SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Thu Apr 18, 2024 9:55 am

View unanswered posts | View active topics


Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC




Post new topic Reply to topic  Page 1 of 1
  [ 5 posts ] 
  Print view Previous topic | Next topic 
Author Message
Ed
 Post subject: Assassin 297
PostPosted: Thu Jul 24, 2014 10:06 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Not as hard as I first thought. Once again, got stuck in the "wrong" area. A bit too much combo work for my taste but one nice step made it a worthwhile solve. It gets a score of 1.50

Assassin 297

Image
code: paste into solver:
3x3::k:2560:7681:7681:7681:7681:7681:2818:2818:2818:2560:7681:9219:2052:2052:3845:6662:6662:6407:2560:9219:6408:6408:8969:3845:6662:6662:6407:9219:9219:9219:6408:8969:3845:3594:6407:6407:3851:9219:6408:6408:8969:3594:3594:6407:3852:3851:3851:9219:8969:8969:8969:4621:4621:3852:1806:1806:7439:7439:4112:3345:3345:4621:3852:5906:5906:7439:7439:4112:3345:4115:4621:2836:5906:7439:7439:1813:1813:4115:4115:4115:2836:
solution: 
+-------+-------+-------+
| 7 8 4 | 5 1 9 | 3 6 2 |
| 1 3 9 | 2 6 4 | 5 8 7 |
| 2 5 6 | 7 8 3 | 9 4 1 |
+-------+-------+-------+
| 4 6 7 | 3 2 8 | 1 5 9 |
| 9 2 8 | 1 5 6 | 7 3 4 |
| 5 1 3 | 9 4 7 | 8 2 6 |
+-------+-------+-------+
| 3 4 1 | 8 9 2 | 6 7 5 |
| 8 9 2 | 6 7 5 | 4 1 3 |
| 6 7 5 | 4 3 1 | 2 9 8 |
+-------+-------+-------+
Cheers
Ed
Top
 Profile  
Reply with quote  
Afmob
 Post subject:
PostPosted: Sat Jul 26, 2014 8:43 am 
Offline
Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Assassin, Ed! At first this one was as hard as the last Assassins since I used a forcing chain but after discovering the crucial step 3d (which one can apply right at the beginning), the forcing chain was not needed anymore. The other important steps 1h and 2e are needed for step 4b which cracks this Killer.
A297 Walkthrough:
1. N578 !
a) Innie N1245 = R5C6 = 6
b) 16(2) = {79} locked for C5+N8
c) Outies N7 = 14(2) = {68} locked for C4+N8+29(6)
d) Naked triple (689) locked in R8C124 for R8; 9 also locked for N7
e) R8C5 = 7, R7C5 = 9
f) 13(3) must have one of (678) -> R7C7 = (678)
g) Outies N36 = 13(3)
h) ! Killer triple (678) locked in R7C47 + Outies N36 for R7
i) 7 locked in R9C23 @ N7 for R9
j) Both 7(2) <> 1

2. C6789 !
a) 1 locked in R789C6 @ N8 for C6
b) 11(2) = [29/38/56]
c) Innies C6789 = 16(2) = {79} locked for C6
d) 35(6) = 89{1467/2367/2457/3456} -> 9 locked for R6+N5; 8 locked for C5
e) Innies N3 = 8(2) <> 4,8,9
f) Innies N3 = 8(2) + 11(2) = 19(4) = {1279/1378/1567/2368/2359}
g) ! 15(3) <> 7 since 7{26/35} blocked by Killer pairs (27,37) of Innies N3 + 11(2)

3. R123 !
a) Outies R1 = 6(3) = {123} locked for N1
b) 10(3) must have one of (567) -> R1C1 = (567)
c) 9 locked in 30(6) @ R1 = 9{12378/12468/13458/13467/23457} since {125679} blocked by R1C1 = (567)
d) ! 30(6) = 49{1268/1358/1367/2357} since {123789} blocked by Killer triple (123) of 8(2) -> 4 locked for R1

4. R123+C9
a) Using Innies N3: Innies C9 = 11(2) <> 1; R4C9 <> 2,7
b) 7 locked in R123C9 @ C9 for N3
c) 4 locked in 26(4) @ N3 = {4589} locked for N3
d) 8 locked in 30(6) @ R1 = 1489{26/35} for N1 -> CPE: R2C45 <> 1
e) R1C6 = 9, R6C6 = 7
f) 8(2) = [26]/{35}
g) Hidden Single: R6C4 = 9 @ R6, R3C4 = 7 @ N2
h) Innies N3 = 8(2) = {26}/[71]
i) 35(6) = 789{146/236/245}: R3C5 <> 1,3 since R456C5 <> 6
j) 1 locked in R2C12 @ R2 for N1

5. R123
a) Hidden Single: R3C9 = 1 @ R3 -> R2C9 = 7, R7C8 = 7 @ C8
b) 11(3) = {236} locked for R1
c) 30(6) = {134589} -> R2C2 = 3
d) 8(2) = [26] -> R2C4 = 2, R2C5 = 6
e) 35(6) = {245789} -> 2,4,5 locked for C5; 2 also locked for N5
f) R1C5 = 1, R9C5 = 3 -> R9C4 = 4, R1C4 = 5, R2C1 = 1, R3C1 = 2
g) 4 locked in R1C23 for N1
h) 25(5) = {13678} since R45C4 = (13) and {13579} blocked by R2C3 = (59) -> R3C3 = 6, R5C3 = 8

6. R789+N4
a) 13(3) = {256} -> R7C7 = 6; 2,5 locked for C6
b) 7(2) @ N7 = [34/52]
c) R1C3 = 4, R9C6 = 1
d) Hidden Single: R7C2 = 4 @ N7 -> R7C1 = 3, R8C8 = 1 @ N9, R7C3 = 1 @ N7, R6C2 = 1 @ R6
e) 15(3) @ N4 = {159} -> R6C1 = 5, R5C1 = 9
f) 2,5 locked in R8C36 for R8
g) R8C9 = 3 -> R9C9 = 8
h) 15(3) @ N9 = {456} -> R7C9 = 5, R5C9 = 4, R6C9 = 6

7. Rest is singles.

Rating:
1.25. I used two Killer triples and a combined cage.


Last edited by Afmob on Wed Aug 06, 2014 5:32 am, edited 1 time in total.

Top
 Profile  
Reply with quote  
Andrew
 Post subject: Re: Assassin 297
PostPosted: Mon Jul 28, 2014 2:12 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin! It felt like a "one trick pony" to me; it took me quite a long time to find the trick (my step 14, Afmob's step 3d).

Here is my walkthrough for Assassin 297:
Prelims

a) R2C45 = {17/26/35}, no 4,8,9
b) R7C12 = {16/25/34}, no 7,8,9
c) R78C5 = {79}
d) R89C9 = {29/38/47/56}, no 1
e) R9C45 = {16/25/34}, no 7,8,9
f) 10(3) cage at R1C1 = {127/136/145/235}, no 8,9
g) 11(3) cage at R1C7 = {128/137/146/236/245}, no 9
h) 23(3) cage at R8C1 = {689}
i) 26(4) at R2C7 = {2789/3689/4589/4679/5678}, no 1

Steps resulting from Prelims
1a. Naked pair {79} in R78C5, locked for C5 and N8, clean-up: no 1 in R2C4
1b. Naked triple {689} in 23(3) cage at R8C1, locked for N7, clean-up: no 1 in R7C12

2. 45 rule on N7 2 outies R78C4 = 14 = {68}, locked for C4 and N8, clean-up: no 2 in R2C5, no 1 in R9C45
2a. Naked triple {689} in R8C124, locked for R8, 9 also locked for N7 -> R78C5 = [97], clean-up: no 2,3,4,5 in R9C9
2b. 1 in N8 only in R789C6, locked for C6

3. 35(6) cage at R3C5 = {146789/236789/245789/345689}, 9 locked for R6 and N5

4. 45 rule on N3 2 innies R23C9 = 8 = {17/26/35}, no 4,8,9

5. 45 rule on C6789 2 innies R16C6 = 16 = {79}, locked for C6

6. 45 rule on R1 1 innie R1C1 = 1 outie R2C2 + 4 -> R1C1 = {567}, R2C2 = {123}
6a. 10(3) cage at R1C1 = {127/136/145/235}
6b. R1C1 = {567} -> no 5,6,7 in R23C1
6c. 10(3) cage = {127/136/235} (cannot be {145} which clashes with R1C1 + R2C2 = [51], IOD clash), no 4 in R23C1
6d. Naked triple {123} in R2C12 + R3C1, locked for N1
6e. Killer triple 1,2,3 in R2C12 and R2C45, locked for R2, clean-up: no 5,6,7 in R3C9 (step 4)

7. 45 rule on N1245 1 innie R5C6 = 6
7a. R5C6 = 6 -> R45C7 = 8 = {17/35}

8. 35(6) cage at R3C5 = {146789/236789/245789/345689}, 8 locked for C5
8a. 7,9 of {146789/236789/245789} only in R6C46 -> no 1,2 in R6C46
8b. 6 of {146789/236789/345689} must be in R3C5 -> no 1,3 in R3C5

9. 45 rule on C9, using R23C9 = 8, 2 remaining innies R14C9 = 11 = [29]/{38/47/56}, no 1 in R1C9, no 1,2 in R4C9

10. 45 rule on N78 1 outie R7C7 = 1 innie R9C6 + 5 -> R7C7 = {678}, R9C6 = {123}

11. 45 rule on R789 3 innies R7C89 + R8C8 = 13 must contain one of 6,7,8 in R7C89
11a. Killer triple 6,7,8 in R7C4, R7C7 and R7C89, locked for R7
11b. 7 in R7 only in R7C789, locked for N9, clean-up: no 4 in R8C9

[25(5) cage at R2C9 and 15(3) cage at R5C9 almost form a combined cage, but the value in R7C9 can be repeated in R45C8 so I can’t see any way to use this observation.]

12. 45 rule on N4 2 outies R2C3 + R3C2 = 1 innie R5C3 + 6, IOU no 6 in R3C2
12a. Min R2C3 + R3C2 = 9 -> min R5C3 = 3

13. 4 in C9 only in R14C9 (step 9) or in 15(3) cage at R5C9 -> 15(3) cage = {159/168/249/348/456} (cannot be {258} which clashes with R89C9, cannot be {267/357}, locking out cages), no 7
[Alternatively 1 in R23C9 and 15(3) cage gives the same result.]
13a. 7 in R7 only in R7C78, CPE no 7 in R6C7

[I can see a contradiction move to eliminate one combination from 35(6) cage at R3C5, but there must be something better. Yes, there is, but it took me a long time to spot part of this step…]
14. 9 in R1 only in 30(6) cage at R2C1 = {124689/134589/134679/234579} (cannot be {125679} which clashes with R1C1, cannot be {123789} which clashes with R2C45), 4 locked for R1, clean-up: no 7 in R4C9 (step 9)
[Cracked. The rest is fairly straightforward.]

15. 7 in C9 only in R12C9, locked for N3
15a. 26(4) cage at R2C7 = {3689/4589}, no 2, 8 locked for N3, clean-up: no 3 in R4C9 (step 9)
15b. 8 in R1 only in R1C23, locked for N1
15c. 30(6) cage at R2C1 (step 14) contains 8 = {124689/134589}, no 7 -> R16C6 = [97]
15c. 30(6) cage = {124689/134589}, CPE no 1 in R2C5, clean-up: no 7 in R2C4
15d. 9 in N1 only in R2C3 + R3C23, CPE no 9 in R4C3

16. R3C4 = 7 (hidden single in N2)
16a. R6C4 = 9 (hidden single in C4)
16b. 1 in R2 only in R2C12, locked for N1
16c. R3C9 = 1 (hidden single in R3), R2C9 = 7 (step 4)
16d. 11(3) cage at R1C7 = {236} (only remaining combination), locked for R1 and N3
16e. R1C1 = 7 (hidden single in R1), R2C2 = 3 (step 6), R23C1 = [12]
16f. R2C4 = 2 (hidden single in R2) -> R2C5 = 6
16g. Clean-up: no 4,6 in R4C9 (step 9), no 4 in R7C1, no 5 in R7C2, no 5 in R9C5

17. R3C6 = 3 (hidden single in N2) -> R24C6 = 12 = {48}, locked for C6, clean-up: no 8 in R7C7 (step 10)

18. R3C3 = 6 (hidden single in N1), R3C4 = 7 -> 25(5) cage at R3C3 = {13678/34567}, no 9
18a. 25(5) cage = {13678/34567}, CPE no 3 in R5C5

19. 45 rule on N4 2 outies R2C3 + R3C2 = R5C3 + 6 (step 12)
19a. R2C3 + R3C2 from {459} = {45/59} (cannot be {49} because no 7 in R5C3), 5 locked for N1 and 36(7) cage at R2C3, no 5 in R4C123 + R5C2 + R6C3
19b. Naked pair {48} in R1C23, locked for R1 and N1
19c. Naked pair {59} in R2C3 + R3C2, locked for N1 and 36(7) cage at R2C3, no 9 in R4C12 + R5C2
19d. R2C3 + R3C2 = {59} = 14 -> R5C3 = 8, R1C23 = [84]
19e. 25(5) cage at R3C3 (step 18) = {13678} (only remaining combination) -> R45C4 = {13}, locked for C4 and N5 -> R1C45 = [51], R9C4 = 4 -> R9C5 = 3

20. 36(7) cage at R2C3 = {2345679} (only remaining combination), no 1
20a. R5C1 = 9, R6C2 = 1, R6C1 = 5 (hidden triple in N4), R7C1 = 3 -> R7C2 = 4
20b. Naked pair {68} in R89C1, locked for C1 and N7 -> R4C1 = 4, R8C2 = 9, R3C2 = 5, R2C3 = 9, R24C6 = [48], R3C5 = 8
20c. R4C2 = 6 (hidden single in N4)

21. R45C7 = {17} (hidden pair in N6), locked for C7 -> R7C7 = 6, R9C6 = 1 (step 10), R7C4 = 8
21a. Naked pair {25} in R7C69, locked for R7 -> R7C3 = 1, R7C8 = 7
21b. Naked pair {25} in R8C36, locked for R8 -> R8C9 = 3 -> R9C9 = 8, R8C78 = [41], R3C78 = [94]
21c. R8C7 = 4, R9C6 = 1 -> R9C78 = 11 = [29], R7C9 = 5, R4C9 = 9 -> R1C9 = 2 (step 9)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A297 at Easy 1.5 because of step 13. If I'd found Afmob's alternative, using a combined cage, then I'd have rated my walkthrough at 1.25.
Top
 Profile  
Reply with quote  
Ed
 Post subject: Re: Assassin 297
PostPosted: Fri Aug 01, 2014 8:52 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
As usual, Afmob and Andrew found this puzzle a lot easier than I did on the first solve, yet I found their key step much earlier than they did! Interesting that Andrew considers Locking-out cages as very routine. They feel that way to me too. I (generally) find them much easier than killer blocks (thirds or fourths) for example.

I did the phase before the 'one trick' differently (guess what technique! :) )to the other two so worth putting up. [Thanks for Afmob for finding some typos]

Start to A297
30 steps:
Preliminaries
Cage 16(2) n8 - cells ={79}
Cage 7(2) n8 - cells do not use 789
Cage 7(2) n7 - cells do not use 789
Cage 8(2) n2 - cells do not use 489
Cage 11(2) n9 - cells do not use 1
Cage 23(3) n7 - cells ={689}
Cage 10(3) n1 - cells do not use 89
Cage 11(3) n3 - cells do not use 9
Cage 26(4) n3 - cells do not use 1

No routine clean-up except where stated
1. "45" on n1245: 1 innie r5c6 = 6
1a. -> r45c7 = 8 = {17/35}(no 2,4,8,9)

2. 16(2)n8 = {79} only: both locked for c5 and n8

3. "45" on n7: 2 outies r78c4 = 14 = {68} only: both locked for c4 and n8
3a. 6 & 8 also locked for 29(6) -> no 6, 8 in r789c3+r9c2

4. Naked triple {689} in r8c124: all locked for r8; 9 also locked for n7
4a. r78c5 = [97]

5. "45" on n78: 1 innie r9c6 + 5 = 1 outie r7c7
5a. r9c6 = (123), r7c7 = (678)

6. 9 in n9 in 16(4)r8c7 = {1249} only or in 11(2) -> [47] blocked from 11(2) since it would leave no 9 for n9 (Locking-out cages)
6a. 11(2)= [29/38/56](no 4,7; no 2,3,5 in r9c9)

7. "45" on n3: 2 innies r23c9 = 8 (no 4,8,9)

8. "45" on c9 (remembering h8(2)r23c9): 2 innies r14c9 = 11 (no 1)

9. 4 in c9 in h11(2) = {47} or in 15(3)r5c9 -> 7 in 15(3) must also have 4 or there would be no 4 for c9 but {744} not possible in a 15(3) -> no 7 in 15(3)r5c9

Andrew found a different way to do this next step
10. "45" on r1: 3 outies r2c12+r3c1 = 6 = {123} only: all locked for n1

11. "45" on r1: 1 innie r1c1 - 4 = 1 outie r2c2
11a. r1c1 = (567)

12. 9 in r1 only in 30(6)
12a. but {125679} blocked by r1c1 = (567)
12b. and {123789}, with 1,2,3 only in r2c2 and r1c456, blocked by 8(2)n2 = 1/2/3 since r2c45 see all of r2c2+r1c456 in 30(6)
12c. ={124689/134589/134679/234579}
12d. must have 4 which is only in r1: 4 locked for r1
12e. no 7 in r4c9 (h11(2)r14c9)

13. 7 in c9 only in n3: locked for n3

14. 4 in n3 only in 26(4) = {4589} only: 5,8 locked for n3
14a. no 3 in r23c9 (h8(2)r23c9)

15. 3 in n3 only in r1: locked for r1

16. 8 in r1 only in 30(6) = {124689/134589}(no 7)
16a. must have 1 which is only in r1c456+r2c2 -> no 1 in r2c456 since they see all those four cells
16b. no 7 in r2c4

17. "45" on c6789: 2 innies r16c6 = 16 = [97] only permutation

18. 35(6)r3c5 must have 7 = {146789/236789/245789}
18a. must have 9 -> r6c4 = 9
18b. must have 8 -> 8 locked for c5
18c. 6 in {146789/236789} must be in r3c5 -> no 1,3 in r3c5

19. Hidden single 7 in n2 -> r3c4 = 7

20. 15(3)r2c6 = {258/348}(no 1)

21. 1 in n2 only in r1: 1 locked for r1 and 30(6)r1c2 -> no 1 in r2c2

22. 11(3)n3 = {236} only: 2 & 6 locked for r1 and n3

23. "45" on r1: 1 innie r1c1 - 4 = 1 outie r2c2 = [73], only permutation

24. Hidden single 3 in n2 -> r3c6 = 3
24a. -> r24c6 = 12 = {48} only: 4 locked for c6

25. 8(2)n2 = [26] only permutation

26. 35(6)r3c5 = {245789}: 2,4,5 all locked for c5

27. 6 in n1 only in r3c23: r46c3 sees both those cells -> no 6 in r46c3

28. Hidden single 6 in c3 -> r3c3 = 6

29. 7(2)n8 = [43] only permutation
29a. r1c45 = [51]

30. "45" on n14: 1 remaining innie r5c3 = 8

On from there.
Cheers
Ed
Top
 Profile  
Reply with quote  
wellbeback
 Post subject: Re: Assassin 297
PostPosted: Wed Aug 06, 2014 11:50 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
This took me a long time at first, until I found the way in. We all seemed to go approximately the same way. Here is mine....

Hidden Text:
1. 16(2)n8 = {79}
-> Outies n7 r78c4 = H14(2) = {68}
-> 23(3)n7 = [{69}8] or [{89}6]
-> 16(2)n8 = [97]

2. r9c789 must contain 9 and one of (68)
Since 16(4) cannot contain both 9 and one of (68) -> r9c9 from (689)
-> 11(2)n9 from [56], [38], [29] (No 147)

3. Innies n1245 -> r5c6 = 6
-> r45c7 either {17} or {35}

4. Innies n3 -> r23c9 = H8(2) - no 489
Outies r1 -> r2c12 + r3c1 = H6(3) = {123}
8(2)n2 must contain one of (123).
Whichever it is goes in r3c1 and also in r1c789
Also whatever is in r2c2 (from 123) must also go in r1c789
-> 11(3)n3 contains two of (123)
-> 11(3)n3 from {128}, {137}, {236}. (No 459)
-> (49) in n3 in the 26(4)

5. Given r23c9 = +8 -> Innies c9 r14c9 = H11(2).
-> 1 in c9 either in r3c9 or in the 15(3)
Whichever it is 7 in c9 cannot go in the 15(3) in c9.
Since r1c9 cannot be a 4 -> r4c9 cannot be 7.
-> 7 in c9 locked in r12c9
-> 26(4)n3 = {4589}
-> r23c9 from [71] or [62]

6. Outies n789 -> r5c9+r6c789 = H20(4)
r23c9 = H8(2) from [71] or [62]
r45c7 in n6 is also an 8(2) (either {17} or {35})

-> Whichever pair is in r23c9 must either both go in r45c7 or both go in r6c78.
If the former - the pair must be {17}.
If the latter - this puts r56c9 = +12, r7c9 = 3 which leaves only place for 1 in c9 in r3c9, so again the pair must be {17}.

-> Either way, r23c9 = [71]
-> 11(3)n3 = {236}
-> r2c2,r3c1 = {23}
-> r2c1 = 1
-> Only possibility is 10(3)n1 = [712] and r2c2 = 3
-> 8(2)n2 = [26]

7. Innies c6789 -> r16c6 = H16(2) = [97]

8. 35(6)r3c5 does not contain a 6.
-> It must be {245789}
-> HS r6c4 = 9
Also HP (13) in c5 -> r19c5 = [13]
-> r9c4 = 4

9. 7 in n6 only in r45c7 -> r45c7 = {17}
-> (17) in n9 in r789c8
-> (since r789c6 = {125}) -> r7c7 = 6, r9c6 = 1, r78c6 = {25}
-> 7(2)n7 = {34}
Also r78c4 = [86]
-> 23(3)n7 = [{89}6]
Also since 16(4)n9 contains an 8 or 9 -> it cannot contain a 7
-> r78c8 = [71]
-> r8c79 = [43]
-> r9c9 = 8
-> r9c78 = {29}
-> r7c9 = 5
-> r78c6 = [25]
-> r7c3 = 1, r8c3 = 2, r9c23 = {57}

Also r6c78 = H10(2) and r56c9 = 10(2)
-> r45c8 = {35}
-> r4c9 = 9
-> r1c9 = 2
-> r56c9 = {46}
-> r6c78 = {28}

10. 1 in n5 in r45c4
-> HS 1 in n4 -> r6c2 = 1
-> r56c1 = [95]
-> HS 3 in r6 -> r6c3 = 3

etc.
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 5 posts ] 

Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC


Who is online

Users browsing this forum: No registered users and 4 guests

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB® Forum Software © phpBB Group