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Hi,

this killer seems to require some work until the end : I was surprised to have to do (with my solving path) quite difficult moves whereas I thought it was cracken since many placements have been done. Several versions have been tried before I get this one with the right difficulty. I hope you will enjoy it.


ASSASSIN 159




3x3::k:2816:5889:4098:4098:4098:4357:4357:4357:4360:2816:5889:5889:4098:5645:5645:5645:1808:4360:5889:3091:3604:3604:3604:5645:2840:1808:4360:5889:3091:3091:8222:5151:2840:2840:8482:8482:8222:8222:8222:5151:1576:1576:8482:1579:1579:5933:3886:3886:8222:5151:2866:2866:8482:8482:5933:3886:4664:4664:4664:4923:2866:3389:2366:2879:5933:5933:4930:4923:4923:4923:3389:2366:2879:5933:4930:4930:4930:5197:5197:5197:2366:

Solution :




SS.Score : 1.36

Thanks manu for a nice Assassin! As you said it requires work right until the end.

I didn't use any difficult moves but because of the length of my solving path I'll rate A159 at 1.25, even though none of my steps are at that level.

Here is my walkthrough; a few minor corrections have been made. Once I'd realised the importance of the 32(5) cage at R4C4 things seemed to flow.

Prelims

a) R12C1 = {29/38/47/56}, no 1
b) R23C8 = {16/25/34}, no 7,8,9
c) R5C56 = {15/24}
d) R5C89 = {15/24}
e) R78C8 = {49/58/67}, no 1,2,3
f) R89C1 = {29/38/47/56}, no 1
g) 11(3) cage in R3C7 = {128/137/146/236/245}, no 9
h) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2
i) 11(3) cage in R6C6 = {128/137/146/236/245}, no 9
j) R789C9 = {126/135/234}, no 7,8,9
k) R9C678 = {389/479/569/578}, no 1,2
l) 32(5) cage at R4C4 = {26789/35789/45689}, no 1, CPE no 8,9 in R5C4
m) 33(5) cage in N6 = {36789/45789}, 7,8 locked for N6

1. Naked quad {1245} in R5C5689, locked for R5

2. 45 rule on R1234 4 innies R4C4589 = 30 = {6789}, locked for R4
2a. Max R4C23 = 9 -> min R3C2 = 3
2b. Max R4C67 = 9 -> min R3C7 = 2

3. 45 rule on N6 2 innies R46C7 = 6 = {15/24}
3a. Naked quad {1245} in R46C7 + R5C89, locked for N6

4. 45 rule on C9 3 innies R456C9 = 19 = {289/469/478/568} (cannot be {379} because R5C9 only contains 1,2,4,5), no 1,3, clean-up: no 5 in R5C8

5. 32(5) cage at R4C4 = {26789/35789} (cannot be {45689} because 4,5 only in R6C4), no 4, CPE no 7 in R5C4
5a. 2,5 only in R6C4 -> R6C4 = {25}
5b. Killer pair 2,5 in R5C56 and R6C4, locked for N5

6. 20(3) cage at R4C5 = {389} (only remaining combination, cannot be {479} because R5C4 only contains 3,6) -> R5C4 = 3, R46C5 = {89}, locked for C5 and N5

7. 32(5) cage at R4C4 (step 5) = {26789} -> R6C4 = 2, 8,9 locked in R5C123, locked for R5 and N4, clean-up: no 4 in R5C56
7a. Naked pair {15} in R5C56, locked for R5 and N5 -> R4C6 = 4
7b. R46C7 = {15} (hidden pair in N6), locked for C7
7c. R6C8 = 3 (hidden single in N6), clean-up: no 4 in R23C8

8. R4C6 = 4 -> R34C7 = 7 = [25/61], R3C7 = [26]
8a. Killer pair 2,6 in R23C7 and R3C8, locked for N3

9. 1 in N9 locked in R789C9, locked for C9
9a. R789C9 = {126/135}, no 4

10. R123C9 = {359/458}, no 7, 5 locked for C9 and N3, clean-up: no 2 in R23C8, no 3 in R789C9 (step 9a)
10a. Naked pair {16} in R23C8, locked for C8 and N3 -> R3C7 = 2, R4C7 = 5 (step 8), R6C7 = 1, clean-up: no 7 in R78C8
10b. Naked triple {126} in R789C9, locked for C9 and N9 -> R5C89 = [24], clean-up: no 8 in R123C9 (step 10)
10c. Naked triple {359} in R123C9, locked for C9 and N3

11. Naked pair {78} in R46C9, locked for N6 -> R4C8 = 9, R5C7 = 6, R46C5 = [89], R46C9 = [78], R4C4 = 6, R6C6 = 7, R7C7 = 3 (cage sum), clean-up: no 4 in R78C8
11a. Naked pair {58} in R78C8, locked for C8 and N9

12. R9C678 = {479} (only remaining combination, cannot be {389/569/578} because 3,5,6,8 only in R9C6) -> R9C6 = 9, R9C78 = {47}, locked for R9 and N9 -> R8C7 = 9, clean-up: no 2,4,7 in R8C1, no 2 in R9C1

13. R1C678 = {278/458/467} (cannot be {368} because 3,6 only in R1C6), no 1,3
13a. 2,5 of {278/458} must be in R1C6 -> no 8 in R1C6

14. R6C23 = {456} -> 15(3) cage at R6C2 = {456} (only remaining combination)

15. 45 rule on N89 2 outies R79C3 = 11 = [56/65/83/92], no 1,2,4,7 in R7C3, no 1,8 in R9C3
[I’d seen “cell cloning” R6C1 = R7C2 first but then looked for a technically simpler step.]

16. 45 rule on N23 2 outies R13C3 = 5 = [14/23/41]
16a. 45 rule on N1 1 remaining innie R3C2 = 1 outie R4C1 + 6 -> R3C2 = {789}

17. 19(4) cage at R8C4 = {1378/1468/1567/2458} (cannot be {2368} because 2,3,6 only in R9C35, cannot be {2467/3457} because 4,7 only in R8C4)
17a. 4,7 only in R8C4 -> R8C4 = {47}
17b. 3 of {1378} must be in R9C3 -> no 3 in R9C5

18. 3 in N8 locked in R8C56, locked for R8, clean-up: no 8 in R9C1
18a. 19(4) cage at R7C6 must contain 3 and 9 = {1369/2359}, no 4,7,8

19. 8 in C6 locked in R23C6, locked for N2 and 22(4) cage at R2C5
19a. 22(4) cage at R2C5 = {1678/2578/3478} (cannot be {3568} because R2C7 only contains 4,7)
19b. 4,7 of {3478} must be in R2C57 -> no 3 in R2C5

20. R1C7 = 8 (hidden single in C7), clean-up: no 3 in R2C1
20a. R1C678 (step 13) = {278/458}, no 6

21. R3C345 = {149/347/356} (cannot be {167} which clashes with R3C8)
21a. 9 of {149} must be in R3C4 -> no 1 in R3C4
21b. 6 of {356} must be in R3C5 -> no 5 in R3C5

22. Hidden killer pair 4,7 in R7C45 and R8C4 for N8 -> R7C45 must contain one of 4,7
22a. R7C345 = {279/459/468/567} (cannot be {189} which doesn’t contain one of 4,7), no 1

23. 22(4) cage at R2C5 (step 19a) = {1678/3478} (cannot be {2578} which clashes with R1C6), no 2,5
23a. 2 in N2 locked in R1C56, locked for R1, clean-up: no 9 in R2C1, no 3 in R3C3 (step 16)

24. Naked pair {14} in R13C3, locked for C3 and N1, clean-up: no 7 in R12C1
24a. 4 in 15(3) cage at R6C2 locked in R67C2, locked for C2
24b. 4 in N7 locked in R7C12, locked for R7

25. R8C4 = 4 (hidden single in N8)

26. R7C345 (step 22a) = {279/567}, no 8, 7 locked for R7, clean-up: no 3 in R9C3 (step 15)
26a. R9C4 = 8 (hidden single in C4)
26b. 1 in C4 locked in R12C4, locked for N2 and 16(4) cage at R1C3 -> R1C3 = 4, R3C3 = 1 (step 16), R23C8 = [16], R1C8 = 7, R1C6 = 2 (step 20a), R2C7 = 4, R9C78 = [74]

27. 22(4) cage at R2C5 (step 23) = {3478} -> R2C5 = 7, R23C6 = {38}, locked for C6 and N2 -> R3C5 = 4, R3C4 = 9 (step 21), R12C4 = [15], R1C5 = 6, R7C4 = 7, clean-up: no 3 in R4C1 (step 16a)

28. R7C345 (step 26) = {279/567}
28a. 6,9 only in R7C3 -> R7C3 = {69}, clean-up: no 6 in R9C3 (step 15)

29. R8C5 = 3 (hidden single in C5), R78C6 (step 18a) = {16}, locked for C6 and N8 -> R5C56 = [15]

30. R79C3 (step 15) = [92] (cannot be [65] which clashes with R6C3), R79C5 = [25], R4C3 = 3, clean-up: no 6 in R8C1

31. Naked pair {16} in R7C69, locked for R7
31a. 6 in 15(3) cage at R6C2 locked in R6C23, locked for R6

32. R8C9 = 2 (hidden single in C9)

33. Naked pair {58} in R8C18, locked for R8

34. R6C3 = 5 (hidden single in C3), R6C12 = [46], R7C2 = 4

35. R4C3 = 3 -> R34C2 = 9 = [72/81]
35a. Killer pair 1,7 in R34C2 and R8C2, locked for C2 -> R9C2 = 3, R9C1 = 6, R8C1 = 5

and the rest is naked singles

Thanks for the new Assassin, manu! I found this Killer a lot easier than SudokuSolver suggested though no push-over since it resists being cracked until the end.

A159 Walkthrough:

1. R456
a) Naked quad (1245) locked in R5C5689 for C5
b) 32(5) = 789{26/35} since {45689} blocked by Killer pair (45) of 6(2) @ N5
-> CPE: R5C4 <> 7,8,9
c) Killer pair (25) locked in 6(2) @ N5 + 32(5) for N5
d) 20(3) = {389} since R5C4 = (36) -> R5C4 = 3; 8,9 locked for C5+N5
e) 32(5) = {26789} -> 8,9 locked for R5+N4; 2 locked for C4+N5
f) 6(2) @ N5 = {15} locked for R5+N5
g) 6(2) @ N6 = {24} locked for N6
h) Innies N6 = 6(2) = {15} locked for C7+N6

2. R456
a) Innies R1234 = 30(4) = {6789} locked for R4
b) R4C6 = 4
c) Hidden Single: R6C4 = 2 @ N5
d) 11(3) @ R6 = 1{37/46} since R6C6 = (67) and R6C7 = (15) -> R6C7 = 1; R7C7 = (34)
e) R4C7 = 5 -> R3C7 = 2
f) Hidden Single: R5C8 = 2 @ C8 -> R5C9 = 4
g) 12(3): R3C2 = (789) since R4C2 = (123)
h) 33(5) = {36789} -> 3 locked for R6
i) 15(3) = 5{37/46} since R6C23 = (4567) and R6C6 = (67) blocks {267}

3. C789
a) 9(3) = 1{26/35} -> 1 locked for C9
b) 17(3) @ C9 = {359} locked for C9+N3 since {368} blocked by Killer pair (36) of 9(3)
c) 7(2) = {16} locked for C8+N3
d) 9(3) = {126} locked for C9+N9
e) Hidden Single: R4C4 = 6 @ R4
f) R6C6 = 7 -> R7C7 = 3, R6C9 = 8, R4C9 = 7, R4C8 = 9
g) 13(2) = {58} locked for C8+N9
h) 20(3) = {479} since R9C78 = (479) -> R9C6 = 9; 4,7 locked for R9+N9
i) R8C7 = 9
j) 17(3) = {278/458/467} since R1C78 = (478); R1C6 = (256)

4. N78
a) 11(2) = {38/56}
b) 23(5) = 1{2389/2479/2569/3478/4567} since other combos blocked by Killer pairs (35,36,58) of 11(2) @ N7
-> 1 locked for N7
c) 19(4) @ R7 = 9{127/136/235} <> 4,8 because {1459} blocked by R5C6 = (15)
d) 19(4) @ R9 <> {2368/2467/3457} since 4,7 only possible @ R8C4 and R89C4 <> 2,3,6

5. C456 !
a) Outies C6789 = 11(3) = {137/146/245} since R5C5 = (15); R28C5 <> 1,5
b) ! Killer pair (15) locked in 19(4) @ R7 + R5C6 for C6
c) 17(3) = 7{28/46} -> 7 locked for R1+N3
d) 22(4) = {3478} -> R2C5 = 7, R2C7 = 4; 3,8 locked for C6+N2
e) R1C8 = 7, R1C7 = 8 -> R1C6 = 2
f) 19(4) @ R7 = {1369} since 2,3 only possible @ R8C5 -> R8C5 = 3; 1,6 locked for C6+N8
g) 19(4) @ R9 = {2458} -> R8C4 = 4; 2,5,8 locked for R9
h) 16(4) = {1456} -> 4,6 locked for R1; R12C4 = {15} locked for C4+N2+16(4)
i) 14(3) @ R3 = {149} since R3C4 = 9 -> R3C4 = 9 , R3C5 = 4, R3C3 = 1
j) R3C8 = 6, R2C8 = 1, R2C4 = 5, R9C4 = 8, R7C4 = 7

6. C123+R8
a) 18(3) = 7{29/56} -> R7C3 = (69)
b) 11(2) @ N7 = [56/83]
c) Naked pair (58) locked in R8C18 for R8
d) 8 locked in R78C1 @ N7 for C1
e) 11(2) @ N1 = [56/92]
f) 3 locked in 23(5) @ N1 = 138{29/56} since {23567} blocked by R2C1 = (26)
-> R4C1 = 1; 8 locked for N1+R2
g) Killer pair (35) locked in 11(2) @ N7 + R3C1 for C1

7. C123
a) R1C1 = 9 -> R2C1 = 2
b) 23(5) @ N7 = {13478} -> R6C1 = 4, R7C1 = 8, R9C2 = 3, R8C2 = 1, R8C3 = 7

8. Rest is singles.

Rating: 1.0 - Hard 1.0. I used Killer pairs and some cage blockers.

Manu

An excellent puzzle - it really does hang on.

Maurice

Well, manu described this puzzle perfectly. Was a hard to see key move that made the big difference (step 15a) for a lot-of-work ending. I don't tend to do much permutation clean-up in my solving so needed a different way than Andrew used. I missed Afmob's ! step 5 also.

See Andrew's WT for the opening to the puzzle since it was so similar. Thanks Manu and Andrew!

Walkthrough for Assassin 159


Andrew's step 14 to above. Mirrored my way very closely, then we diverged. I've taken it to singles my way.

Great to have a puzzle with many ways to proceed. Thanks manu!

15. "45" n8: 2 outies r79c3 = h11(2)n7 (no 1)
15a. = [92/83] ({56} blocked by 15(3)n4 needing at least one of 5/6 in r6c3+r7c2)

Above was the key step: now missing lots of cleanup trying to eventually getting it to singles. However, it's not totally cracked until step 28!
16. 19(4)r8c4 must have 2/3 for r9c3 and cannot have both of {47}
16a. = {1378/2458}(no 6) ({2368} blocked by no 2,3,6 in r89c4)
16a. = [2/3..], not both -> 2,3 only in r9c3
16b. = [4/7..] -> r8c4 = (47)
16c. must have 8 -> r9c4 = 8

17. 3 in n8 only in 19(4)r7c6 = 39{16/25}(no 4,7) = [1/5...]
17a. 3 locked for r8

18. Killer pair 1,5 between 19(4)r7c6 and r9c5: both locked for n8

19. Naked pair {47} in r78c4: both locked for c4 & n8

20. Naked triple {159} in r123c4: 1,5 locked for n2
20a. no 7 in r2c7 (i/o n3: 1 outie r1c6 + 2 = 1 remaining innie r2c7)

21. 8 in c6 only in 22(4)n2 -> no 8 in r2c7
21a. r2c7 = 4
21b. 17(3)n2 = [287] (only permutation)

22. "45" n2: 2 outies r13c3 = 5 = {14}: both locked for n1 & c3

23. r12c4 cannot have both {59} = 14 because it's a 16(4) cage
23a. must have 1: locked for c4 & 16(4)n1
23b. ->r13c3 = [41]

24. r3c45 = 13 = [94](last permutation)
24a. r23c8 = [16]
24b. r12c4 = [15]
24c. r1c5 = 6 (cage sum)

25. r7c345 = 18 = [972](last permutation)
25a. r9c3 = 2 (h11(2)n7)
25b. r8c4 = 4, r9c5 = 5 (cage sum)
25c. no 6 in r8c1

26. Naked pair {58} in r8c18: both locked for r8
26a. r6c3 = 5 (hsingle c3)

27. r4c3 = 3
27a. r34c2 = 9 = [81/72]
27b. r1c2 = 5 (hsingle c2)

28. hidden pair {58} in n7 in r7c1 + r8c1: both locked for c1

29. r12c1 = [92] (last permutation)

30. r345c1 = [317]
30a. r89c1 = [56]

Rest are singles.
Cheers
Ed