Last Killer of 2006

Post by **Ruud** » Sun Dec 31, 2006 1:41 pm

Here is my final Killer Sudoku for the year 2006. It is tougher than the average Assassin, but can be solved with lots of logic.

3x3::k:5632:5632:5378:5378

3333

7687:7687:5641:5632:5632:5378

3333:7687:7687

5641:5632

3604:6166

2839:7687

5641:5641

6166:6166:6166

3601

1572

3613:4903:4903:4903

2347

6701:6701

3376

7220:7220:6701:5687

1336

2875

4413:7220:6701:5687:5687:4418

3652:4413:4413:7220:5687:5687:4418:4418

3652

4413:4413:

See you 'round next year!

Ruud

sudokuEd · Post by **sudokuEd** » Thu Jan 04, 2007 9:40 am

Ruud, what a bomb!

OK, this is as far as I can get this one. I found one way to make progress beyond this point - but it involves complicated contradiction moves within n5. The final steps of this partial walk-through provide the groundwork for these moves.

But, am hoping there are easier ways than through the minefield. Anyone?

1a. 11(2) n23, 11(2) n89, 19(3)n5 & 26(4)n47 cannot have 1;
1b. 13(4)n58 cannot have 8 or 9 and must have 1 -> no 1 in r4c5
1c. 14(4) n36 & 9(2)n6: no 9
1d. 28(4)n69 = 89(47/56} -> no 8 in r45c9
1e. 17(4)n9 = 123{47/56} -> 123 locked for n9, -> no 8,9 r7c6

2. "45" r1234:r4c37 = 4 = {13} locked for r4

3. "45" r6789:r6c37 = 13 = {49/58/67} (no 123)

4."45" r5: r5c37 = 11 (no 1)

5. 6(2)n4 = {15/24} = [1/4, 4/5..]

6. 14(3)n4 must have 1 or 3 = {158/167/239/347/356} ({149} blocked by 6(2)n4) = [1/3] not both -> no 3 r5c3

7. 9(2)n6 = {18/27/36} ({45} blocked by 6(2)r5)

8. 19(3) r5 = {289/379/469/478} (no 5) ({568} blocked since this means 9(2) r5 = {27} but this leaves no 2 or 5 for 6(2)r5)

9. "45" c12 -> r28c3 = 8 = {17/26/35} (no 4,8,9)

10. "45" c3 -> r1379c3 = 23 = {1589/2489/3479/4568}
10a. {1679} blocked by 14(3) (step 6)
10b. {2579} blocked by 8(2) (step 9)
10c. {2678} blocked by 14(3) (step 6)
10d. {3569} dito
10e. {3578} dito

11. "45" c89 -> r28c7 = 8 = {17/26/35} no 4,8.9

12. 14(3) c7 must have 1 or 3 = {149/158/239/347/356} ({167} blocked by 9(2)n6) = [1/3] not both -> no 3 r5c7

13. "45" c7:r1379c7 = 23(4) = {1589/2489/2678/3479/3578/4568}
13a. {1679} -> 8(2) = {35} but 1 or 3 needed for 14(3)c7 -> {1679} blocked from 23(4)
13b. {2579} blocked by 8(2)c7 (step 11)
13c. {3569} blocked by 8(2)c7 (step 11)

14. "45"c1234: r456c4 = 11 (no 9)
14a. min r45c4 = [23] = 5 -> max r6c4 = 6

15. "45"c6789: r456c6 = 19 (no 1)

16. 5(2) c5 = {14/23}

17. 14(2) c5 = {59/68}

18. "45"n5: r456c5 = 15 = {159/168/267/357} (no 4) = {5/6..]
18a. {249} blocked by 5(2)c5 (step 17)
18b. {258} blocked by 14(2) (step 18)
18c. {348} blocked by 5(2) (step 17)
18d. {456} blocked by 14(2) (step 18)

19. "45"n5:r37c5 = 11 = {29/38/47} ({56} blocked by 15(3)c5 (step 18))
19a. -> no 5,6 r37c5
19a. max. r7c5 = 7 -> min r3c5 = 4

20. from step 19
20a.r3c5 = 4 -> rest of 24(4) = {569/578}. r7c5 = 7 -> rest of 13(4) = {123}
20b.r3c5 = 7 -> rest of 24(4) = {269/458}. r7c5 = 4 -> rest of 13(4) = {126/135}
20c.r3c5 = 8 -> rest of 24(4) = {259/457}. r7c5 = 3 -> rest of 13(4) = {127/145} : But these both are blocked by 24(4) in n5
-> no [83] r37c5
20d.r3c5 = 9 -> rest of 24(4) = {258/456} ({267} blocked by 19(3)step 8). r7c5 = 2 -> rest of 13(4) = {137/146}

21. (step 19):r37c5 = 11 = [92]/{47} = [2/4..] -> Killer pair on {24} with 5(2)c5 -> 2 and 4 locked for c5
21a. (step 18) 15(3)c5 = {159/168/357} = [591/{68}1]{357}-> r4c5 = {5678}, r5c5 = {36789}, r6c5 = {1357}
21b. from step 20a,b,d: r4c456 = {569/578/269/458/258}/456}
21c. from step 20a,b,d: r6c456 = {123/126/135/137/146}

22. from step 14, 11(3)n5 = {128/146/236/245} (no 7) ({137}blocked by 15(3)c5 step 18)

23. from step 15, 19(3) = {289/379/469/478} (no 5)({568} blocked by 11(3) step 22)
23a. {289} combination is the only one with 2 -> no 2 in r45c6

24. from step 18. r456c5 = 15 = [591/{68}1/{357}]

25. from the two parts of 20a.+ 19(3)(step 8) r456 n5 =
25a. {569}{478}{123}
25b. {578}{469}{123}

26. from the two parts of 20b. + 19(3) (step 8) r456n5 =
26a. {269}{478}{135}
26b. {458}{379}{126}

27. from the two parts of 20d. + 19(3) (step 8) r456n5 =
27a. {258}{379}{146}
27b. {258}{469}{137}
27c. {456}{289}{137}

Code: Select all

.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
|&#40;22&#41;                   |&#40;21&#41;                   |&#40;5&#41;        |&#40;13&#41;                   |&#40;30&#41;                   |
| 123456789   123456789 | 456789      456789    | 1234      | 123456789   123456789 | 123456789   123456789 |
&#58;-----------.           '-----------.           |           |           .-----------'           .-----------&#58;
|&#40;22&#41;       |                       |           |           |           |                       |&#40;14&#41;       |
| 123456789 | 123456789   123567    | 456789    | 1234      | 123456789 | 123567      123456789 | 12345678  |
|           |           .-----------'-----------+-----------+-----------'-----------.           |           |
|           |           |&#40;14&#41;                   |&#40;24&#41;       |&#40;11&#41;                   |           |           |
| 123456789 | 123456789 | 5689        5689      | 479       | 23456789    23456789  | 123456789 | 12345678  |
|           '-----------+-----------.-----------'           '-----------.-----------+-----------'           |
|                       |&#40;14&#41;       |                                   |&#40;14&#41;       |                       |
| 2456789     2456789   | 13        | 24568       5678        46789     | 13        | 245678      24567     |
&#58;-----------------------&#58;           &#58;-----------------------------------&#58;           &#58;-----------------------&#58;
|&#40;6&#41;                    |           |&#40;19&#41;                               |           |&#40;9&#41;                    |
| 1245        1245      | 2456789   | 23468       36789       346789    | 2456789   | 123678      12367     |
&#58;-----------------------&#58;           &#58;-----------------------------------&#58;           &#58;-----------------------&#58;
|&#40;26&#41;                   |           |&#40;13&#41;                               |           |&#40;28&#41;                   |
| 23456789    23456789  | 456789    | 123456      1357        23467     | 456789    | 456789      456789    |
|           .-----------+-----------'-----------.           .-----------'-----------+-----------.           |
|           |&#40;22&#41;       |&#40;5&#41;                    |           |&#40;11&#41;                   |&#40;17&#41;       |           |
| 23456789  | 123456789 | 1234        1234      | 247       | 234567      456789    | 1234567   | 456789    |
|           |           '-----------.-----------+-----------+-----------.-----------'           |           |
|           |                       |&#40;17&#41;       |&#40;14&#41;       |&#40;14&#41;       |                       |           |
| 23456789  | 123456789   123567    | 123456789 | 5689      | 123456789 | 123567      1234567   | 456789    |
&#58;-----------'           .-----------'           |           |           '-----------.           '-----------&#58;
|                       |                       |           |                       |                       |
| 123456789   123456789 | 123456789   123456789 | 5689      | 123456789   456789    | 1234567     1234567   |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'

Code: Select all

.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789   123456789 | 456789      456789    | 1234      | 123456789   123456789 | 123456789   123456789 |
&#58;-----------.           '-----------.           |           |           .-----------'           .-----------&#58;
| 123456789 | 123456789   123567    | 456789    | 1234      | 123456789 | 123567      123456789 | 12345678  |
|           |           .-----------'-----------+-----------+-----------'-----------.           |           |
| 123456789 | 123456789 | 5689        5689      | 479       | 23456789    23456789  | 123456789 | 12345678  |
|           '-----------+-----------.-----------'           '-----------.-----------+-----------'           |
| 2456789     2456789   | 13        | 24568       5678        46789     | 13        | 245678      24567     |
&#58;-----------------------&#58;           &#58;-----------------------------------&#58;           &#58;-----------------------&#58;
| 1245        1245      | 2456789   | 23468       36789       346789    | 2456789   | 123678      12367     |
&#58;-----------------------&#58;           &#58;-----------------------------------&#58;           &#58;-----------------------&#58;
| 23456789    23456789  | 456789    | 123456      1357        23467     | 456789    | 456789      456789    |
|           .-----------+-----------'-----------.           .-----------'-----------+-----------.           |
| 23456789  | 123456789 | 1234        1234      | 247       | 234567      456789    | 1234567   | 456789    |
|           |           '-----------.-----------+-----------+-----------.-----------'           |           |
| 23456789  | 123456789   123567    | 123456789 | 5689      | 123456789 | 123567      1234567   | 456789    |
&#58;-----------'           .-----------'           |           |           '-----------.           '-----------&#58;
| 123456789   123456789 | 123456789   123456789 | 5689      | 123456789   456789    | 1234567     1234567   |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'

Nasenbaer · Post by **Nasenbaer** » Fri Jan 05, 2007 11:35 am

Nice work, Ed. Especially steps 20 and 21, didn't see them. Here are some additions:

28. 45 on r5 : r5c37 has no 3 -> no 8 possible
29. r3 : 11(2) = {29|38|47} -> {56} not possible, one is needed in 14(2)
30. N6 : r4c7 = {13}, 9(2) has 1 or 3 -> 9(2) = [81]{36} -> no 2,7
31. N36 : 14(4) : {1346} not possible, one of {136} needed in r5c9 -> 2 locked in 14(4) -> no 8 in r23c9 possible, {13} is there required for {1238}
32. r5 : 19(3) : {379} only possible with 3 in r5c4 -> no 3 in r5c56
33. r5 : 3 in r5c4 or 9(2) -> no 6 in r5c4
34. c5 : 15(3) : {357} only possible with 5 in r4c5 -> no 5 in r6c5

That leaves us here:

Code: Select all

.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789   123456789 | 456789      456789    | 1234      | 123456789   123456789 | 123456789   123456789 |
&#58;-----------.           '-----------.           |           |           .-----------'           .-----------&#58;
| 123456789 | 123456789   123567    | 456789    | 1234      | 123456789 | 123567      123456789 | 1234567   |
|           |           .-----------'-----------+-----------+-----------'-----------.           |           |
| 123456789 | 123456789 | 5689        5689      | 479       | 234789      234789    | 123456789 | 1234567   |
|           '-----------+-----------.-----------'           '-----------.-----------+-----------'           |
| 2456789     2456789   | 13        | 24568       5678        46789     | 13        | 245678      24567     |
&#58;-----------------------&#58;           &#58;-----------------------------------&#58;           &#58;-----------------------&#58;
| 1245        1245      | 245679    | 2348        6789        46789     | 245679    | 368         136       |
&#58;-----------------------&#58;           &#58;-----------------------------------&#58;           &#58;-----------------------&#58;
| 23456789    23456789  | 456789    | 123456      137         23467     | 456789    | 456789      456789    |
|           .-----------+-----------'-----------.           .-----------'-----------+-----------.           |
| 23456789  | 123456789 | 1234        1234      | 247       | 234567      456789    | 1234567   | 456789    |
|           |           '-----------.-----------+-----------+-----------.-----------'           |           |
| 23456789  | 123456789   123567    | 123456789 | 5689      | 123456789 | 123567      1234567   | 456789    |
&#58;-----------'           .-----------'           |           |           '-----------.           '-----------&#58;
| 123456789   123456789 | 123456789   123456789 | 5689      | 123456789   456789    | 1234567     1234567   |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'

Nasenbaer · Post by **Nasenbaer** » Fri Jan 05, 2007 12:01 pm

Further steps will be added to this post until someone else posts.

35. r5 : 9(2) = [81]|{36}
= [81] = -> 19(3) = {379}
= {36} = -> 19(3) = {289|478}
-> {467} not possible in 19(3) -> no 6 in 19(3)

36. c5 : 15(3) has only one of {789} -> r5c5 = {789} -> r4c5 = {56}, r6c5 = {13}

Edit: postings overlapped, cleaned up and reposted below.

rcbroughton · Post by **rcbroughton** » Fri Jan 05, 2007 2:13 pm

37. On r7, r7c5={2/4/7} and 5(2)={14}/{32}
a) if r7c5=2 then 5(2)={41} -> 11(2) cannot be {47} (4 used)
b) if r7c5=4 then -> 11(2) cannot be {47} (4 used)
c) if r7c5 = 7 then 5(2)={32} -> 11(2) cannot be {47} (7 used)

therefore 11(2) cannot be {47}

Nasenbaer · Post by **Nasenbaer** » Fri Jan 05, 2007 2:18 pm

Wonderful! I'm cleaning up my post above and repost it here with correct numbering.

No eliminations, but might be useful:

38. N36 : 14(4) = {1238|1247|1256|2345}
38a. {1238} : r23c9 = {13}, r4c89 = [82]
38b. {1247} : r23c9 = 1{2|4|7}, r4c89 = {47|27|24}
38c. {1256} : r23c9 = {16}, r4c89 = {25} ({26|56} not possible in r4c89 because 1 in r23c9 -> 9(2) = {36})
38d. {2345} : r23c9 = 3{2|4|5}, r4c89 = {45|25|24}

39. 45 on N3 : r13c7 + r23c9 = 15
39a. r23c9 : min: 3, max: 8 (6 not possible, see step 37)
39b. r13c7 : min: 8, max: 12 (9 not possible)

Now I'm stuck. Has anybody a new idea?

Peter

Para · Post by **Para** » Fri Jan 05, 2007 2:53 pm

Two eliminations.

40. 45 on N7 -->> R7C13 + R8C1+ R9C3 = 23
40a. R7C3 = max 4 so R78C1 + R9C3 = min 19
40b. eliminate 1 from R9C3

41. R5C3 can't be a 9
41a. 14(3) N4: R5C3 = 9 ----> R46C3 = {1,4}
41b. R46C3 can't be {1,4} because of N4: 6(2)

Hope it helps. Hasn't helped me much though.

Para

ps. i had more eliminations but you all covered that in the last 3 posts so this is all that is left. Seems we are on the same track.

Nasenbaer · Post by **Nasenbaer** » Fri Jan 05, 2007 3:48 pm

42. looking at 9 in N9 :
42a. 9 in r78c9 -> 9 in r56c7 no 9 in r13c7
42b. 9 in r79c7 -> no 9 in r13c7
-> 9 can be eliminated from r13c7 -> no 2 in r3c6

43. from step 41 -> no 2 in r5c7 -> 2 locked in r4c89 for r4 and 14(4)

44. N25 : 24(4) = 45{69|78} -> 5 locked in r4c45 for r4 and N5

45. c4 : 11(3) : {128} only possible with 8 in r4c4 -> no 8 in r5c4

46. r5 : 19(3) has one of {234} which is in r5c4 -> no 4 in r5c6

47. c4 : 11(3) : r4c4 can't be 4 and r6c4 can't be 6
47a. 11(3) = {146} -> r4c4 has to be 6
47b. 11(3) = {245} -> r4c4 has to be 5
47c. 11(3) = {236} -> r4c4 has to be 6

rcbroughton · Post by **rcbroughton** » Fri Jan 05, 2007 4:16 pm

I'll make this 48 as I was too slow!!

48. Look at 13(4) in n58. r7 is {2/4/7}
a) if this is 2 then r6 must be 7 (otherwise 5(2) in n2 would have no options) and the other two cells must be 1 and 3
b) if this is 7 then the other 3 cells must be 123
c) if this is 4 then no other cell can be 4

In any scenario r6c46 cannot be 4

rcbroughton · Post by **rcbroughton** » Fri Jan 05, 2007 4:19 pm

49 following the last couple of posts, 4 is now locked in row 5 in n5 - cannot appear in r5 in n4 or n6

Nasenbaer · Post by **Nasenbaer** » Fri Jan 05, 2007 4:41 pm

rcbroughton wrote:49 following the last couple of posts, 4 is now locked in row 5 in n5 - cannot appear in r5 in n4 or n6

4 is still possible in r4c6 ! -> 4 still possible in r5 for N4 and N6 !

50. N36 : 14(4) : no 5 in r4c89 -> (step 38c) {1256} not possible -> no 6 in 14(4)

51. N6 : 14(3) = {347} -> r4c89 = [82] -> {347} not possible, nothing left for 9(2) -> no 7 in 14(3) -> no 4 in r5c3

Para · Post by **Para** » Fri Jan 05, 2007 4:59 pm

Ok cleaned this up after previous post

52a. R4C8 can't be 8. R4C8 = 8 --> R4C9 = 2 and R5C89 = {36} --->> R6C89 = {75} which interferes with 28(4) N69. So 14(4)N36 isn't {1238} and 8 can be eliminated from R4C8
52b. 14(4) N36 = {1247|2345} So 4 locked in 14(4) N36 and can be eliminated from R6C9.

53. No 6 in R6C89: either 1 or 6 in 14(3) N6 and 9(2) N6. So no 1 or 6 anywhere else in N6.

Nasenbaer · Post by **Nasenbaer** » Fri Jan 05, 2007 5:27 pm

54. r1c7 can't be 1 or 6.
54a. r23c9 = 5 = {14} or r23c9 = 8 = {17|35}
54b. r23c9 = 5 -> r13c7 = 10 = {28|37} ([64] not possible, 4 used in r23c9)
54c. r23c9 = 8 -> r13c7 = 7 = {34}|[52]

Para · Post by **Para** » Fri Jan 05, 2007 5:34 pm

this is a really crude step, not pretty but effective.

55. No 6 in R5C3:
55a. R5C3=6 -->> R5C9= 1 -->> R4C89 no 7 (14(4) = {2345})
R5C3=6 -->> R6C7=6; R5C7=5; R4C7=3 -->> R4C3=1; R6C3=7 -->> R6C89 no 7. No place for 7 in N6. So no 6 in R5C3
55b. 6 locked in R5 for N6. No 6 anywhere else in N6.
55c. No 5 in R5C7 -->> 5 locked in N6 for R6 no 5 anywhere else in R6

Nasenbaer · Post by **Nasenbaer** » Fri Jan 05, 2007 5:37 pm

56. N3 : 6,9 locked in 30(5) = 69{258|348|357} -> no 1 -> 1 locked in r23c9 for N3 and c9 -> no 7 in r8c7 -> N36 : 14(4) = {1247}

57. -> N6 : 9(2) = {36} -> 3,6 locked for N6 and r5 -> r4c7 = 1 -> r4c3 = 3

58. r5 : r5c4 = {24} -> 6(2) = {15} -> 1,5 locked for N4 and r5

59. r5 : 19(3) = 8{29|47} -> 8 locked in 19(3) for N5 and r5

60. -> r4c45 = {56} -> 24(4) in N25 = {4569} -> 5,6 locked for r4 and N5

Edit: Overlapping posts, cleaned up, reposted.