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Here is a "non consecutive killer". The rules are the same as for a killer sudoku, with one further condition : adjacent cells (in a row of a column) cannot have consecutive digits. For instance, the 11(2) cage at n6 cannot be {56}. You certainly will find other examples !
This puzzle is not solvable without the non-consecutive condition.

I hope this one will be the beginning of a long series. So, try it and enjoy !



3x3::k:6656:6656:6656:6656:7428:7428:2566:2566:4104:6656:3338:3338:3338:7428:3342:3342:3342:4104:6162:6162:2324:2324:7428:7428:2328:2328:4104:6162:3100:8989:8989:8989:3872:2328:1826:1826:6162:3100:3622:3622:8989:3872:3872:2859:5932:2605:2605:4143:3622:8989:8989:8989:2859:5932:2870:4143:4143:4921:4921:2875:2875:5932:5932:2870:4160:4160:4160:4921:3908:3908:3908:6983:2870:3657:3657:4921:4921:6983:6983:6983:6983:

Solution :



PS: You can use (for instance) SSsolver : paste, and click on : File -> Puzzle Type -> Non Consecutive.

An image for those of you who like to scribble and solve the Joe Casey way:

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Thanks manu! This is only the second non-consecutive killer I've done (see below my walkthrough for more about the first one which was created by Nasenbaer). Manu said that he hopes this is the beginning of a long series so I'll call this NonCon 2, following on from Nasenbaer's puzzle.

As you said it's not solvable without the non-consecutive condition. It's needed right through to the end; without it there would be several URs.

Ed told me that he solved this puzzle earlier this week, probably before I found it, but wouldn't be able to post his walkthrough before the weekend so I should go ahead and post my one. Thanks Ed! I'll be interested to see your walkthrough; I hope you found an easier breakthrough than I did.


Here is my walkthrough for NonCon 2. It's fairly long because I've given non-consecutive eliminations, usually as separate sub-steps.

Prelims (including non-consecutive eliminations)

a) R1C78 = {19/28/37/46}, no 5
b) R3C34 = {18/27/36} (cannot be {45} which are consecutive), no 4,5,9
c) R45C2 = {39/48/57}, no 1,2,6
d) R4C89 = {16/25} (cannot be {34} which are consecutive)
e) R56C8 = {29/38/47} (cannot be {56} which are consecutive), no 1,5,6
f) R6C12 = {19/28/37/46}, no 5
g) R7C67 = {29/38/47} (cannot be {56} which are consecutive), no 1,5,6
h) R9C23 = {59/68}
i) 9(3) cage at R3C7 = {126/135} (cannot be {234} because at least two consecutive numbers must be adjacent), no 4,7,8,9
j) 11(3) cage in N7 = {128/137/146/236/245} (note that no combinations have been eliminated at this stage because consecutive numbers can be in R79C1), no 9
k) 19(5) cage in N8 = {12349/12358/12367/12457/13456}

Steps resulting from Prelims
1a. 9(3) cage at R3C7 = {126/135}, CPE no 1 in R12C7, clean-up: no 9 in R1C8
1b. 19(5) cage in N8 = {12349/12358/12367/12457/13456}, 1 locked for N8

2. 45 rule on N3 2 outies R2C6 + R4C7 = 3 = {12}, CPE no 2 in R2C7
2a. Killer pair 1,2 in R4C7 and R4C89, locked for R4 and N6, clean-up: no 9 in R56C8
2b. R2C6 and R4C7 = {12} -> no 1,2 in R1C6, R2C5, R3C6, R3C7 and R4C8 (adjacent cells cannot have the same or consecutive values), clean-up: no 5,6 in R4C9
2c. 9(3) cage at R3C7 = {126/135} = [531/612/621] (because R3C8 and R4C8 cannot be consecutive), no 3 in R3C7, no 5,6 in R3C8
2d. R3C7 = {56} -> no 5,6 in R2C7 + R3C6 (adjacent cells cannot have the same or consecutive values)

3. R3C34 = {18/27} (cannot be {36} which clashes with R3C78), no 3,6
3a. 45 rule on R12 3 outies R3C569 = 17 = {269/359/458/467} (cannot be {179/278} which clash with R3C34, cannot be {368} which clashes with R3C78), no 1
3b. Killer pair 5,6 in R3C569 and R3C7, locked for R3

4. 13(3) cage at R2C6 = {139/148/157/238/247} (cannot be {256} which clashes with R3C7, cannot be {346} which doesn’t contain 1 or 2), no 6
4a. R2C6 = {12} -> no 1,2 in R2C8

5. 45 rule on N7 2 outies R6C3 + R8C4 = 12 = {39/46/57}/[66], no 1,2

6. 45 rule on R2 3 innies R2C159 = 19 = {289/379/469/478/568}, no 1

7. 45 rule on N12 3(2+1) innies R2C6 + R3C12 = 13, max R2C6 = 2 -> min R3C12 = 11, no 1
7a. 45 rule on N12 2 outies R45C1 = 1 innie R2C6 + 11, min R2C6 = 1 -> min R45C1 = 12, no 1,2 in R5C1

8. 45 rule on N1247 3(2+1) innies R2C6 + R45C3 = 1 outie R8C4
8a. Min R2C6 + R45C3 = 5 -> min R8C4 = 5, clean-up: no 8,9 in R6C3 (step 5)
8b. Max R8C4 = 9 -> max R2C6 + R45C3 = 9 -> max R45C3 = 8, no 8,9 in R4C3, no 6,7,8,9 in R5C3

9. Hidden killer pair 1,2 in R5C3 and R6C12 for N4, R6C12 cannot contain both of 1,2 -> R5C3 and R6C12 must each contain one of 1,2
9a. R5C3 = {12}, R6C12 = {19/28} (cannot be {37/46} which don’t contain 1 or 2), no 3,4,6,7
9b. R45C1 = R2C6 + 11 (step 7a), R2C6 = {12} -> R45C1 = 12,13 = {39/48/49/57/58} (cannot be {67} which are consecutive), no 6
9c. Killer triple 7,8,9 in R45C1, R45C2 and R6C12, locked for N4, clean-up: no 5 in R8C4 (step 5)

10. 7 in N4 locked in R45C12, CPE no 7 in R3C2
10a. 6 in N4 locked in R46C3, locked for C3, CPE no 6 in R6C567, clean-up: no 8 in R9C2

11. 14(3) cage at R5C3 = {149/158/167/239/248/257} (cannot be {347/356} which don’t contain 1 or 2)
11a. R5C3 = {12} -> no 1,2 in R56C4

12. 45 rule on N124 4(3+1) innies R2C6 + R456C3 = 12
12a. R46C3 must contain 6 (step 10a) -> remaining three innies = 6 = {114/123}, no 5 in R46C3, clean-up: no 7 in R8C4 (step 5)
12b. At least one of R2C6 + R5C3 must contain 1, CPE no 1 in R2C3

13. 1,2 in N5 locked in R56C56 -> they must be in either R5C5 + R6C6 or R5C6 + R6C5 (otherwise there would be adjacent consecutive numbers) -> R56C6 must contain one of 1,2
13a. Killer pair 1,2 in R2C6 and R56C6, locked for C6, clean-up: no 9 in R7C7

14. Hidden killer pair 5,7 in R45C1 and R45C2 for N4, R45C2 must contain both or neither of 5,7 -> R45C1 must contain both or neither of 5,7 -> R45C1 (step 9b) = {39/48/49/57} (cannot be {58} which only contains one of 5,7)
14a. 24(4) cage at R3C1 = {3489/3579/4578} (cannot be {2589} which doesn’t contain any of the combinations for R45C1), no 2
14b. 5 of {3579/4578} must be in R45C1 -> 7 of these combinations must also be in R45C1, no 7 in R3C1

15. R2C6 + R3C12 = 13 (step 7), R2C6 = {12} -> R3C12 = 11,12 = {38/39/48}, R3C34 = {18/27} -> combined cage R3C1234 = {3827/3918/3927/4827}
15a. R3C569 (step 3a) = {359/458/467} (cannot be {269} which clashes with R3C1234), no 2

16. Hidden killer pair 1,2 in R3C34 and R3C8 for R3, R3C34 must contain one of {12} -> R3C8 = {12}
16a. 9(3) cage at R3C7 = {126} (only remaining combination) -> R3C7 = 6, clean-up: no 4 in R1C78
16b. R3C7 = 6 -> no 7 in R2C7 + R3C6 (adjacent cells cannot have consecutive values)
16c. R3C8 + R4C7 = {12}, CPE no 2 in R1C7, clean-up: no 8 in R1C8

17. R3C569 (step 15a) = {359/458}, no 7
17a. 7 in R3 locked in R3C34 = {27}, locked for R3 -> R3C8 = 1, R4C7 = 2, R4C9 = 1, R4C8 = 6, R2C6 = 1 (step 2), clean-up: no 9 in R1C7, no 9 in R7C6
17b. 13(3) cage at R2C6 (step 4) = {139/148} (cannot be {157} because 5,7 only in R2C8), no 5,7
17c. R4C7 = 2 -> no 3 in R4C6 + R5C7 (adjacent cells cannot have consecutive values)
17d. R4C8 = 6 -> no 7 in R5C8 (adjacent cells cannot have consecutive values), clean-up: no 4 in R6C8

18. 5 in N3 locked in R123C9, locked for C9
18a. 16(3) cage in N3 = {259/457} (cannot be {358} which clashes with R2C78), no 3,8

19. R6C3 = 6 (hidden single in C3) -> R7C23 = 10 = {19/28/37}, no 4,5
19a. R6C3 = 6 -> no 5,7 in R6C4, no 7 in R7C3 (adjacent cells cannot have consecutive values), clean-up: no 3 in R7C2

20. R6C3 = 6 -> R8C4 = 6 (step 5), R8C23 = 10 = {19/28/37}, no 4,5
20a. R8C4 = 6 -> no 5,7 in R7C4, R8C3, R8C5 and R9C4 (adjacent cells cannot have consecutive values), clean-up: no 3 in R8C2

21. 4 in N7 locked in R789C1, locked for C1, clean-up: no 8 in R45C1 (step 14)
21a. 11(3) cage in N7 = {146/245}, no 3,7,8

22. 7 in N7 locked in R78C2, locked for C2, clean-up: no 5 in R45C2
22a. 3 in N7 locked in R78C3, locked for C3 -> R4C3 = 4, R5C3 = 1 (step 12a), clean-up: no 8 in R45C2, no 9 in R6C12, no 9 in R7C2 (step 19), no 9 in R8C2 (step 20)
22b. R4C3 = 4 -> no 3 in R4C2, no 3,5 in R4C4 (adjacent cells cannot have consecutive values) -> R45C2 = [93] , clean-up: no 8 in R6C8, no 5 in R9C3

23. 35(7) cage at R4C3 containing 4 must also contain 6 -> R5C5 = 6 (hidden single in this cage), R1C6 = 6 (hidden single in C6)

24. Naked pair {57} in R45C1, locked for C1, clean-up: no 2 in 11(3) cage in N7 (step 21a)
24a. Naked triple {146} in 11(3) cage in N7, locked for C1 and N7 -> R9C2 = 5, R9C3 = 9
24b. R9C3 = 9 -> no 8 in R8C3 and R9C4 (adjacent cells cannot have consecutive values), clean-up: no 2 in R8C2 (step 20)

25. R45C1 = {57} -> 24(4) cage at R3C1 (step 14a) = {4578} (only remaining combination, cannot be {3579} because 3,9 only in R3C1) -> R3C12 = [84], R6C12 = [28], R8C2 = 7, R7C2 = 2, R1C2 = 1, R2C2 = 6, R8C3 = 3, R7C3 = 8, clean-up: no 3 in R7C67
25a. R2C2 = 6 -> no 7 in R2C3 (adjacent cells cannot have consecutive values)
25b. R3C1 = 8 -> no 9 in R2C1, no 7 in R4C1 (adjacent cells cannot have consecutive values) -> R12C1 = [93], R45C1 = [57], clean-up: no 9 in R2C78 (step 17b)
25c. R7C3 = 8 -> no 9 in R7C4 (adjacent cells cannot have consecutive values)

26. 35(7) cage at R4C3 = {1345679} (only remaining combination), no 8 -> R4C45 = [73], R4C6 = 8, R6C5 = 1
26a. R5C6 = 2 (hidden single in N5), R5C7 = 5 (cage sum), R6C67 = [59], R56C4 = [94], R3C34 = [72]
26b. R3C6 = 3 (hidden single in R3, or from non-consecutive)

27. Naked pair {48} in R2C78, locked for R2 and N3 -> R2C34 = [25], R1C34 = [58], R3C5 = 9, R12C5 = [47], R7C5 = 5, R2C9 = 9, R3C9 = 5, R1C9 = 2 (cage sum)
27a. R1C9 = 2 -> no 3 in R1C8 (adjacent cells cannot have consecutive values) -> R1C78 = [37], R6C8 = 3, R5C8 = 8, R2C78 = [84], R56C9 = [47], R7C8 = 9, R7C9 = 3 (cage sum), R9C8 = 2
27b. R7C5 = 5 -> no 4 in R7C6 (adjacent cells cannot have consecutive values) -> R7C67 = [74]

and the rest is naked singles.

The first non-consecutive killer that I did was Nasenbaer's NonCon Killer which was first posted on Ruud's site in February 2007; it's available on this site in Archive A, page 5. I found it a lot easier than this one so, if you are finding this puzzle hard, please have a go at Nasenbaer's one and then come back and try this one again.

I've posted a short message on the Killer Puzzles forum to let Assassin fans know that Non-Consecutive Killers and Texas Jigsaw Killers are available in this forum. If there are any other types of puzzle that you feel should be included in that message, please let me know and I'll edit it.

Really enjoyable Non-Con killer manu since it kept giving eliminations. Thanks! My optimised solution makes it look easier than it felt. The non-con allows some really interesting combo work in otherwise boring cages and "45s". See Andrew's prelim i for example! However, I avoided the routine cage placement that Andrew does in his walk-through but a different one of these turned out to be the departure point from mine and Andrew's WTs (My WT step 7b)! It's basically cracked by step 10.

Walkthrough for A non-consecutive killer sudoku
Many thanks to Andrew for a number of corrections and some extra steps. Much appreciated.
Prelims: including Non-Consecutive (NC) eliminations in 2-cell cages
i. 10(2)n3: no 5
ii. 9(2)n1: no 4,5,9 (NC)
iii. 9(3)n3: no 7,8,9
iv. 12(2)n4: no 1,2,6
v. 7(2)n6: no 3,4,7,8,9 (NC)
vi. 11(2)n6: no 1,5,6 (NC)
vii. 10(2)n4: no 5
viii. 11(3)n7: no 9
ix. 11(2)n8: no 1,5,6 (NC)
x. 14(2)n7 = {59/68}

1. "45" on n3: 2 outies r2c6 + r4c7 = 3 = {12}
1a. no 1 or 2 in any of the eight NC cells (r13c6 etc)
1b. no 5 or 6 in r4c9
1c. no 5,6 in r3c8 (NC)
1d. no 1,2 in r3c9 (NC)

2. Naked pair {12} in r4c79: both locked for r4 & n6
2a. no 9 in 11(2)n6

3. "45" on r123: 3 outies r4c7 + r45c1 = 14
3a. -> r45c1 = 12/13 -> cannot have 1,2,6 (can't be {67} from NC)

4. "45" on n7: 2 outies r6c3 + r8c4 = 12 (no 1,2)

5. Hidden killer pair 1,2 in n4
5a. -> r5c3 = (12)
5b. 10(2)n4 must have 1/2 = {19/28}(no 3,4,6,7)
5c. no 1,2 in r5c4 (NC)

6. 6 in n4 only in c3: locked for c3
6a. no 3 in r3c4
6b. no 8 in r9c2

7. "45" on n1234: 1 outie r4c7 + 9 = 3 innies r456c3
7a. -> r456c3 = 10/11 and must have 6 (step 6)
7b. -> the two cells that don't have 6 = 4/5 = {13/14}({23} blocked by Non-Con since 2 must be in the middle cell r5c3)
7c. -> r5c3 = 1
7d. r46c3 = 9/10 = 6{3/4}(no 5,7,8,9)
7e. no 8 in r3c4
7f. r8c4 = (689)(Outies n7=12)

8. 10(2)n4 = {28}: both locked for r6 & n4
8a. no 4 in 12(2)n4

9. 35(7)n4 must have 5 (combos) which is only in n5 or r6c7 -> no 5 in r6c4 (CPE)

10. r56c4 = 13 = {49} only ({67} not valid from NC; no 5,8 in r6c4): both locked for n5 & c4
10a. no 3 in r6c3 (Outies n7)

Puzzle is close to cracked but is frustratingly stubborn to get to a single solution stage! Only essential clean-up is done from now on.
11. 4 in r4 only in n4: locked for n4

12. r6c3 = 6
12a. r8c4 = 6 (Outies n7)

13. the two 16(3) at r6c3 & r8c2 now have two cells each = 10 (no 5)
13a. both = [19]{28/37}(no 4): no 9 in r78c2

14. 4 in n7 only in c1: 4 locked for c1
14a. 11(3)n7 must have 4 = 4{16/25}(no 3,7,8)

15. r4c3 = 4 (hidden single n4)
15a. naked quad {3579} in r45c12 -> no 3,5,7,9 in r3c2 (CPE)

16. "45" on n1234: one remaining outie r4c7 = 2
16a. r2c6 = 1 (1 remaining outie n3)
16b. r4c89 = [61]

17. r3c78 = 7 = [61] only ({34} blocked by NC)

18. r6c5 = 1 (hsingle n5)
18a. no 2 in r5c5 (NC)

19. r5c6 = 2 (hsingle n5)
19a. r4c6 + r5c7 = 13 = {58}

20. 35(7)n4 must have 1 & 4 & 5 = 145{3679} (last combo)(no 8)
20a. must have 9 -> r6c7 = 9
20b. must have 6 -> r5c5 = 6

21. r4c6 = 8 (hsingle n5)
21a. r5c7 = 5
21c. no 5 or 7 in r4c5 (NC)
21d. r4c5 = 3
21e. r56c4 = [94]

22. no 4 in r5c8 (NC)
22a. 11(2)n6 = [83]
22b. r56c9 = [47]

23. r1c6 = 6 (hsingle n2)

24. 9(2)n1 = {27}: both locked for r3

25. "45" on r123: 2 remaining innies r3c12 = 12 = [84]

26. 29(5)n2 must have 4 for n2 = 46{379}(no 2,5,8) (46{289} blocked by no 2 or 8 for r3c56)
26a. r3c56 = [93]
26b. r12c5 = {47}: both locked for n2 & c5
26c. r3c34 = [72]

27. r6c6 = 5, r4c4 = 7

28. r5c1 = 7 (hsingle c1), r5c2 = 3
28a. r4c2 = 9, r4c1 = 5
28b. r6c12 = [28]

29. 11(3)n7 = {146}: 1 & 6 locked for c1 and n7

30. naked pair {58} in r12c4: both locked for c4

31. 11(2)n8 = {47}: both locked for r7

32. r7c23 = [28]
32a. r9c23 = [59]

33. r7c5 = 5
33a. no 4 in r7c6 (NC)
33b. r7c67 = [74]

34. r7c89 = [93] (cage sum)

35. 16(3)n3 = {29}[5]: 2 locked for c9 & n3

36. 10(2)n3 = [37] (last permutation)

Finally got it to singles.

Cheers
Ed

Congratulations Ed for the breakthrough in your step 7b!

I see that I'd been fairly close to it with my steps 12 and 12a. If only I'd looked at R456C3, rather than just R2C6 + R456C3, I might have found that breakthrough; I'll go further and say that I probably would have found it. However in that case I might not have posted a WT; I knew that Ed had finished first but he let me go ahead because he knew that I'd used to a harder step (the combined cage in step 15).


I look forward to further non-con killers in the Other Variants forum. I hope whoever posts the next one will go along with my suggestion that this one was Non-Con 2 and make the next one Non-Con 3.

I might even have a go at TJKs sometime; I once did a jigsaw killer on a different site. They are difficult for me to produce diagrams on my Excel worksheets. I use colours for the cages so would have to add thick lines for the jigsaw house boundaries; I'm not very good at doing that. Diagrams for jigsaws aren't a problem; I use colours for the houses.

That's clearly a good way for non-con killer creators to make sure that a new puzzle is unique and of the wanted level of difficulty It's also a good way to find out the SS score, if one wants to do that. However I hope that solvers will do like Ed and I did and work out their one non-consecutive eliminations, including doing their own NC clean-ups, rather than relying on the software to do it for them.