles possible” when I’m doing outies from a nonet.
48. 5 in R1 only in R1C4 or R1C5, 1 in R2 only in R2C2 or R2C5 48a. If R12C5 = [52], R2C2 = 1, if R12C5 = [61], R1C4 = 5 -> 26(5) cage in N12 must contain 1 or 5 but not both 48b. 9 locked in R12C4 48c. 26(5) cage = {12689/13679/23579/24569} 48d. 5,9 only in R12C4 -> no 4 in R12C4
49. 45 rule on N4 2 innies R46C2 – 9 = 1 outie R5C4 49a. Min R46C2 = 11 -> no 1 in R5C4 49b. 1 in 13(4) cage locked in R456C3, locked for C3 and N4
50. 1 in C1 locked in R37C1 50a. 45 rule on C1 2 innies R37C1 – 1 = 1 outie R5C2 -> R5C2 = R3C1 or R7C1 with the other being 1 50b. No 2,7 in R5C2 -> no 2,7 in R37C1 50c. No 9 in R37C1 -> no 9 in R5C2
51. 3 in N4 locked in 23(4) cage 51a.23(4) cage = 3{479/569/578}, no 2 51b. 5,7 only in R46C1 -> no 8 in R6C1 51c. 2 in N4 locked in R456C3, locked for C3 -> no 2 in R5C4 Para wrote “This step created a hidden single 2 in R1C2 for R1. And that breaks open the puzzle to a few naked pairs and singles. I noticed this because the moved that broke the puzzle for me was that the 2 in R1 was locked in R1C234 in 26(5) in R1C2.”
That would be correct if I hadn’t missed 2 locked in R1C23 at step 48, which would have eliminated {13579} but probably not any candidates. With 2 locked in R1C23 then step 51c would have created the hidden single. In that sense I didn’t miss a hidden single at this stage.
52. R5C4 cannot be 3 52a. If R5C4 = 3 => R456C3 = {127} (step 23) clashes with R46C2 = 12 = [57] (step 49) -> no 3 in R5C4 [Typo corrected. Thanks Para.] 52b. 13(4) cage in N45 (step 23) = {1246}, no 7, no 4,6 in R5C12 52c. 4 in R5 locked in R5C34 -> no 4 in R6C3 52d. No 4,6 in R5C2 -> no 4,6 in R37C1 (step 50a)
53. R7C1 = 1 (naked single), R67C2 = 13 = [76/94]
54. 2,7 in R7 locked in R7C456, locked for N8 -> R9C4 = 1 [Alternatively R9C4 = 1 (hidden single) after step 53. I saw the locked 2,7 first.] 54a. 2,7 locked in R7C456 for N8 and 22(5) cage in N58 (step 42) = 27{148/346}, no 5 = 247{18/36}, no 2 in R6C6 54b. 1 only in R6C6 -> no 8 in R6C6 [My final logic flaw was to assume from step 54a that 4 was also locked in R7C456 rather than just in the 22(5) cage. Fortunately that was not correct or I might have ended with a "solution" based on false logic which Ed would have spotted pretty quickly.]
55. Naked pair {46} in R58C4, locked for C4
56. 22(5) cage in N58 (step 54a) = 247{18/36} 56a. 4 only in R6C6 for {23467} combination -> no 3 in R6C6 Para wrote “This also created a Hidden single 3 in R6C4 for N5”
Thanks. Missed that one.
57. 23(4) cage (step 51a) = 3{479/569/578} 57a. R5C12 = {389} -> no 3,9 in R46C1 57b. 3 in N4 locked in R5C12, locked for R5
58. 45 rule on C1234 4 innies R3467C4 = 20 = {2378} (only remaining combination), no 5, 3,7,8 locked for C4
59. R12C4 = [59] (naked singles) -> R12C5 = [61], R12C8 = [97], clean-up: no 3 in R1C1, no 4 in R2C1, no 4 in R12C6 = [82]
60. Naked pair {47} in R1C13, locked for R1 and N1 -> R12C9 = [34], R1C2 = 2 60a. Naked pair {36} in R2C12, locked for N1 -> R3C12 = [81], R4C2 = 6 (cage sum), R5C2 = 8 (step 50a)
and the rest is naked singles
Para wrote “That hidden single 2 could have saved you some work. I don't know if you regularly scan the grid for hidden singles? I usually do this after every few steps just to make sure. Even if i don't expect any.”
Good point. I should do it more often. They aren’t always easy to see on the Excel spreadsheet that I use for solving Sudokus. Maybe they are easier to see for people using software such as SumoCue but I’ve no current plans to download it. I like the way that I can save positions in Excel, make copies of positions on multiple worksheets and add notes below the diagram.
Glyn: what a one to pick for my first try sudokuEd: While I enjoy ruudiculous V2s that need a tag solution, V2s that are (humanly & humanely) solvable are the best sudokuEd:Mike's sychronizing the 5(2) cages in N39 is amazingly clever, inventive and productive (steps 30 & 38) Andrew in 2011: Mike's synchronised cages (steps 30 and 38) were very interesting, as was ... step 31a. I'll rate my walkthrough...at Hard 1.25; none of my steps were difficult although some weren't easy to spot.
Walkthrough by mhparker:
All quiet on the Western Front...
Maybe everybody's still struggling with JC's V2?
Therefore I thought I'd generate a bit of interest by posting a walkthrough for it. Here it is:
Edit: Modifications to steps 20,23,29,31,38b,40c,43c Edit: Simplified logic for steps 34 & 37, removed unnecessary step 36
16. Innies R89: R8C37 = 9/2: [54|63|81] 16a. Cleanup R7C3: no 5, R7C7: no 3
17. 11/2 at R2C3 cannot be {56} (blocked by 14/2 at R7C3) -> {29|38} 17a. 11/2 at R2C3 and 14/2 at R7C3 form killer pair on {89} -> no 8,9 elsewhere in C3
18. Innies R12 (step 15): R2C37 = 14/2 = [95] -> R3C37 = [27] 18a. Cleanup: no 7 in 9/2 at R1C1 -> 7 in N1 now locked in 27/5 at R1C2 = {7...}, no 7 in R12C4 18b. Cleanup: no 3 in R1C5, no 4 in R1C1, no 3,8 in R7C5 (step 14)
19. 14/2 at R7C3 = {68}, locked for C3 and N7 19a. Cleanup: no 2,4 in 10/2 at R8C1 = {19|37} 19b. Cleanup: no 4 in R8C7 (step 16) -> no 1 in R7C7
20. {268} unavailable for in R456C3 for 14/4 at R4C3 -> 14/4 = {1247} (with 2 in R5C4), {1346} (with 6 in R5C4) or {2345} (with 2 in R5C4) -> R5C4 = {26}, 4 locked in R456C3 for C3 and N4
21. 26/4 at R4C7: cannot have both of {57} -> {9(278|368|458|467)} -> no 9 in R5C89 21a. 5,7 only available in R5C6 -> no 2,4 in R5C6
22. Innies C89: R1289C8 = 27/4 = {9(378|468|567)} (no 1,2), 9 locked for C8
23. <deleted>
24. 14/3 at R3C8 = {149|239|158|248|167|347|356} ({257} unplaceable) 24b. 2,5,7 only available in R4C8 -> no 3,6,8 in R4C8
25. 18/3 at R6C8: 9 only available in R7C9 -> no 1,2 in R7C9
26. Innie/outie difference, C9: R5C8 = R37C9 + 14 26a. Max. of R37C9 = R5C8 + 17 -> R5C8 = {123} -> R3C9 = {689}, R7C9 = {6789} 26b. 14/3 at R3C8 can only have one of {689} (step 24), which must now come from R3C9 -> no 6,8 in R3C8
27. Innie/outie difference, C9: R345C8 = R7C9 = 6,7,8 or 9 -> no 7 in R4C8
28. Common Peer Elimination (CPE): R7C9 can see all candidate positions for 7 in C8 -> no 7 in R7C9 28a. R37C9 cannot now sum to 16 (7 unavailable) -> no 2 in R5C8 (step 26) 28b. 9 now locked in R37C9 for C9 28c. 9 in N6 now locked in R456C7 -> not elsewhere in C7, no 9 in R5C6
29. 17/4 at R4C9 = {1268|1358|2348|1367|1457|2357} 29a. Of these, {2348} is blocked by 5/2 at R1C9 29b. Therefore 17/4 at r4C9 must contain 1 of {56} -> 14/3 at R3C8 cannot contain both of {56} -> no 6 in R3C9 29c. 6 in N3 now locked in 27/5 at R1C6 = {6...} -> no 6 in R12C6
30. Important observation: 9/2 at R8C9 must contain 1 of {1234} 30a. Therefore, whichever combination it contains, it directly determines the combinations {14|23} in the two 5/2 cages at R1C9 and R7C7 30b. These two 5/2 cages are therefore synchronized (i.e., must contain the same combination) 30c. Thus, they also lock the same 2 digits into R456C8 (i.e., 2 of these 3 cells must sum to 5) (no eliminations yet)
31. 17/4 at R4C9 = {1268|1358|1367|1457|2357} 31a. AIC: (2)r456c9-(2=14)r12c9-(14=3)r3c8-(3=1)r5c8 -> if 17/4(R4C9) contains a 2, it must also contain a 1 31b. {2357} can thus be rejected as possible combination 31c. Therefore, 1 is locked for N6 in 17/4 at R4C9 -> not elsewhere in N6
32. Innie/outie difference, N6: R5C6+R7C89 = R4C8 + 16 -> no 2 in R7C8 (Reason: 2 in R7C8 forces R4C8 to at least 4, requiring R5C6+R7C9 to be at least 18 - unreachable)
33. 2 in C8 now locked in N6 -> not elsewhere in N6
34. 2 in C9 locked in 5/2 at R1C9 or 9/2 at R8C9 34a. Therefore, either 5/2 at R1C9 = {23}, or 9/2 at R8C9 = {27} 34b. In either case, 9/2 at R8C9 cannot be {36} -> no 3,6 in 9/2 at R8C9
35. 2 in C9 already locked in 5/2 at R1C9 and 9/2 at R8C9 35a. Due to synchronization of 5/2 cages (step 30b), 2 must therefore also be locked in N9 in 5/2 at R7C7 and 9/2 at R8C9 -> no 2 elsewhere in N9
36. <deleted>
37. R46C8 = {2..} (step 33), i.e., one of these 2 cells is a 2 37a. Innie/outie difference(N6) (R46C8 - R5C6 = 2) -> other cell in R46C8 = R5C6 37b. Thus, R46C8 cannot contain any candidate (apart from 2) not in R5C6 -> no 4 in R46C8
38. Hidden 5/2 pair in R456C8 (step 30c) must now be {23} (4 unavailable) 38a. Therefore (steps 30b, 30c) 5/2 at R7C7 = [23] and 5/2 at R1C9 = {23}, locked for C9 and N3 38b. Cleanup: no 7 in R89C9, no 7 in R9C5, no 7 in R9C1
39. 14/2 at R7C3 = [86] (step 16) 39a. Cleanup: no 4 in R9C5
40. 14/3 at R3C8 = {(15|24)8} -> R3C9 = 8 -> R7C9 = 9 (step 28b) -> R5C8 = 3 (step 26) 40a. Cleanup: no 1 in 9/2 at R8C9 = {45}, locked for C9 and N9 40b. R456C9 = {167}, locked for N6 40c. R456C7 = {489} -> R5C6 = 5; {489} locked for C7 and N6 40d. Split 9/2 at R67C8 = [27] (only remaining combination/permutation)
43. Hidden single (HS) in C5 at R1C5 = 5 -> R2C5 = 3 43a. R12C9 = [32] 43b. Cleanup: 9/2 at R1C1 = {18}, locked for C1 and N1 43c. Cleanup: 10/2 at R8C1 = [73], locked for C1 and N7
44. NS at R19C3 = [75]
The rest is all naked and hidden singles.
P.S. I went in from the opposite side to the one that JSudoku took, just to show that there's more than one way to peel an onion (as Richard would say) and also to make it a bit more interesting
Maiden Walkthrough by Glyn:
Here is my walkthrough of V2, what a one to pick for my first try.
Redone following earlier booboo
1 ) R12 Innies=14 R2C37={59}|[68] (R2C7=6 not possible in 12(2)) Cleanup R3C3={256},R3C7={347} (Combo sum must=9 Outties R12)
2) In N1 11(2)R23C3=[92]|{56} must contain 5|9 leaves only {68} combo for 14(2) in N7.
3) Naked pair {68} in R3 and N7.
4) In N1 11(2)=[92]. R2C2=9 & R3C2=2.
5) Innies R12 = 14. => R2C7=5 & R3C7=7.
6) Innies R89 = 9. R8C37=[63]|[81] => R7C7=2|4.
7) Combinations for 14(4) cage in N45 (R456C3+R5C4)={134}6,{147}2,{345}2 other combos prohibited by repeated digits or exceeding cage sum. => R5C4=2|6.
8) 4 locked in C3 for 14(4) cage of N4.
9) Cage 26(4) in N56 = {2789},{3689},{4589},{4679},{5678} Possible Combos for Cage 26 R5C6+R456C7= 3{689}|5{489}|6{389}|7{469}|7{289}|8{369}|9{368}. R5C6<>124
10)Clean up in N1 9(2)={18}{36}[54], in N2 8(2)={17}(26}[53], in N7 10(2)={19}{37}
11) 7's in N1 locked in 27(5) cage. Not elsewhere in cage R12C4<>7.
15) R456C3 sum to either 8 or 12. Cage(14)-(2|6).Therefore R4C2+R6C2=9|13. Possible combos are [36][72][81][76][85] => R4C2<>5,9. R6C2<>3,7
16) Revisit the Outties of N1 R12C4+R4C2=[91]8|{28}8|[92]7|{38}7|{46}8|[56]7|[96]3 =>R1C4<>1.
17) Trying all combination with R46C2 in N4. a) R46C2=[36] R456C3={147} Cage 24(4)={2589} b) R46C2=[72] R456C3={345} Cage 24(4)={1689} c) R46C2=[81] R456C3={345} Cage 24(4)={2679} d) R46C2=[76] R456C3={134} Cage 24(4)={2589} e) R46C2=[85] R456C3={134}.Cage 24(4)={2679}.
18) Thanks to Ed a)2 in R6C2 blocks all 2's in N7 b)6 in R6C2 forces R7C12={13} blocks all combos of cage 10(2) in N7.
19) Now I can do it only better. All combos for R46C2 from step 17) require R4C2=8. Cage 24(4) in N4={2679}.
20) 16(3) cage N14={358} => R3C12={35} locked for N1 and R3.
21) 9(2) cage N1 R12C1={18} locked for C1 and N1.
22) Naked single R1C3=7.
23) Hidden single R7C1=4.
24) R89C1={37} locked for C1 and N7.
25) Naked singles R3C12=[53].
26) Hidden single R5C2=7.
27) Naked singles R78C7=[23], R89C1=[73].
28) Innies R89=9. R8C3=6=> R7C3=8.
29) Hidden pair R89C2={29} locked for Cage 24(5) in N78. Remaining combos {12489}|{12579}. No 6.
30) Naked pair R12C2={46} locked for 27(2) cage in N12. Remaining combos {14679}|{24678}. No 3,5. => R12C4=[91]|{28}.
31) From Step 9. Remaining combos for 26(4) cage in N56 are 3{689}|5{489}. Others blocked by 12(2) and 5(2) cages in C7 or by R5C2.
32) 8 and 9 locked in R456C7 for N6 and C7.
33) Mandatory inclusion of a 1 in 24(5) cage Nonets 7 and 8 at either R9C3 or R89C4. Elimate from common peers R9C56<>1.
34) Innies C5=10 R37C5={19}|[46].
35) a) If R37C5={19} sole remaining combos for 10(2) cage in N8 are {28}|[46] leaves only {35} combo for 8(2) in N2. b) If R37C5=[46] eliminates {26} combo from cage 8(2) in N2. Cleanup 8(2) cage R12C5= [17]|[53]
36) Cleanup 10(2) cage in N8=[19]|{28}|[46].
37) N69 18(3) cannot contain 1.
38) N9 9(2) cannot contain 6 or 7.
39) 3's on N8 locked in 26(5). R6C46<>3.
40) outties of R123=18 R4C468 sum to 10. Maximimum value R4C468=7.
41) Innies and Outties C9 R37C9=R5C8+14 Possible LHS exceeding 14 are 15,16,17 => R5C8=1|2|3 R37C9={69}|[87]|[97]|[89]
42) N36 14(3) remaining combos {149}{158}{167}{248} Combo {257} blocked as only one cell is available containing 2 and 7. Arrangements only formed from R3C8=1|4 R3C9=6|8|9 R4C8=1|2|4|5|7.
43) Cell R3C8 forces cage 5(2) of N3 to {23}. Naked pair {23} in C9 and N3.
44) Lets do something different an AIC 3[R5C8]=3[R6C8]-{69}[R7C89]=1[R7c5]=5[R7C2]=1[R6C2]-{345}[R456C3]=2[R5C4]- which implies that if R5C8<>3 then R5C8<>2. (Obviously if R5C8=3 then R5C8<>2).
45) Remaining combos for 17(4) in N6 are {1367}|{1457} must contain 1 and 7. The 7 is locked in C9 of N6.
46) Unplaceable candidate R3C9<>6.
47) R3 6's locked in N2 and cage 24(5)
48) Cage 18(3) in N69 R6C8<>6.
49) The remaining combo for from Step 41) is R37C9=[89] & R5C8=3.
50) Naked single R5C6=5.
51) Hidden single R1C5=5 => R2C5=3.
52) Hidden single R2C6=7.
53) Naked single R2C9=2 => R1C9=3.
54) Hidden single R6C3=3.
55) Hidden single R1C8=9
56) Cage 27(5) in N12 remaining combo {24678} => R12C4=[28]
57) Naked singles R12C1=[81].
58) 9(2) cage R89C9={45} locked for C9 and N9.
59) Naked single R5C4=6 => 14(4) in N4 ={1346} => R45C3={14} => R9C3=5.
60) Just singles from here on.
Hope it makes sense.
All the best,
Glyn
Walkthrough by Para:
Hi all
Here is my walk-through for JC's V2 with some interesting and also a bunch of redundant moves but those are always going to be in my walk-throughs. This took a bit more searching for the breakthrough move.
Walkthrough Assassin 49 V2
1. R1C12 + R89C9 = {18/27/36/45}: no 9
2. R12C5 = {17/26/35}: no 4, 8, 9
3. R12C9 + R78C7 = {14/23}: no 5, 6, 7, 8, 9
4. R23C3 = {29/38/47/56}: no 1
5. R23C7 = {39/48/57}: no 1, 2, 6
6. 26(4) in R4C7 = {2789/3689/4589/4679/5678}: no 1
7. 10(3) in R6C2 = {127/136/145/235}: no 8, 9
8. 14(2) in R78C3 = {59/68}: no 1, 2, 3, 4, 7
9. R89C1 + R89C5 = {19/28/37/46}: no 5
10. 45 on R12: 2 innies: R2C37 = 14 = {59}/[68] 10a. Clean up: R3C3: no 3, 4, 7, 8, 9; R3C7: no 5, 8, 9
11. R23C3: no {56}: clashes with R78C3 -->> R23C3 = [92] 11a. R23C7 = [57] 11b. R78C3 = {68}: locked for C3 and N7 11c. Clean up: R1C1: no 4,7; R2C1: no 7; R1C5: no 3; R89C1: no 2, 4
12. 14(4) in R4C3 needs 3 of {13457} in R456C3 -->> 14(4) = {1247/1346/2345}: R5C4 = {26} 12a. 4 locked in 14(4) cage in R456C3 -->> locked for C3 and N4 12b. 24(4) in R4C1 can’t have both {37}(one needed in 14(4) cage) -->> 24(4) = {1689/2589/2679}: no 3; 9 locked in 24(4) for N4
13. 45 on R89: 2 innies: R8C37 = 9 = [63/81] 13a. Clean up: R7C7: no 1, 3
14. 45 on C5: 2 innies: R37C5 = 10 = {19/46}/[37]/[82]: R3C5: no 5; R7C5: no 3, 5, 8
15. 10(3) in R6C2: no {136}: only possible with R7C12 = {13} which clashes with R89C1 -->> R6C2: no 6
17. 16(3) in R3C1 = {18}[7]/{68}[2]/{35}[8]/{36}[7]/{45}[7] 17a. R4C2: no 6 17b. R6C2: no 3(step 16 b)
18. 3 in N4 locked for C3 18a. 3 in N4 locked for 14(4) in R4C3 -->> 14(4) = {1346/2345}: no 7
19. 6 in N4 locked in 24(4) -->> 24(4) = {1689/2679}: no 5
20. 7 in N1 locked in 27(5) cage in R1C2: R12C4: no 7 -->> 27(5) = {12789/14679/15678/23679/24579/24678/34578}
21. When 8(2) in R1C5 = {17/26}, 5 in C5 locked in 17(3) in R4C5 21a. When 8{2} = [53], no 7 in R37C5 + R89C5 (both 10(2)) so 7 in C5 locked in 17(3) 21b. 17(3) in R4C5 needs one of {57} -->> 17(3) = {179/278/359/458/467}
22. 14(3) in R3C8 = {149}/{18}[5]/{16}[7]/{39}[2]/{48}[2]/{36}[5]: no {34}[7] clashes with R12C9 -->> R4C8: no 3, 6, 8
23. 10(3) in R6C2 = {127/145}-->> R89C2: no 1 23a. 10(3) = {235} (3 in R7C12) -->> R89C1 = {19} -->> R89C2: no 1 23b. Conclusion R89C2: no 1
24. 45 on C9: 5 outies : R34567C8 = 18 = {12348/12357/12456}: no 9; 1,2 locked for C8
25. 26(4) in R4C7 needs 3 of {234689} in R456C7 -->> 26(4) = [7]{289}/{3689}/[5]{489}/[7]{469} -->> R5C6: no 2,4; 9 locked in 26(4) cage: R5C9: no 9
26. Only place for {45} in C1 are R1237C1: R12C1 can only contain both {45} or neither so R37C1 can only contain both {45} or neither.
28. R6C2: no 2: sees all 2’s in C1 28a. Clean up: R4C2: no 7(step 16b) 28b. 16(3) in R3C1 = {68}[2]/{35}[8]: no 1, 4 28c. Clean up: R7C1: no 5; R5C2: no 1 (step 27)
29. Killer Pair {58} in R12C1 + R3C12 locked for N1
30. Killer Pair {24} in R7C12 + R7C7 locked for R7 30a. Clean up: R3C5: no 6, 8 (step 14)
31. 5 in C1 locked in R13C1 for N1 -->> R3C2: no 5
32. Clean up: R3C1: no 3; R7C1: no 7 (step 27)
33. 27(5) in R1C2 needs one of {36} in R12C2 (only place left in N1) and 2 of {147} in R1C12 + R2C2 -->> 27(5) = {14769/15678/24679/34579}: R12C4: no 3, 6 33a. Only place for 9 is R1C4 -->> R1C4: no 1, 4
34. 3 in N1 locked for C2
35. 3’s in N1 35a. R12C2 = 3 -->> R12C4 = [58] -->> R3C46: no 5 35b. R3C2 = 3 -->> R3C1 = 5 -->> R3C46: no 5 35c. Conclusion R3C46: no 5
37. R12C1 = {18} locked for C1 and N1 37a. R1C3 = 7; R89C1 = [73] 37b. Naked Triple {269} locked for N4 37c. R5C2 = 7 37d. Clean up: R89C9: no 6, 7; R9C5: no 7; R7C5: no 7
38. Hidden pair {29} in R89C2 locked for 24(5) in R8C2 -->> 24(5) = {12489/12579}: no 6; 38a. Naked Pair {46} in R12C2 locked for 27(5) in R1C2 -->> 27(5) = 7{1469/2468}: no 5; R12C4 = [28/82/91]
39. R12C9 = {23}: {14} clashes with R89C9 -->> {23} locked for C9 and N3
40. 3 in C8 locked in R56C8: R34567C8 = {12348/12357}(step 24): no 6
41. 26(4) in R4C7 needs 3 of {4689} in R456C7 -->> 26(4) = [3]{689}/[5]{489}: R5C6 = {35}; {89} locked in R456C7 for C7 and N6
42. 17(4) in R4C9 = {1367/1457/2357}: {2456} clashes with R456C7 -->> 7 locked in 17(4) in R46C9: locked for C9 and N6
43. 14(3) in R3C8 = {1[9]4}/{18}[5]/{48}[2]: no 6
44. 6 in R3 locked for N2 and 24(5) in R3C4 44a. Clean up: R12C5: no 2
45. 5’s in N2 45a. R1C5 = 5 -->> R2C5 = 3: R1C6: no 3 45b. R1C6 = 5: R1C6: no 3 45c. Conclusion: R1C6: no 3 45d. Hidden Single: R1C9 = 3; R2C9 = 2 45e. Clean up : R1C4: no 8
46. Naked Pair {18} in R2C14 locked for R2 46a. Naked Pair {46} in R2C28 locked for R2
Another puzzle from my backlog, which I'd started at the time but hadn't got very far. As noted after my step 2, when I started work on this puzzle again I found some useful sub-steps which I'd originally missed.
Thanks J-C for a nice variant.
Mike's synchronised cages (steps 30 and 38) were very interesting, as was his forcing chain in step 31a.
I'm sure others will have congratulated Glyn on posting his first walkthrough; I'll belatedly add my congratulations.
I've now got into the habit of immediately following Prelims with Steps Resulting From Prelims, which is why I automatically did step 1 before looking for 45s; in this case it proved to be the best order to do these steps.
Here is my walkthrough for A49 V2.
Prelims
a) R12C1 = {18/27/36/45}, no 1 b) R12C5 = {17/26/35}, no 4,8,9 c) R12C9 = {14/23} d) R23C3 = {29/38/47/56}, no 1 e) R23C7 = {39/48/57}, no 1,2,6 f) R78C3 = {59/68} g) R78C7 = {14/23} h) R89C1 = {19/28/37/46}, no 5 i) R89C5 = {19/28/37/46}, no 5 j) R89C9 = {18/27/36/45}, no 9 k) 10(3) cage at R6C2 = {127/136/145/235}, no 8,9 l) 14(4) cage at R4C3 = {1238/1247/1256/1346/2345}, no 9 m) 26(4) cage at R4C7 = {2789/3689/4589/4679/5678}, no 1
1. R23C3 = {29/38/47} (cannot be {56} which clashes with R78C3), no 5,6
2. 45 rule on R12 2 innies R2C37 = 14 = [95], R3C3 = 2, R3C7 = 7, clean-up: no 4,7 in R1C1, no 3 in R1C5, no 7 in R2C1, no 5 in R78C3 2a. Naked pair {68} in R78C3, locked for C3 and N7, clean-up: no 2,4 in R89C1 2b. 2 in N7 only in R7C12 + R89C2, CPE no 2 in R6C2 2c. 7 in N1 only in R1C23 + R2C2, locked for 27(5) cage at R1C2, no 7 in R12C4 [I don’t usually go back and re-work when I’ve missed something not particularly obvious but step 2b was so important that I’ve done it this time to simplify later steps. I only spotted step 2b when I was working on steps 10 and 11. Then while checking my walkthrough I found an error and had to do a bigger re-work so I’ve also added step 2c, which I originally missed; this simplified step 16 and changed some later steps.]
3. 45 rule on R89 2 innies R8C37 = 9 = [63/81], clean-up: no 1,3 in R7C7
4. 45 rule on C89 4 innies R1289C8 = 27 = {3789/4689/5679}, no 1,2, 9 locked for C8 4a. Max R67C8 = 15 -> min R7C9 = 3
5. 45 rule on C5 2 innies R37C5 = 10 = {19/46}/[37/82], no 5, no 3,8 in R7C5
6. 16(3) cage at R3C1 = {169/178/268/349/358/367/457} (cannot be {259} because 2,9 only in R4C2) 6a. 7,9 of {169/178} must be in R4C2 -> no 1 in R4C2 6b. 7,9 of {349/457} must be in R4C2 -> no 4 in R4C2 6c. 2,7,9 of {169/268/367} must be R4C2 -> no 6 in R4C2
7. 14(3) cage at R3C8 = {149/158/167/239/248/356} (cannot be {257} because 2,5,7 only in R4C8, cannot be {347} which clashes with R12C9) 7a. 2,5 of {239/356} must be in R4C8 -> no 3 in R4C8 7b. 5,7 of {167/356} must be in R4C8 -> no 6 in R4C8 7c. 2,5 of {158/248} must be in R4C8 -> no 8 in R4C8
8. 14(4) cage at R4C3 = {1247/1346/2345} (cannot be {1238/1256} because 2,6,8 only in R5C4), no 8 8a. 2,6 only in R5C4 -> R5C4 = {26} 8b. 14(4) cage = {1247/1346/2345}, 4 locked for C3 and N4
9. 26(4) cage at R4C7 = {2789/3689/4589/4679} (cannot be {5678} because 5,7 only in R5C6), CPE no 9 in R5C9 9a. 5,7 of {2789/4589/4679} must be in R5C6 -> no 2,4 in R5C6
10. 10(3) cage at R6C2 = {127/145/235} (cannot be {136} = 6{13} which clashes with R89C1), no 6 10a. Killer pair 2,4 in 10(3) cage and R7C7, locked for R7, clean-up: no 6,8 in R3C5 (step 5)
12. 6,9 in N4 only in 24(4) cage = {1689/2679}, no 3,5
13. 3 in N4 only in R456C3, locked for C3 13a. 14(4) cage at R4C3 (step 8) = {1346/2345}, no 7
14. 16(3) cage at R3C1 (step 6) = {268/358}, no 1,4, CPE no 8 in R12C2 14a. 16(3) cage = {35}8/{68}2 [Added to make steps 14b, 14c and 15 clearer.] 14b. R12C1 = [18/54/81] (cannot be {36} which clashes with 16(3) cage), no 3,6 14c. Killer pair 5,8 in R12C1 and 16(3) cage, locked for N1
15. 14(3) cage at R3C8 (step 7) = {149/158/167/239/248} (cannot be {356} = {36}5 which clashes with 16(3) cage at R3C1) 15a. 9 of {239} must be in R3C9 -> no 3 in R3C9
16. 45 rule on N1 3(2+1) outies R12C4 + R4C2 = 18 = 10(2) + 8 (cannot be 16(2) + 2 because no 7 in R12C4) -> R4C2 = 8, R12C4 = 10 = {28/46}/[91], no 3,5, no 1 in R1C4
17. 45 rule on N1 3 remaining innies R1C23 + R2C2 = 17 = {467} (only remaining combination) -> R1C3 = 7, R12C2 = {46}, locked for C2, N1 and 27(5) cage at R1C2, no 4,6 in R12C4, clean-up: no 1 in R2C5 17a. Naked pair {35} in R3C12, locked for R3 and N1, clean-up: no 7 in R7C5 (step 5) 17b. Naked pair {18} in R12C1, locked for C1, clean-up: no 9 in R89C1 17c. Naked pair {37} in R89C1, locked for C1 and N7 -> R3C12 = [53] 17d. Naked triple {269} in R456C1, locked for C1 and N4 -> R7C1 = 4, R7C7 = 2, R8C7 = 3, R8C3 = 6 (step 3), R7C3 = 8, R89C1 = [73], clean-up: no 4,7 in R9C5, no 6,7 in R9C9
19. Naked pair {29} in R89C2, locked for 24(5) cage at R8C2, no 2,9 in R89C4 19a. R89C2 = {29} = 11 -> R8C4 + R9C34 = 13 = {148/157}, no 6, CPE no 1 in R9C56, clean-up: no 9 in R8C5 19b. 7 of {157} must be in R9C4 -> no 5 in R9C4
20. R12C9 = {23} (only remaining combination, cannot be {14} which clashes with R89C9), locked for C9 and N3
21. 26(4) cage at R4C7 (step 9) = {3689/4589} 21a. 3,5 only in R5C6 -> R5C6 = {35} 21b. 26(4) cage = {3689/4589}, 8,9 locked for C7 and N6
22. 18(3) cage at R6C8 = {279/369/459/567}, no 1
23. R1289C8 (step 4) = {4689} (only remaining combination, cannot be {5679} which clashes with R7C8), locked for C8 -> R3C8 = 1, clean-up: no 9 in R7C5 (step 5)
24. 14(3) cage at R3C8 (step 15) = {158/167} (cannot be {149} because 4,9 only in R3C9) -> R3C9 = {68}, R4C8 = {57} 24a. Naked pair {57} in R47C8, locked for C8
25. R7C9 = 9 (hidden single in C9) -> 18(3) cage at R6C8 (step 22) = {279} (only remaining combination) -> R67C8 = [27], R4C8 = 5, R3C9 = 8 (step 24), R5C8 = 3, R5C6 = 5, clean-up: no 1 in R89C9
Andrew: A tough challenge Para: I spent a while looking for a nicer way ... But can't find anything mhparker: As far as difficult V1 Assassins go... add A50V1 to the list... In terms of techniques, the A50V1 was harder than this one (A55) A 2021 forum Revisit to this puzzlehere
24. If r7c5 = 9 -> r4c6 = 9 -> r2c6 <> 9 If r7c6 = 9 -> r2c6 <> 9 Either case, r2c6 <> 9.
25. Killer combination in N1: If 13(3) = 247, r1c3 = 6; if 13(3) = 256, r1c3 = 4 -> r23c2 <> 6 -> split cage 25(4) r2378c2 = {1789/3589}
26. Killer combination in c9: If 12(2) = 39, r89c9 = 17; if 12(2) = 57, r89c9 = 13 -> r125c9 <> 3,7
27. Outies - Innies c9: r19c8 - r5c9 = 6 -> r19c8 = 8, 10, 11 or 15 -> If 8, r19c8 = {17/35}; if 10, r19c8 = 37; if 11, r19c8 = 38; if 15, r19c8 = 78 -> r1c8 = 13578
28. Outies - Innies c1: r19c2 - r5c1 = 4 -> r5c1 <> 2 since can't make 6 from candidates in r19c2. If r5c1 = 6, r19c2 = 10 = 46; if r5c1 = 7, r19c2 = 11 = 56 -> r1c2 <> 2 -> at least one of r1c2, r5c1, r9c2 = 6 -> r45c2 <> 6.
29. Outies - Innies r1: r2c19 - r1c5 = 3 -> r1c5 <> 1 since can't make 4 from candidates in r2c19; r1c5 <> 2 since can't make 5 from candidates in r2c19.
31. Split 25(4) in r2378c2 = {1789/3589} If 3589, r7c2 must be 3 -> r238c2 <> 3
32. Breakthrough move!! If r1c4 = 7 -> r1c3 = 6 -> 13(3) in N1 = 247 -> r1c1 = 2, r1c2 = 4, r2c1 = 7 If r1c4 = 9 -> r1c3 = 4 -> 13(3) in N1 = 256 -> r1c1 = 2 (Can't have both 56 in r1c12 due to {56} in r9c12). Either case r1c1 = 2 -> r1c9 = 59 -> 14(3) in N3 = {257/149/239} -> r1c8 <> 8, r2c9 <> 5,9 -> 19(4) in N3 must have 6 and 8: {1468/2368}; 19(4) <> 5,7,9 -> 9 locked to r13c9 -> r5c9 <> 9
33. HS: r1c5 = 8 -> r2c19 = 11 (from step 29) -> r2c1 = 7, r2c9 = 4 leading to several naked and hidden singles and it is relatively straightforward from there with a few cages then having only one combination option.
Thanks to Para for pointing out an error in my original step 5 - now amended. Fortunately only one other step needed amendment as a result. Took somewhat longer than no. 49 but got there in the end. Think I'll leave the V2 for the experts who have more free time.
Edit: Where is everybody today? I think the V2 is impossible to solve by humans without serious T&E - even JC's software cannot solve it - actually not even a single placement!!
Walkthrough by Para & ALT ending by mhparker:
Hi
This is how i solved it. I spent a while looking for a nicer way (without a uniqueness move like Cathy). But can't find anything. some interesting moves in there. Especially step 33, which i hoped would break it but just stalled a bit further along again.
Walkthrough Assassin 50
1. R1C34, R67C1 and R9C67 = {49/58/67}: no 1,2,3
2. R1C67 = {17/26/35}: no 4,8,9
3. R34C1 = {13}, locked for C1
4. R34C9 = {39/48/57}: no 1,2,6
5. 11(3) in R6C3 and R8C9 = {128/137/146/236/245}: no 9
10. In N1 no combinations with {13}, {14}, {36} and {46} 10a. 13(3) in R1C1 = {157/238/247/256}: no 9; Only place for 3 in R1C2 -->> R1C2: no 8 10b. 25(4)in R2C2 = {1789/2689/3589/4579}
11. 45 on N3: 2 innies : R1C7+ R3C9 = 12 = [39/57/75] 11a. Clean up: R1C6 = {135}; R4C9 = {357} 11b. R67C9 = {68}: {59} clashes with R34C9 -->> {68} locked for C9 in R67C9
12. In N3 no combinations with {35}, {37}, {59} and {79} 12a. 14(3) in R1C8 = {149/158/167/239/248/257} 12b. 19(4) in R2C7 = {1369/1468/1567/2368/2458/2467}
23. 8 and 9 in N1 locked in 25(4) in R2C2 -->> 25(4) = {1789/2689/3589}: no 4 23a. 4 in N1 locked for R1
24. 13(3) in R1C1 = {157/247/256}: no 3
25. 14(3) in R1C8 needs 2 of {2459} in R12C9 -->> 14(3) = [1]{49}/[3]{29}/[7]{25}/[8]{24}: R1C8 = {1378}
26. 45 on C12 : 4 outies: R2378C3 = 20 = {1379}(9 locked and no 2 or 4, so only combination left) -->> locked for C3 26a. 25(4) in R2C2 = {1789/3589} (needs 2 of {1379} in R23C3): no 2, 6 26b. 2 in N1 locked for C1; 2 locked in 13(3) in R1C1 cage -->> 13(3) = {247/256}: no 1 26c. 5 and 8 in C3 locked for N4
27. 11(3) in R6C3 needs one of {458} in R6C3 -->> 11(3) = {45}[2]/[416]/[812]: no 3,7; R6C4: no 2 27a. Naked triple {256} in R7C478 locked for R7
28. 45 on R1: 2 outies – 1 innie: R2C19 – R1C5 = 3: min R2C19 = 6 -->> Min R1C5 = 3
29. 9 in N6 locked in 22(4) in R4C8 cage -->> 22(4) = {1489/1579/2389/2479}
30. 13(3) in R3C4 needs one of {4568} in R4C3 -->> 13(3) = {148/157/238/247/256/346}: no 9
31. 24(4) in R1C5 can’t have both {79}(clashes with R1C4) -->> 24(4) = {1689/2589/2489/3678/4569/4578} (needs one of {79}) 31a. Killer Pair {79} in R1C4 + 24(4) in R1C5: locked for N2
32. 19(4) in R2C7 can’t have both {12},{24} and {29} because of 14 (3) in R1C8(step 25) 32a. 19(4) = {1369/1468/1567/2368}
Pushing it now (this is more readable i think): 33. 45 on R12: 4 outies = R3C2378 = 26 = {2789/3689/4589/4679/5678}: combining with combinations for 25(4) in R2C2 + 19(4) in R2C7.
33g. Conclusions: R2C23 = [17/53/59/71/81/83]: R2C2: no 3,9; R3C23 = [59/79/83/89/97]R3C2: no 3; R2C78 = {13/16/19/28/36}: no 5, 7; R3C78 = {28/36/48}/[69]: no 5, 7
34. 45 on C89: 4 outis: R2378C7 = 19 = [1864]/{38}{26}/{28}[54]/{48}[52] -->> no 6 in R23C7; 8 locked in R23C7 for C7 and N3 34a. 8 locked in 19(4) cage in R2C7 -->> 19(4) = {1468/2368}: no 9 34b. 9 in N3 locked for C9
35. 8 and 9 in N6 locked in 22(4) cage in R4C8 -->> 22(4) = {1489/2389}: no 5,7 35a. 22(4) needs one of {24} and it has to go in R5C9 -->> R456C8: no 2,4
37d. Conclusions: R2C3: no 9, R2C7: no 2, 4; R2C8: no 1, 3, 4; R3C3: no 3; R3C7: no 2, 4; R3C8: no 3
38. 9 in N1 locked for R3 38a. Clean up: R34C9 = {57} -->> locked for C9; R1C7: no 3(step 11); R1C6: no 5 38b. Naked pair {13} in R89C9 -->> locked for N9 38c. R9C8 = 7 38d. Naked Pair {13} in R1C68 -->> locked for R1
39. Hidden singles: R7C8 = 5; R1C5 = 8
40. 45 on R1: 2 outies: R2C19 = 11 = [29/74]: R2C1: no 5, 6; R2C9: no 2
41. Building on step 37: R2C2378 = [8136]/[5382]/[8316]: no {17}[82] clashes with R2C19(step 40:needs one of {27}) 41a. R2C2: no 1,7; R2C3: no 7 41b. 3 locked in R2C2378 for R2
42. 13(3) in R1C1 = [247]/{256}: [742] clashes with R1C34 -->> R1C1: no 7
43. 18(3) in R6C6 = [819/{27}[9]/[8]{37}/[549] -->> R6C6: no 1,3; R6C7 = no 5
44. 45 on C12: 4 innies: R2378C2 = 25 = [8719/8917/8539/5839] -->> R7C2: no 7; R8C2: no 3
Ok this breaks it, but there must be something nicer. But as number 51 is almost up this will do. 45. Small chain from 4’s in N1: either R1C2 or R1C3 = 4 45a. R1C2 = 4 -> R2C1 = 7 -> 25(4) in R2C2 = {3589} -> R3C1 = 1 45b. R1C3 = 4 -> R1C4 = 9 -> R1C7 = 7(hidden) -> R1C6 = 1 45c. Either way R3C456 <> 1
And we are done. I read Cathy’s walk-through, which has a uniqueness shortcut that I tried to by-pass but it is not the easiest to by-pass. But I rather not use uniqueness moves in killer solving. Just a personal taste.
greetings
Para
ALT ending by mhparker Thanks for the walkthrough, Para. Much appreciated.
In case anyone's interested, I found a variation on Para's step 45 (the move that finally broke the puzzle), which only involves a single loop, and which does not require using the 25/4 cage at R2C2:
This leaves a hidden single in R1 at R1C8 = 1, which is also easily enough to break the puzzle.
Walkthrough by Andrew:
A tough challenge, as was to be expected for Assassin 50. It needed a lot of combination work as can be seen in Cathy's and Para's walkthroughs.
I must admit that I missed the pointing pairs and pointing triple in Cathy's walkthrough. I must train myself to look out for them. Clearly any nonet with two outies totalling 3, 4, 16 or 17 must give either naked or pointing pairs. In this particular puzzle I don't think it matter that I missed them but I'm still annoyed with myself that I did.
The second pointing pair and the pointing triple were neat. She made good use of the shape of the 45 cage.
As I said in my previous message I was stuck (after step 42) and went off to work on other puzzles until I happened to see Mike's contradiction move.
Here is my walkthrough
1. R1C34 = {49/58/67}, no 1,2,3
2. R1C67 = {17/26/35}, no 4,8,9
3. R34C1 = {13}, locked for C1
4. R34C9 = {39/48/57}, no 1,2,6
5. R67C1 = {49/58/67}, no 1,2,3
6. R67C9 = {59/68}
7. R9C34 = {19/28/37/46}, no 5
8. R9C67 = {49/58/67}, no 1,2,3
9. 11(3) cage in N458 = {128/137/146/236/245}, no 9
10. 19(3) cage in N7 = {289/379/469/478/568}, no 1
11. 11(3) cage in N9 = {128/137/146/236/245}, no 9
17. 19(3) cage in N7 = {568} (only remaining combination) -> R8C1 = 8 17a. R9C12 = 11 = {56}, locked for R9 and N7
18. 11(3) cage in N9 R9C89 = {137} -> R8C9 = {137} -> 17(4) cage = {2456} 18a. R89C9 = {13/17} ({37} clashes with R34C9) -> 1 locked in R89C9 for C9 and N9 18b. Killer pair 3/7 in R34C9 and R89C9, locked for C9
19. 13(3) cage in N1 min R12C1 = 7 -> max R1C2 = 6
20. 8,9 in N1 locked in 25(5) cage = 89{17/26/35}, no 4
21. 4 in N1 locked in R1C23, locked for R1
22. 45 rule on R12 4 outies R3C2378 = 26 = {2789/3689/4589/4679/5678}, no 1
23. 13(3) cage in N1 = {157/247/256} (cannot be {346} because 3,4 only in R1C2), no 3 23a. No 2 in R1C2 because R12C1 = {56} clashes with R9C1
24. 45 rule on R789 3 innies R7C456 = 18 = {279/369/567}, no 1
25. 1 in R7 locked in R7C23, locked for N7
26. 45 rule on R89 4 outies R7C2378 = 15 with 1 locked in R7C23 = 1{257/356} (cannot be {1239} because 1,3,9 only in R7C23) = 15{27/36}, no 9 26a. 5 in R7C2378 locked in R7C78, locked for R7 and N9 26b. 9 in N7 locked in R8C23, locked for R8 26c. R7C456 (step 24) = 9{27/36}, 15(4) cage in N8 = 15{27/36}
27. 18(3) cage in N658 max R6C67 = 15 -> min R7C6 = 3
29. 2 in N4 locked in 16(4) cage = 2{158/167/347/356} [1/3] 29a. Killer pair 1/3 in R4C1 and 16(4) cage for N4
30. 45 rule on C123 4 innies R1456C3 = 23 = {4568} (only remaining combination), locked for C3 30a. 5,8 in C3 locked in R456C3, locked for N4 30b. 16(4) cage (step 29) = 27{16/34}
31. 8 in C2 locked in R23C2 and must be the only even number in the 25(4) cage (because R23C3 only contain odd numbers) = 89{17/35} [1/3], no 2,6 [The combinations for the 25(4) cage would have given the same result but spotting this even/odd case, a type of move that I like, saved me having to work them out this time.] 31a. Killer pair 1/3 in R3C1 and 25(4) cage for N1
32. 2 in C2 locked in R456C2 -> no 2 in R5C1 32a. 13(3) cage in N1 = 2{47/56}
33. 11(3) cage in N458 (step 9) = {128/146/245} (cannot be {137/236} because no 1,2,3,6,7 in R6C3), no 3,7 33a. All combinations require 2 or 6 in R7C4 -> no 2 in R6C4
34. R7C456 (step 26c) = 9{27/36}, R7C4 = {26} -> no 2,6 in R7C56
35. 18(3) cage in N658 = {189/279/378/459} 35a. 4 only in R6C7 -> no 5 in R6C7
36. 13(3) cage in N254 = {148/157/238/247/256/346} (cannot be {139) because no 1,3,9 in R4C3), no 9
37. 45 rule on C89 4 innies R2378C8 = 17 = {1259/1268/1457/2348/2357/2456} (cannot be {1349/1358/1367} because no 1,3,7,8,9 in R78C8) 37a. 1 only in R2C8 -> no 9 in R2C8
38. 14(3) cage in N3 = {149/239/248/257} (cannot be {158/167/347/356} because no 1,3,6,7,8 in R12C9), no 6 38a. 1,3 only in R1C8 -> no 9 in R1C8 38b. 7 only in R1C8 -> no 5 in R1C8 38c. 3,7,8 only in R1C8 -> no 2 in R1C8 38d. {239} can only be [329] ([392] clashes with R1C467), {257} can only be [725] ([752] clashes with R1C67) -> no 5 in R1C9, no 2 in R2C9 38e. 6 in N3 locked in 19(4) cage = 6{139/148/157/238} (cannot be {2467} which clashes with the 14(3) cage)
39. 45 rule on R1 2 outies R2C19 – 3 = 1 innie R1C5, min R2C19 = 6 -> min R1C5 = 3 39a. R2C19 cannot be 8 -> no 5 in R1C5
40. 45 rule on R123 5 innies R3C14569 = 19 = 1{2349/2358/2367/2457/3456} 40a. {12349} must have 9 in R3C9 -> no 9 in R3C56
41. R1C4 = {79} -> 24(4) cage cannot contain both 7 and 9 41a. 24(4) cage = {1689/2589/3489/3678/4569/4578} (cannot be {2679/3579}
42. 45 rule on C1234 4 innies R258C4 + R5C3 = 23 with R5C3 = {4568} If R5C3 = 4, R258C4 = [496] (cannot be {379} which clashes with R1C4) If R5C3 = 5, R258C4 = {369/459/567} (cannot be {279} which clashes with R1C4) If R5C3 = 6, R258C4 = {359/467} (cannot be {179} which clashes with R1C4, cannot be {269} which clashes with R7C4) If R5C3 = 8, R258C4 = {159/249/357/456} (cannot be {267} which clashes with R7C4) 42a. Only combination with 2 is {249}8, 4,9 only in R25C4 -> no 2 in R25C4
At this stage I was stuck although I hadn’t looked seriously for contradiction moves. Then I happened to see Mike’s step on the forum which works at this stage. If I’d looked seriously for contradiction moves I might have found it since there are only two positions for 1 in R1, the sort of thing that points toward contradiction moves. Alternatively I might have found Para's contradiction move based on the two positions for 4 in R1.
43. (Mike’s step) R1C6=1 -> R3C456<>1 -> R3C1=1 -> R1C3=6 -> R1C4=7 -> R1C67<>{17} -> R1C6<>1 (contradiction) -> R1C6<>1 Nice one Mike! 43a. R1C8 = 1 (hidden single in R1), clean-up: no 7 in R1C7 43b. R12C9 = 13 = [94], R1C4 = 7, R1C3 = 6, clean-up: no 3 in R4C9
Mike’s step was clearly the breakthrough that I needed, the rest was routine. If I’d realised how close I was to finishing this puzzle, I would have looked harder for that move instead of going off to work on other puzzles including Assassin 50V0.2
mhparker: rating 3.0: "Ruudiculous", requiring a team effort and massive hypotheticals to solve, if it can be solved at all. The A50V2 ..... could be considered ...this. Ruud, lead-in: could be one of the toughest killers I made so far. Glyn: I am struggling with it here. Tried making a huge implication chain round the outside, knocks out a few candidates but nothing worth reporting. mhparker: Wow, (JSudoku 1.3b1) can to the Assassin 50 V2! JSudoku solver log:here mhparker: However, before you all get too excited, here are the stats and the HUGE solver log (including a finned jellyfish found near the start!) in TT. It's clearly way off the scale of anything that can be reasonably posted on any forum without ending up on the "Unsolvables" list. Glyn: at last my tryfurcation can be consigned to history Andrew (in 2015): When I started on this puzzle again, having not got very far when it first appeared, I wondered how far I'd get. However I found that it's about the same difficulty as Assassin 39 V2, which I did recently, but a bit shorter walkthrough; then I realised that I can omit my heaviest steps, so I've also posted a simplified walkthrough.
Original walkthrough by Andrew:
Prelims a). R1C34 = {79} b). R1C67 = {19/28/37/46}, no 5 c). R34C1 = {29/38/47/56}, no 1 d). R34C9 = {18/27/36/45}, no 9 e). R67C1 = {19/28/37/46}, no 5 f). R67C9 = {18/27/36/45}, no 9 g). R9C34 = {39/48/57}, no 1,2,6 h). R9C67 = {14/23} i). 11(3) cage at R3C4 = {128/137/146/236/245}, no 9 j). 11(3) cage at R6C3 = {128/137/146/236/245}, no 9 k). 14(4) cage at R7C2 = {1238/1247/1256/1346/2345}, no 9 l). and, of course, 45(9) cage at R3C5 = {123456789}
1. Naked pair {79} in R1C34, locked for R1, clean-up: no 1,3 in R1C67
6. 45 rule on C12 4 outies R2378C3 = 14 = {1238/1247/1256/1346/2345}, no 9
7. 45 rule on C1234 4(3+1) innies R5C3 + R258C4 = 26 7a. Max R258C4 = 23 (cannot be {789} which clashes with R1C4) -> min R5C3 = 3
8. 45 rule on N1 1 innie R1C3 = 1 outie R4C1 + 4, 45 rule on N7 1 innie R9C3 = 1 outie R6C1 + 5 -> R9C3 cannot be 1 more than R1C3 -> R19C3 = [79/97/98] (cannot be [78]), 9 locked for C3 8a. 9 in one of R19C3, R1C3 + R3C1 = 15 (step 2), R7C1 + R9C3 = 15 (step 4) -> 6 in one of R37C1, locked for C1
9. 9 in N4 only in 23(4) cage at R4C2 = {1589/1679/2489/2579/3479} (cannot be {3569} which clashes with R4C1) 9a. Hidden killer pair 7,8 in 23(4) cage and R456C3 for N4, 23(4) cage contains one of 7,8 -> R456C3 must contain one of 7,8 9b. Killer pair 7,8 in R19C3 and R456C3, locked for C3
10. 13(3) cage at R1C8 = {139/157/238/346} (cannot be {148/247/256} which clash with R1C7 + R3C9) 10a. 7,9 of {139/157} must be in R2C9 -> no 1,5 in R2C9
[The next few steps are mostly analysis of R5C3 + R258C4. With hindsight this could probably have been left until later, when it would have been simpler, but at the time it seemed to be the obvious place to work and there were some interesting steps.]
11. R5C3 + R258C4 = 26 (step 7) = 3{689}/4{589}/5{489/678}/6{389/569/578}/7{289/469/478/568}/8{189/369/378/459/468/567} (cannot be 4{679}/5{579}/6{479}/7{379}/8{279} which clash with R1C4) 11a. 9 in C4 only in R1C4 or R258C4 -> R5C3 + R258C4 = 3{689}/4{589}/5{489/678}/6{389/569/578}/7{289/469}/8{189/369/378/459/468/567} (cannot be 7{478/568} which clash with R1C34 = [79]) 11b. 8 in C3 only in R456C3 or R9C3 -> R5C3 + R258C4 = 3{689}/4{589}/5{489/678}/6{389/569/578}/7{289}/8{189/369/378/459/468/567} (cannot be 7{469} which clashes with R9C34 = [84])
12. Consider combinations for R2378C3 (step 6) = {1256/1346/2345} 12a. R2378C3 = {1256} => 3,4 in C3 only in R456C3, locked for N4 => R6C1 = 2, R7C1 = 8, R9C3 = 7 (step 4), R9C4 = 5 => R5C3 + R258C4 cannot be 4{589} or R2378C3 = {1346/2345}, 4 locked for C3 -> no 4 in R5C3
13. Consider permutations for R4C1 = {35} R4C1 = 3 => R3C1 = 8, R1C3 = 7 (step 2), R1C4 = 9, R9C3 = 9 (hidden single in C3) => R9C4 = 3, 8 in C3 must be in R456C3, R5C3 + R258C4 (step 11b) = 5{678}/6{578}/8{567} (cannot be 8{468} because remaining candidates in C4 are 1,2,5,7 and 11(3) cages at R3C4 and R6C3 cannot be 8{12} which clashes with 8{468}, cannot be 5{15} and 3{17} which clashes with R4C1) or R4C1 = 5 => R3C1 = 6, R1C3 = 9 (step 2), R1C4 = 7 => R258C4 must contain 9 -> R5C3 + R258C4 (step 11a) = 3{689}/5{489/678}/6{389/569/578}/7{289}/8{189/369/459/567} 13a. Killer pair 7,9 in R1C4 and R258C4, locked for C4
14. 23(4) cage at R4C2 (step 9) = {1589/1679/2489/2579/3479} 14a. Consider permutations for R4C1 = {35} R4C1 = 3 => R3C1 = 8, R1C3 = 7 (step 2), R9C3 = 9 (hidden single in C3) => 8 in C3 must be in R456C3, locked for N4 => 23(4) cage = {1679/2579/3479} or R4C1 = 5 => 23(4) cage = {1679/2489/3479} -> 23(4) cage = {1679/2489/2579/3479}
15. R5C3 + R258C4 (step 13) = 3{689}/4{589}/5{489/678}/6{389/569/578}/7{289}/8{189/369/459/567} 15a. Consider combinations for 11(3) cages at R3C6 and R6C3 15b. R3467C4 contain 1,2,3,4,5,6,8 R3467C4 cannot be {1356} because {13} would leave 5,6 for the other 11(3), {15} would make an 11(3) 5{15} and {16} would leave the other 11(3) as 3{35} => R3467C4 must contain at least one of 2,4,8 R3467C4 containing 2 blocks R5C3 + R258C4 = 7{289} R3467C4 containing 4 => R9C3 = {79} => naked pair {79} in R19C3, locked for C3 R3467C4 containing 8 blocks all combinations for R5C3 + R258C4 containing 8 in C4 -> R5C3 + R258C4 cannot be 7{289} -> R5C3 + R258C4 = 3{689}/5{489/678}/6{389/569/578}/8{189/369/459/567}, no 7 in R5C3, no 2 in R258C4
[Now that I can’t see any way to make further progress on R5C3 +R258C4, I’ll move on to other areas.]
16. 16(3) cage at R8C1 = {169/178/259/349/358/457} (cannot be {268/367} which clash with R7C1 + R9C3) 16a. Consider combinations for R7C1 + R9C3 (step 4) = [69/78/87] R7C1 + R9C3 = [69] => R6C1 = 4, R3C1 = 8 => R4C1 = 3, R9C4 = 3, R9C67 = {14}, locked for R9 => 16(3) cage = {178} = [178] or R7C1 + R9C3 = {78}, locked for N7 => 16(3) cage = {169/259/349} -> 16(3) cage = {169/178/259/349}, no 7,8 in R8C1, no 8 in R9C1, no 7 in R9C2 16b. R7C1 + R9C3 = {78} or 16(3) cage = {178}, 7,8 locked for N7
[I ought to have spotted this much earlier; fortunately it only becomes useful for step 18.] 17. R34C9 = [27/45/81] (cannot be [63] which clashes with R34C1 = [65/83], killer combo clash), no 6 in R3C9, no 3 in R4C9, no 4 in R1C7 (step 3), no 6 in R1C6
18. 16(3) cage at R8C1 (step 16a) = {169/178/259/349} 18a. Consider permutations for R34C1 = [65/83] R34C1 = [65] or R34C1 = [83] => R7C1 = 6 (hidden single in C1), R6C1 = 4, R9C3 = 9 (step 4), 16(3) cage = {178} = [178], remaining candidates in C1 = 2,5,9 -> 12(3) cage at R1C1 = [219] (only possible permutation, cannot be {25}5) => R1C67 = [46] => R3C9 = 4 (step 3), R4C9 = 5, R5C1 = 5 (hidden single in C1) -> 5 in R4C19, locked for R4, 5 in R45C1, locked for C1 and N4, also no 6 in R1C2
19. 12(3) cage at R1C1 = {129/138/147/237/345} 19a. 7,9 of {129/237} must be in R2C1 -> no 2 in R2C1 19b. Consider permutations for R34C1 = [65/83] R34C1 = [65] => R4C9 = {17}, R3C9 = {28} => R1C7 + R3C9 (step 3) = {28} => R1C67 = {28}, locked for R1 or R34C1 = [83] -> no 8 in R1C12 19c. 7,8,9 of {129/138/147} must be in R2C1 -> no 1 in R2C1
20. 16(3) cage at R8C1 (step 16a) = {169/178/259/349} 20a. Consider permutations for R7C1 + R9C3 = [69/78/87] R7C1 + R9C3 = [69] => 16(3) cage = {178} or R7C1 + R9C3 = [78] => R9C4 = 4, R9C67 = {23}, locked for R9 or R7C1 + R9C3 = [87] => R9C4 = 5 => 9 in 16(3) cage = {169/349} -> no 2 in R9C12
21. 12(3) cage at R1C1 (step 19) = {129/138/147/237/345}, 16(3) cage at R8C1 (step 16a) = {169/178/259/349} 21a. Consider permutations for R34C1 = [65/83] R34C1 = [65] => R4C9 = {17}, R3C9 = {28} => R1C7 + R3C9 (step 3) = {28} => R1C67 = {28}, locked for R1 or R34C1 = [83] => R7C1 = 6 (hidden single in C1), R9C3 = 9 (step 4) => 16(3) cage = {178} = [178] -> 12(3) cage = {129/138/147/345} (cannot be {237} which clashes with R1C67 = {28} or R9C1 = 7)
22. 13(3) cage at R1C8 (step 10) = {139/238/346} (cannot be {157} which clashes with 12(3) cage at R1C1), no 5,7, 3 locked for N3
[And now to use the 45(9) cage for the first time, and get the first placements.] 23. 12(3) cage at R1C1 (step 21a) = {129/138/147/345} 23a. Consider placements for 5 in R1 R1C2 = 5 => R12C1 = {34}, locked for C1 => R4C1 = 5 or R1C5 = 5 => 5 in 45(9) cage at R3C5 only in R5C467, locked for R5 => R4C1 = 5 (hidden single in C1) -> R4C1 = 5, R3C1 = 6, R1C3 = 9 (step 2), R1C4 = 7, clean-up: no 4 in R3C9, no 6 in R1C7 (step 3), no 4 in R1C6, no 4 in R6C1, no 3 in R9C4 23b. Naked pair {28} in R1C67, locked for R1 23c. Naked pair {28} in R1C7 + R3C9, locked for N3 23d. Naked pair {78} in R7C1 + R9C3, locked for N7
24. 9 in C4 only in R258C4 24a. R5C3 + R258C4 (step 15b) = 3{689}/6{389/569}/8{189/369} (cannot be 8{459} which clashes with R9C4), no 4 in R258C4
25. 5 in C3 only in R2378C3 (step 12) = {1256/2345}, 2 locked for C3
26. 16(3) cage at R8C1 (step 16a) = {169/259/349} 26a. 6 of {169} must be in R9C2 -> no 1 in R9C2 26b. Consider combinations for 12(3) cage at R1C1 (step 21a) = {138/147/345} 12(3) cage = {138} => R2C1 = 8, R7C1 = 7, R6C1 = 3, R1C1 = 1, R9C3 = 8, R9C4 = 4, R9C67 = {23}, locked for R9 => 16(3) cage = {259} => R8C1 = 2, R9C2 = 5 or 12(3) cage = {147} => R2C1 = 7 => R7C1 = 8, R6C1 = 2 => R9C3 = 7 => R9C4 = 5 or 12(3) cage = {345}, 3 locked for C1 => R6C1 = 2 => R7C1 = 8 => R9C3 = 7 => R9C4 = 5 -> 2 in R68C1, locked for C1, 8 in R27C1, locked for C1, 5 in R9C24, locked for R9
27. 13(3) cage at R1C8 (step 22) = {139/346} 27a. 6 of {346} must be in R1C89 (R1C89 cannot be {34} which clashes with 12(3) cage at R1C1) -> no 6 in R2C9
28. 16(3) cage at R8C9 = {169/178/259/268/358/367} (cannot be {349} which clashes with R7C9 + R9C7, cannot be {457} = 5{47} which clashes with R9C34), no 4
29. 12(3) cage at R1C1 (step 21a) = {138/147/345}, R2378C3 (step 25) = {1256/2345} 29a. Consider combinations for 16(3) cage at R8C1 (step 16a) = {169/259/349} 16(3) cage = {169}, locked for N7 => max R78C3 = {45} = 9 => min R23C3 = 5 => max R23C2 = 13 cannot contain both of 7,8 => R2C1 = {78} (hidden killer pair 7,8 in R2C1 and 18(4) cage at R2C2 for N1) => 12(3) cage = {138/147} or 16(3) cage = {259} => 12(3) cage = {138/147} or 16(3) cage = {349} => 12(3) cage = {138/147} (cannot be {345} which clashes with 16(3) cage) -> 12(3) cage = {138/147}, 1 locked for R1 and N1 29b. Naked pair {78} in R27C1, locked for C1
30. R1C5 = 5 (hidden single in R1) 30a. 22(4) cage at R1C5 = {2569/3568}, no 1,4 30b. Killer pair 2,8 in 22(4) cage and R1C6, locked for N3 30c. 1,4 in N2 only in R3C456, locked for R3 30d. 45(9) cage at R3C5 = {123456789}, 5 locked for R5
31. 13(3) cage at R1C8 (step 27) = {346} (only remaining combination), locked for N3
[And right round the outer ring to get the next placement] 32. Consider combinations for 12(3) cage at R1C1 (step 29a) = {138/147} 12(3) cage = {138} => R2C1 = 8 => R7C1 = 7, R9C3 = 8, R9C4 = 4, R9C67 = {23} => R7C9 + R9C7 (step 5) = {23} or 12(3) cage = {147}, 4 locked for R1 => R2C9 = 4 (hidden single in N3) -> no 4 in R7C9, clean-up: no 5 in R6C9, no 1 in R9C7 (step 5), no 4 in R9C6 32a. R8C9 = 5 (hidden single in C9) 32b. 16(3) cage at R8C9 (step 28) = {259/358}, no 1,6,7 [Cracked. The rest is fairly straightforward.]
33. R9C67 = [14] (cannot be {23} which clashes with 16(3) cage at R8C9), R7C9 = 1 (step 5), R6C9 = 8, R34C9 = [27], R1C67 = [28], R9C4 = 5, R9C3 = 7, R7C1 = 8, R6C1 = 2, clean-up: no 3,9 in R9C8 (step 32b) 33a. R2C1 = 7 -> R1C12 = 5 = {14}, locked for R1 and N1, R2C9 = 4 (hidden single in N3) 33b. 22(4) cage at R1C5 (step 30a) = {3568} (only remaining combination), 3,8 locked for R2 and N3 33c. Naked pair {25} in R2C23, locked for R2 and N1 -> R3C23 = [83] 33d. Naked pair {19} in R2C78, locked for N3
34. 3 in N4 only in 23(4) cage at R4C2 (step 14a) = {3479}, 4 locked for N4 34a. Naked triple {168} in R456C3, locked for C3
6. 45 rule on C12 4 outies R2378C3 = 14 = {1238/1247/1256/1346/2345}, no 9
7. 45 rule on C1234 4(3+1) innies R5C3 + R258C4 = 26 7a. Max R258C4 = 23 (cannot be {789} which clashes with R1C4) -> min R5C3 = 3
8. 45 rule on N1 1 innie R1C3 = 1 outie R4C1 + 4, 45 rule on N7 1 innie R9C3 = 1 outie R6C1 + 5 -> R9C3 cannot be 1 more than R1C3 -> R19C3 = [79/97/98] (cannot be [78]), 9 locked for C3 8a. 9 in one of R19C3, R1C3 + R3C1 = 15 (step 2), R7C1 + R9C3 = 15 (step 4) -> 6 in one of R37C1, locked for C1
9. 9 in N4 only in 23(4) cage at R4C2 = {1589/1679/2489/2579/3479} (cannot be {3569} which clashes with R4C1) 9a. Hidden killer pair 7,8 in 23(4) cage and R456C3 for N4, 23(4) cage contains one of 7,8 -> R456C3 must contain one of 7,8 9b. Killer pair 7,8 in R19C3 and R456C3, locked for C3
10. 13(3) cage at R1C8 = {139/157/238/346} (cannot be {148/247/256} which clash with R1C7 + R3C9) 10a. 7,9 of {139/157} must be in R2C9 -> no 1,5 in R2C9
[The next few steps were mostly analysis of R5C3 + R258C4. With hindsight this could have been left until later, when it would have been simpler, or even completely omitted but at the time it seemed to be the obvious place to work and there were some interesting steps.]
11. Omitted
12. Omitted
13. Omitted
14. Omitted
15. Omitted
[Then I moved on to other areas.]
16. 16(3) cage at R8C1 = {169/178/259/349/358/457} (cannot be {268/367} which clash with R7C1 + R9C3) 16a. Consider combinations for R7C1 + R9C3 (step 4) = [69/78/87] R7C1 + R9C3 = [69] => R6C1 = 4, R3C1 = 8 => R4C1 = 3, R9C4 = 3, R9C67 = {14}, locked for R9 => 16(3) cage = {178} = [178] or R7C1 + R9C3 = {78}, locked for N7 => 16(3) cage = {169/259/349} -> 16(3) cage = {169/178/259/349}, no 7,8 in R8C1, no 8 in R9C1, no 7 in R9C2 16b. R7C1 + R9C3 = {78} or 16(3) cage = {178}, 7,8 locked for N7
[I ought to have spotted this much earlier; fortunately it only becomes useful for step 18.] 17. R34C9 = [27/45/81] (cannot be [63] which clashes with R34C1 = [65/83], killer combo clash), no 6 in R3C9, no 3 in R4C9, no 4 in R1C7 (step 3), no 6 in R1C6
18. 16(3) cage at R8C1 (step 16a) = {169/178/259/349} 18a. Consider permutations for R34C1 = [65/83] R34C1 = [65] or R34C1 = [83] => R7C1 = 6 (hidden single in C1), R6C1 = 4, R9C3 = 9 (step 4), 16(3) cage = {178} = [178], remaining candidates in C1 = 2,5,9 -> 12(3) cage at R1C1 = [219] (only possible permutation, cannot be {25}5) => R1C67 = [46] => R3C9 = 4 (step 3), R4C9 = 5, R5C1 = 5 (hidden single in C1) -> 5 in R4C19, locked for R4, 5 in R45C1, locked for C1 and N4, also no 6 in R1C2
19. 12(3) cage at R1C1 = {129/138/147/237/345} 19a. 7,9 of {129/237} must be in R2C1 -> no 2 in R2C1 19b. Consider permutations for R34C1 = [65/83] R34C1 = [65] => R4C9 = {17}, R3C9 = {28} => R1C7 + R3C9 (step 3) = {28} => R1C67 = {28}, locked for R1 or R34C1 = [83] -> no 8 in R1C12 19c. 7,8,9 of {129/138/147} must be in R2C1 -> no 1 in R2C1
20. 16(3) cage at R8C1 (step 16a) = {169/178/259/349} 20a. Consider permutations for R7C1 + R9C3 = [69/78/87] R7C1 + R9C3 = [69] => 16(3) cage = {178} or R7C1 + R9C3 = [78] => R9C4 = 4, R9C67 = {23}, locked for R9 or R7C1 + R9C3 = [87] => R9C4 = 5 => 9 in 16(3) cage = {169/349} -> no 2 in R9C12
21. 12(3) cage at R1C1 (step 19) = {129/138/147/237/345}, 16(3) cage at R8C1 (step 16a) = {169/178/259/349} 21a. Consider permutations for R34C1 = [65/83] R34C1 = [65] => R4C9 = {17}, R3C9 = {28} => R1C7 + R3C9 (step 3) = {28} => R1C67 = {28}, locked for R1 or R34C1 = [83] => R7C1 = 6 (hidden single in C1), R9C3 = 9 (step 4) => 16(3) cage = {178} = [178] -> 12(3) cage = {129/138/147/345} (cannot be {237} which clashes with R1C67 = {28} or R9C1 = 7)
22. 13(3) cage at R1C8 (step 10) = {139/238/346} (cannot be {157} which clashes with 12(3) cage at R1C1), no 5,7, 3 locked for N3
[And now to use the 45(9) cage for the first time, and get the first placements.] 23. 12(3) cage at R1C1 (step 21a) = {129/138/147/345} 23a. Consider placements for 5 in R1 R1C2 = 5 => R12C1 = {34}, locked for C1 => R4C1 = 5 or R1C5 = 5 => 5 in 45(9) cage at R3C5 only in R5C467, locked for R5 => R4C1 = 5 (hidden single in C1) -> R4C1 = 5, R3C1 = 6, R1C3 = 9 (step 2), R1C4 = 7, clean-up: no 4 in R3C9, no 6 in R1C7 (step 3), no 4 in R1C6, no 4 in R6C1, no 3 in R9C4 23b. Naked pair {28} in R1C67, locked for R1 23c. Naked pair {28} in R1C7 + R3C9, locked for N3 23d. Naked pair {78} in R7C1 + R9C3, locked for N7
24. Omitted
25. 5 in C3 only in R2378C3 (step 6) = {1256/2345}, 2 locked for C3
26. 16(3) cage at R8C1 (step 16a) = {169/259/349} 26a. 6 of {169} must be in R9C2 -> no 1 in R9C2 26b. Consider combinations for 12(3) cage at R1C1 (step 21a) = {138/147/345} 12(3) cage = {138} => R2C1 = 8, R7C1 = 7, R6C1 = 3, R1C1 = 1, R9C3 = 8, R9C4 = 4, R9C67 = {23}, locked for R9 => 16(3) cage = {259} => R8C1 = 2, R9C2 = 5 or 12(3) cage = {147} => R2C1 = 7 => R7C1 = 8, R6C1 = 2 => R9C3 = 7 => R9C4 = 5 or 12(3) cage = {345}, 3 locked for C1 => R6C1 = 2 => R7C1 = 8 => R9C3 = 7 => R9C4 = 5 -> 2 in R68C1, locked for C1, 8 in R27C1, locked for C1, 5 in R9C24, locked for R9
27. 13(3) cage at R1C8 (step 22) = {139/346} 27a. 6 of {346} must be in R1C89 (R1C89 cannot be {34} which clashes with 12(3) cage at R1C1) -> no 6 in R2C9
28. 16(3) cage at R8C9 = {169/178/259/268/358/367} (cannot be {349} which clashes with R7C9 + R9C7, cannot be {457} = 5{47} which clashes with R9C34), no 4
29. 12(3) cage at R1C1 (step 21a) = {138/147/345}, R2378C3 (step 25) = {1256/2345} = 14 29a. Consider combinations for 16(3) cage at R8C1 (step 16a) = {169/259/349} 16(3) cage = {169}, locked for N7 => max R78C3 = {45} = 9 => min R23C3 = 5 => max R23C2 = 13 cannot contain both of 7,8 => R2C1 = {78} (hidden killer pair 7,8 in R2C1 and 18(4) cage at R2C2 for N1) => 12(3) cage = {138/147} or 16(3) cage = {259} => R9C2 = 5 => 12(3) cage = {138/147} or 16(3) cage = {349} => 12(3) cage = {138/147} (cannot be {345} which clashes with 16(3) cage) -> 12(3) cage = {138/147}, 1 locked for R1 and N1 29b. Naked pair {78} in R27C1, locked for C1
30. R1C5 = 5 (hidden single in R1) 30a. 22(4) cage at R1C5 = {2569/3568}, no 1,4 30b. Killer pair 2,8 in 22(4) cage and R1C6, locked for N3 30c. 1,4 in N2 only in R3C456, locked for R3 30d. 45(9) cage at R3C5 = {123456789}, 5 locked for R5
31. 13(3) cage at R1C8 (step 27) = {346} (only remaining combination), locked for N3
[And right round the outer ring to get the next placement] 32. Consider combinations for 12(3) cage at R1C1 (step 29a) = {138/147} 12(3) cage = {138} => R2C1 = 8 => R7C1 = 7, R9C3 = 8, R9C4 = 4, R9C67 = {23} => R7C9 + R9C7 (step 5) = {23} or 12(3) cage = {147}, 4 locked for R1 => R2C9 = 4 (hidden single in N3) -> no 4 in R7C9, clean-up: no 5 in R6C9, no 1 in R9C7 (step 5), no 4 in R9C6 32a. R8C9 = 5 (hidden single in C9) 32b. 16(3) cage at R8C9 (step 28) = {259/358}, no 1,6,7 [Cracked. The rest is fairly straightforward.]
33. R9C67 = [14] (cannot be {23} which clashes with 16(3) cage at R8C9), R7C9 = 1 (step 5), R6C9 = 8, R34C9 = [27], R1C67 = [28], R9C4 = 5, R9C3 = 7, R7C1 = 8, R6C1 = 2, clean-up: no 3,9 in R9C8 (step 32b) 33a. R2C1 = 7 -> R1C12 = 5 = {14}, locked for R1 and N1, R2C9 = 4 (hidden single in N3) 33b. 22(4) cage at R1C5 (step 30a) = {3568} (only remaining combination), 3,8 locked for R2 and N3 33c. Naked pair {25} in R2C23, locked for R2 and N1 -> R3C23 = [83] 33d. Naked pair {19} in R2C78, locked for N3
34. 3 in N4 only in 23(4) cage at R4C2 (step 9) = {3479}, 4 locked for N4 34a. Naked triple {168} in R456C3, locked for C3
[And now one way to continue would be to use R5C3 + R258C4 = 26 which now cannot contain 2. However there’s an easier way to finish …]
36. 11(3) cage at R6C3 = {146} (only possible combination), 1 locked for R6, 4 locked for C3 36a. R3C4 = 1 -> R4C34 = 10 = [82], R5C34 = [68]
37. 45(9) cage at R3C5 = {123456789} -> R5C7 = 2
38. R5C9 = 9 -> R456C8 = 11 = {146} (only possible combination), 1,6 locked for C8 and N6
39. R4C7 = 3 -> R34C6 = 13 = {49}, locked for C6
40. Naked pair {46} in R6C48, locked for R6 40a. R6C7 = 5 -> R67C6 = 13 = [76]
and the rest is naked singles.
Rating Comment:
It's interesting that Mike defined typical examples for 3.0 as A50 V2 and A60RP. I haven't (yet?) solved A60 RP but maybe Mike overestimated the difficulty level for A50 V2.
Since Mike quoted A50 V2 as a typical 3.0, I haven't changed the entry in the rating table. However I would rate my original walkthrough the same as I rated A39 V2 and my simplified walkthrough a bit lower.
Ruud: This version 0.2 has the same difficulty rating as a recent Moderate on http://www.sudoku.org.uk Glyn: I did it before I had the beer though Andrew: Don't know about that (Ruud's rating). It was definitely routine so V0.2 is a fair rating. However as someone who still does the killers on the other website it took me longer than any daily killer there.
Walkthrough by Andrew:
I took a break from Assassin 50, where I've currently ground to a halt, and did V0.2
Ruud wrote:
This version 0.2 has the same difficulty rating as a recent Moderate on http://www.sudoku.org.uk
Don't know about that. It was definitely routine so V0.2 is a fair rating. Maybe SumoCue rates it the same as that recent Moderate. However as someone who still does the killers on the other website it took me longer than any daily killer there.
50V0.2 doesn't really need a posted walkthrough. However I'm posting my one because I feel that all Assassins and other puzzles posted on this forum should have at least one posted walkthrough or, for the hardest puzzles, a tag solution.
1. R1C34 = {89}, locked for R1
2. R1C67 = {16/25/34}, no 7
3. R34C1 = {15/24}
4. R34C9 = {18/27/36/45}, no 9
5. R67C1 = {17/26/35}, no 4,8,9
6. R67C9 = {13}, locked for C9, clean-up: no 6,8 in R34C9
7. R9C34 = {39/48/57}, no 1,2,6
8. R9C67 = {29/38/47/56}, no 1
9. 18(3) cage in N1 = {279/369/378/459/468/567} (cannot be {189} because 8,9 only in R2C1), no 1 9a. 8,9 only in R2C1 -> no 2,3,4 in R2C1
10. 20(3) cage in N254 = {389/479/569/578}, no 1,2
11. 22(3) cage in N256 = 9{58/67}
12. 19(3) cage in N9 = {289/379/469/478/568}, no 1
13. 45 rule on N1 2 innies R1C3 + R3C1 = 11 -> R1C3 = 9, R3C1 = 2, R1C4 = 8, R4C1 = 4, clean-up: no 5 in R3C9, no 7 in R4C9, no 6 in R67C1, no 4 in R9C3, no 3 in R9C4
14. 45 rule on N3 2 innies R1C7 + R3C9 = 13 -> R1C7 = 6, R3C9 = 7, R1C6 = 1, R4C9 = 2, clean-up: no 5 in R9C6
15. 18(3) cage in N1 (step 9) = {378/567} (cannot be {468} because no 4,6,8 in R1C1), no 4 = 7{38/56}, 7 locked for N1 15a. 6,8 only in R2C1 -> no 5,7 in R2C1 15b. 7 locked in R1C12 for R1 15c. 16(4) cage in N1 = 14{38/56}
16. 45 rule on N7 2 innies R7C1 + R9C3 = 12 = {57}, locked for N7, clean-up: R6C1 = {13}, R9C4 = {57} 16a. Naked pair {57} in R9C34, locked for R9, clean-up: no 4,6 in R9C67
20. At last a digit in the 45 cage, R5C4 = 1 (hidden single in C4) -> R4C8 = 1 (hidden single in N6)
21. 13(4) cage in N8 = {1246} (only remaining combination), 2,4,6 locked for R8 and N8
22. Naked pair {18} in R8C23, locked for R8 and N7
23. Naked pair {57} in R8C78, locked for N9 -> R7C78 = [28] [R7C7 was a hidden single after step 21 but I used the naked pairs which are more obvious.]
24. 25(4) cage in N4 = {3589} (only remaining combination), locked for N4, 3 locked for C2
25. R7C2 = 6 (hidden single in C2), R7C3 = 4,
26. 16(3) combination in N2 = {2347} (only remaining combination), locked for N2, 4 locked for R2 -> R2C23 = [13], R3C23 = [48], R8C23 = [81]
27. Naked pair {59} in R2C78, locked for N3 -> R3C78 = [13]
28. R56C8 = 15 = {69}, locked for C8 and N6 -> R2C78 = [95], R8C78 = [57]
29. R5C6 = 3 (hidden single in 45 cage, may have been there for some time) -> R5C2 = 9, R6C2 = 5, R4C2 = 3, R56C8 =[69]
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