sudokuEdThis is a real toughie. See what you mean Mike and Para. First attempt couldn't get anywhere, so had to put the creative hat on.
Seems like I've been able to make some progress with some interesting techniques. Can someone check through to make sure its all valid?
[EDIT: Rewritten from step 22 + new marks pic. Thanks Mike for finding the mistake. EDIT2: problem with new step 27 and other typos fixed: thanks Para and Mike] Add some more too if you like
. I probably won't be able to look at it again till the weekend.
Seems like we need to add
Killer LoL to our jargon to account for the effect of cage combinations on LoL. I also use 'overlap' to describe the congruence between combinations. Might need to find a different name so it is not confused with the normal 'overlap' technique. Names and the need for them is not my forte.....
Texas Jigsaw Killer 181. 23(3)r3c6 = {689}: all locked for n3
2. "45" r123: r4c6 - 7 = r3c9
2a. r3c9 = {12}
2b. r4c6 = {89}
2c. 6 in n3 only in r3: 6 locked for r3
3. Already resorting to nibbles.
3a. no 1 r2c1. Here's how.
3b. 1 in r2c1 -> r3c12 = {89}
3c. But this clashes with r3c67.
4. Killer LoL (KLoL) chain r123: no 2 r2c1. Here's how.
4a. LoLr123: 4 innies r2c1 + r3c129 = 4 outies r4c456 + r5c5
4b. only one 2 is possible in outies -> only one 2 is possible in innies.
4c. 2 in r2c1 -> r3c12 = {79} -> r4c6 = 9 -> r3c9 = 2 (step 2)
4d. but this means two 2's in r123 innies. Not possible.
5.KLoL r123: no {567} combo in 18(3)r4c6. Here's how.
5a.LoLr123 same as step 4a. Outies must have 8/9 (r4c6) -> innies must have 8/9
5b. ->18(3)r2c1 {567} combo. blocked
6. KLoL r123: no 2 r3c12. Here's how.
6a. 2 in r3c12 -> rest of 18(3) = {79}(no 8)
6b. 2 in r3c12 -> r3c9 = 1 -> r4c6 = 8 (step 2)
6c. But we know from LoLr123 that there can be no 8 in outies when 2 in r3c12.
7. 22(3)r5c3 = 9{58/67}
7a. 9 locked for n6(r5c3)
8. "45" c12: r4c3 + 4 = r6c2
8a. r4c3 = 1..5
9. "45" r89: 3 innies r8c136 = 8 = h8(3)r8
9a. = 1{25/34}
9b. 1 locked for r8
10. 1 in n9(r8c2) only in r9: 1 locked for r9
11. 21(3)r8c8 = {489/579/678} = [4/7..]
12. KLoL r89: no {457} combo in 16(3)r8c7. Here's how.
12a. LoL r89: 6 innies r8c1367 + r9c78 = 6 outies r56c67 + r7c78
12b. and both = 24 ie h24(6)r89innies = 24(6)r89outies
12c. 6 outies must have 1,2 & 3 for n8(r5c6)
12d. -> 6 innies must have 1,2 & 3
12e. note: 6 innies cannot have any repeats since the 6 outies are all in the same nonet.
12f. -> when h8(3)r8 = {125}, 16(3)r8c7 must be 3....
12g. -> when h8(3)r8 = {134}, 16(3) must be 2...
12h. -> {457} blocked from 16(3)
13. KLoL r89: no {358} combo. in 16(3)r8c7
13a. since the 6 outies in LoL r89(step 12) are all in the same nonet, there can be no repeats in the 6 innies
13b. since h8(3)r8 = {125/134} = [3/5..]
13c. -> {358} combo blocked from 16(3)
13d. -> the valid combinations in the h24(6)r89innies are
i. {125/349} = {123459}
ii. {125/367} = {123567}
iii. {134/259} = {123459}
iv. {134/268} = {123468}
13e. = 123{459/468/567} = [4/7..] not both.
14. KLoL r89: {147} combo blocked from both 12(3) cages in n8(r5c6): clash with 21(3)r8c8 = 4/7..] step 11 (thanks Mike for this much easier way).
15. 16(3)r8c7 = {259/268/349/367}
15a. ->{456} blocked from 15(3)r7c5
15b. ->{239/356} blocked from 14(3)r5c4
16. "45" r789: r6c7 + 3 = r7c9
16a. min r7c9 = 4, max r6c7 = 6
17. "45" c1234: r6c5 - 2 = r4c4
17a. max r4c4 = 7, min. r6c5 = 3
18. "45" c789: r135c7 = 19 = h19(3)c7
18a. no 1
19. LoLc789: 4 innies r189c7 + r9c8 = 4 outies r3456c6
19a. no 1 in innies -> no 1 in r56c6 [edit typo]
20. 1 in n8 only in 12(3)r6c7 = {129/138/156}(no 4,7)
21. 12(3)r5c6 = {237/246/345}(no 8,9)
22. KLoL Over-lap c789: no {259} combo. in 16(3)r8c7. Here's how.
22a. Lol c789: 4 innies r189c7 + r9c8 = 4 outies r3456c6
22b. the 12(3)r5c6 has 2/4 cells in the outies.
22c. the 16(3)r8c7 has 3/4 cells in the innies
22d. -> the valid combination in the 12(3) must overlap with 2 of the candidatates from the 16(3) combination
(
IF that combo has at most 1 of 6/8/9 corresponding to r34c6 in outies: this is what I missed first WT)
22e. since 12(3) combinations are {237/246/345} and since {259} combo in 16(3)r8c8 has ONLY 1 of 6/8/9 AND does not have 2 candidates overlapping with 12(3)
22f. ->{259} combo blocked
23. 16(3)r8c8 = {268/349/367}(no 5)
24. KLoL + (double)Overlap c789: r56c6 no 5 [edit out invalid part]. Here's how.
24a...d (same reasoning as steps 22a..d)
24e. the 12(3) combinations are {237/246/345}
24f. the {349/367} combo's from 16(3) must have a double-overlap candidates with the 12(3) -> r56c6 = {34/37}
24g. for the {268} combo from 16(3), r3456c3 = {68}2{3/4/7} -> r56c6 = {23/24/27}(no 5)
24h. finally, the {268} combo from 16(3) could also double-overlap with 12(3) -> r56c6 = {26}
24h. In summary: r56c6 = {23/24/26/27/34/37}(no 5)
25. LoLc789: no 5 in outies -> no 5 in r1c7
26. "45" c6789: 3 innies r789c6 = 13 = h13(3)c6 [edit:typo]
26a. = {139/148/157/256} others blocked by r56c6 (step 24h.)
27. {148} combo blocked from h13(3)c7. Here's how. [edit: true but flawed reason: see Mikes preamble to step 37]
27a. 15(3)r7c5 = {159/168/249/258/267/357} ({348} blocked by 16(3)r8c7)
[edit: following steps are still valid]
28. h13(3)c6 = {139/157/256}(no 4,8)
28a. r78c6 + r9c6 = [913]/{15}[7]/[751]/{25}[6]/[625]
28b. ({13}[9]/[931]/{17}[5]/{56}[2] blocked by combinations unavailable in 15(3))
28c. no 3 r78c6, no 2 or 9 in r9c6 [edit:typos]
29. 15(3)r7c5 = [591]/9{15}/[375]/8{25}/[762] = {159/258/267/357} = [5/7..]
29a. r7c5 = {35789}
30. 14(3)r5c4: {257} blocked by 15(3)
Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789 123456789 | 12345678 12345678 | 123456789 | 123456789 2346789 | 123457 123457 |
:-----------. :-----------. | | .-----------'-----------. |
| 3456789 | 123456789 | 123456789 | 12345678 | 123456789 | 123456789 | 123457 123457 | 123457 |
| '-----------: '-----------: :-----------'-----------. :-----------:
| 1345789 1345789 | 12345789 12345789 | 12345789 | 689 689 | 123457 | 12 |
:-----------------------'-----------.-----------'-----------: .-----------'-----------: |
| 123456789 123456789 12345 | 1234567 12345678 | 89 | 123456789 123456789 | 123456789 |
:-----------------------.-----------+-----------. :-----------'-----------. | |
| 123456789 123456789 | 56789 | 123456789 | 12345678 | 23467 234567 | 123456789 | 123456789 |
| .-----------' | '-----------: .-----------+-----------'-----------:
| 123456789 | 56789 56789 | 123456789 3456789 | 23467 | 12356 | 123456789 123456789 |
:-----------'-----------.-----------'-----------.-----------'-----------: '-----------. |
| 12345678 12345678 | 12345678 12345678 | 35789 125679 | 1235689 1235689 | 456789 |
| .-----------: .-----------+-----------. :-----------.-----------'-----------:
| 12345 | 23456789 | 12345 | 456789 | 23456789 | 125 | 2346789 | 456789 456789 |
:-----------' :-----------' | '-----------: '-----------. |
| 123456789 123456789 | 456789 456789 | 123456789 13567 | 2346789 2346789 | 456789 |
'-----------------------'-----------------------'-----------------------'-----------------------'-----------'
Richard (rcbroughton)Hi Ed
haven't picked up all the techniques for Jigsaw Killers yet. I might need to review the tutorials.
Picking up from you marks pic,
31. 45 Rule on R789. r7c9 = r6c7+3 - eliminates 7 from r7c9
32. 45 on r123. outies total 19.
32a when r4c6=8 r4c9<>8 = {29}/[38]/{47}/{56}
32b when r4c6=9 r4c9<>9 = [19]/{37}/{46} (can't be {28} because of 12(3) cage)
32c. r4c9 can't be 8 and r5c9 can't be 1
33. 45 on c789 - innes total 19
33a. r1c7 can't be 2
34. 45 on r1234 outies r5c58 minus innies r34c9 equals 5
34a no combos with 1 allowed :
out [71] - in {12} - 2 1's in nonet
out [81] - in {13} - 2 1's in nonet
35. 45 on c6789 - outies r789c5 total 14
35a. no combo with 8 at r9c5
36. 45 on c9 - outies r68c8 minus innies r12c9 equals 3 - innies limited to total of 11,10,9,8,7 or 5.
36a. 11 - 8 - no 1 in r6c8
36b. 7 - outies = [19] - but innies can only be {34} - {34} and 1 blocked by 12(3) r3459
36c. 5 - outies = [17]/[26]/[35] - but [17] blocked because r1c8 needs to be 7 to fit 12(3)
36d. -> no 1 at r6c8
Mike (mhparker)Hi guys,
sudokuEd wrote "27b. Each combo in the h13(3)c7 must have 2 cells from the 15(3).
No available combination in 15(3) has 2 of {148} -> {148} not possible"How about {168} - that has 2 of {148}?
Fortunately, h13(3)c6 = {148} implies 15(3)r7c5 = {168} and vice versa.
Due to observation in step 37a below, h13(3)c6 = {148} and 15(3)r7c5 = {168} together block all possible combinations for 16(3)r8c7
Therefore, we can indeed deduce that h13(3)c6 <> {148} and 15(3)r7c5 <> {168}.
The walkthrough is therefore not invalidated.
Here are some further steps...
37. Because 16(3)r8c7 maps to 3 of r3456c6 (LoL c789), of which r9c6 is a peer...
37a. ...r9c6 cannot duplicate any digit in 16(3)r8c7
37b. -> {367} combo for 16(3)r8c7 blocked by h13(3)c7 (see step 28)
37c. -> no 7 in 16(3)r8c7
38. 16(3)r8c8 = {268/349}
38a. -> blocks {248} combo from 14(3)r5c4
38b. -> 14(3)r5c4 = {149/158/167/347} (no 2)
39. LoL c6789: outies r56c4+r67c5 = innies r129c6+r1c7
39a. no 2 in outies -> no 2 in innies r12c6
40. LoL r89: outies r56c67+r7c78 = innies r8c1367+r9c78
40a. no 7 in innies -> no 7 in outies (r5c67+r6c6)
40b. -> 12(3)r5c6 = {246/345} = {(5/6)..}
40c. -> 4 locked for n8
41. {156} combo for 12(3)r6c7 blocked by 12(3)r5c6 (step 40b)
41a. -> 12(3)r6c7 = {129/138} (no 5,6)
42. LoL c789 (see step 19)
42a. no 7 in outies -> no 7 in innie r1c7
43. 7 no longer available for h19(3)c7 (step 18)
43a. -> no 3 in r15c7
44. LoL r789: outies r5c34+r6c2345 = innies r7c789+r8c89+r9r9
44a. no 2 in outies -> no 2 in innies r7c78
44b. -> no 8,9 in r7c9
45. LoL r789: outies r5c467+r6c4567 = innies r7c12349+r8c13
45a. no 9 in innies -> no 9 in outies
45b. -> 14(3)r5c4 = {158/167/347} (no 9)
45c. -> no 7 in r4c4 (step 17)
46. {357} combo for 15(3)r7c5 blocked by 14(3)r5c4 (step 45b)
46a. -> 15(3)r7c5 = {159/258/267} (no 3)
47. 15(3)r7c5 must contain one of {12} in r78c6
47a. -> no 1 in r9c6, otherwise h13(3)c6 cage total can't be reached (see step 26)
48. LoL c1234: outies r4589c5+r9c6 = innies r1c3+r1256c4
48a. no 9 in innies -> no 9 in outies r89c5
49. h19(3)c7 (step 18) = {289/469/568} (3,7 unavailable)
49a. -> if 16(3) = {268}, 6 must go in r9c8
49b. -> no 6 in r89c7, and no 2,8 in r9c8
50. n9(r8c2) confined to r89
50a. -> remaining cells in r89 (r8c136789+r9c789) must contain the digits 1..9 (no duplicates)
50b. -> r8c9 <> r9c8
50c. -> r89c89+r7c8 (innies, LoL c89) contain 5 different digits
50d. -> r34c67+r2c7 (outies, LoL c89) contain (same) 5 diffent digits
50e. -> no 6,8,9 in r4c7 (since these digits are already taken in 23(3)r3c6
50f. -> no 1 in r4c8
50g. no 2 in innies (step 50c)
50h. -> no 2 in outies r24c7
51. 6 in c7 now only in h19(3)c7 (step 18)
51a. -> h19(3)c7 = {469/568}
51b. -> no 2 in r5c7
52. LoL c89: outies r56c6+r4567c7 = innies r1239c8+r12c9
52a. no 8 in innies -> no 8 in outie r7c7
52b. 8 in 12(3)r6c7 now only in r7c8
52c. -> no 3 in r7c8
53. no 6 in r9c5 (due to {124} unavailable in r9c6 and 1 unavailable in r8c5)
54. no 8 in r12c6 (no permutations for 16(3)r1c6 w/ 8 in r12c6)
54a. h13(3)c7 (step 28) blocks {16} combo in r12c6
54b. -> no 6 in r12c6 (no remaining permutations available for 16(3)r1c6)
55. 8 in c6 locked in n3(r1c8)
55a. -> no 8 in r3c7
marks pic after step 55a:
Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789 123456789 | 12345678 12345678 | 123456789 | 134579 4689 | 123457 123457 |
:-----------. :-----------. | | .-----------'-----------. |
| 3456789 | 123456789 | 123456789 | 12345678 | 123456789 | 134579 | 13457 123457 | 123457 |
| '-----------: '-----------: :-----------'-----------. :-----------:
| 1345789 1345789 | 12345789 12345789 | 12345789 | 689 69 | 123457 | 12 |
:-----------------------'-----------.-----------'-----------: .-----------'-----------: |
| 123456789 123456789 12345 | 123456 12345678 | 89 | 13457 23456789 | 12345679 |
:-----------------------.-----------+-----------. :-----------'-----------. | |
| 123456789 123456789 | 56789 | 1345678 | 12345678 | 2346 456 | 23456789 | 23456789 |
| .-----------' | '-----------: .-----------+-----------'-----------:
| 123456789 | 56789 56789 | 1345678 345678 | 2346 | 123 | 23456789 123456789 |
:-----------'-----------.-----------'-----------.-----------'-----------: '-----------. |
| 12345678 12345678 | 12345678 12345678 | 5789 125679 | 139 189 | 456 |
| .-----------: .-----------+-----------. :-----------.-----------'-----------:
| 12345 | 23456789 | 12345 | 456789 | 2345678 | 125 | 23489 | 56789 56789 |
:-----------' :-----------' | '-----------: '-----------. |
| 123456789 123456789 | 456789 456789 | 123457 3567 | 23489 3469 | 56789 |
'-----------------------'-----------------------'-----------------------'-----------------------'-----------'
ParaI have no vision today. Can only see these 2 steps. Maybe better tomorrow evening.
56. 15(3) at R7C5 only has 6 in R7C6 -> R7C6: no 7
57. Hidden13(3) at R78C6 + R9C6 = [913]/{15}[7]/{25}[6]/[625] : {3/5...}/{3/6/7}/{1/6/9}
57a. 16(3) at R1C6: {358} blocked, R12C6 would be {35}, blocked by hidden 13(3)
57b. 16(3) at R1C6: {367} blocked, R12C6 would be {37}, R1C7 = 6 -> R3C6 = 6(hidden single), blocked by hidden 13(3)
57c. 16(3) at R1C6: {169} blocked, R12C6 = {16}, R1C7 = 9 -> R34C6 = {89} or R12C6 = {19}, R1C7 = 6 -> R3C6 = 6, either way would force {169} in C6, but blocked by hidden 13(3)
57d. Conclusion: 16(3) at R1C6 = {17}[8]/{57}[4]/{349}: no 6
Mike (mhparker)Thanks Para.
Here's the next small batch of moves (still got that sinking feeling about this puzzle though
). Hopefully, one of us will have a "Eureka!" moment:
58. 11(3)r1c3 = {128/137/146/236/245}
58a. {137} and {146} both blocked by 16(3)r1c6 (step 57d)
58b. -> 11(3)r1c3 = {128/236/245}
58c. -> no 7, 2 locked for n2
59. Nishio: if r6c7 = 3, then
59a. 3 in n7(r5c4) forced into r9c8 (cannot go in r5c4 due to LoL r789)
59b. -> 3 in n3(r1c8) forced into c9
59c. but this would leave nowhere to place the 3 in n5(r3c9)
59d. -> no 3 in r6c7
59e. -> no 6 in r7c9 (step 16)
60. 18(3)r4c7 = {189/279/369/459/378/468/567}
60a. {459} blocked by r7c9
60b. -> only combo with 4 is {468}
60c. {68} only in r45c8 -> no 4 in r45c8
61. h15(3)r7 (at r7c789 = innies r789) = [384]/{19}[5]
61a. -> {519} blocked from 15(3)r4c8
(would require 9 in both r6c8 and r7c7, leaving nowhere to place 9 in c9)
61b. -> no 1 in r6c9
62. 15(3)r4c8 = {249/258/267/348/357/456}
62a. {258} blocked because of r789 i/o difference "pincer" (r7c9 = 5 -> r6c7 = 2)
62b. only other combo with 8 is {348}
62c. but when [348}, 8 must go in r6c9, otherwise clash w/ h15(3)r7 (step 61)
62d. Conclusion: no 8 in r6c8
63. 12(3)r7c3 = {138/147/237/246/345} ({156} blocked by 22(3)r5c3)
63a. either r7c9 = 5, or r7c789 = [384] -> {345} combo blocked for 12(3)r7c3
63b. Either way, no 5 in r7c34
New marks pic after step 63b:
Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789 123456789 | 1234568 1234568 | 13456789 | 134579 489 | 123457 123457 |
:-----------. :-----------. | | .-----------'-----------. |
| 3456789 | 123456789 | 123456789 | 1234568 | 13456789 | 134579 | 13457 123457 | 123457 |
| '-----------: '-----------: :-----------'-----------. :-----------:
| 1345789 1345789 | 12345789 12345789 | 1345789 | 689 69 | 123457 | 12 |
:-----------------------'-----------.-----------'-----------: .-----------'-----------: |
| 123456789 123456789 12345 | 123456 12345678 | 89 | 13457 2356789 | 12345679 |
:-----------------------.-----------+-----------. :-----------'-----------. | |
| 123456789 123456789 | 56789 | 1345678 | 12345678 | 2346 456 | 2356789 | 23456789 |
| .-----------' | '-----------: .-----------+-----------'-----------:
| 123456789 | 56789 56789 | 1345678 345678 | 2346 | 12 | 2345679 23456789 |
:-----------'-----------.-----------'-----------.-----------'-----------: '-----------. |
| 12345678 12345678 | 1234678 1234678 | 5789 12569 | 139 189 | 45 |
| .-----------: .-----------+-----------. :-----------.-----------'-----------:
| 12345 | 23456789 | 12345 | 456789 | 2345678 | 125 | 23489 | 56789 56789 |
:-----------' :-----------' | '-----------: '-----------. |
| 1234578 123456789 | 456789 456789 | 123457 3567 | 23489 3469 | 56789 |
'-----------------------'-----------------------'-----------------------'-----------------------'-----------'
Mike (mhparker)TJK18 - Never-Ending StoryFound some more, although it doesn't make the puzzle any less impossible!
I can't even see how it can be solved using hypotheticals...
The reason for this pessimism is that it's possible to fill up over two-thirds of the grid with a near solution (consisting of almost all the wrong digits), including every cell outside of r12345c12345. Therefore, any contadiction of this "near-solution" must involve pulling in at least one cell from this region. Unfortunately, there's very little we have to go on there. The 2 locked in 11(3)r1c3 doesn't help (both solution and near-solution have 2 in the outies if doing LoL on c1234 or c12345), and the innie/outie difference on c12 (step 8) is too weak to have a significant short range effect in the absence of a massive hypothetical.
64. 21(3)r8c8 cannot contain both of {89}
64a. -> r456c9 must contain at least one of {89}
64b. -> 18(3)r4c7 cannot contain both of {89}
64c. -> no 1 in r4c7
65. 1 in n5(r3c9) now locked in 12(3)r3c9 -> not elsewhere in c9
65a. 12(3)r3c9 = {129/138/147/156}
65b. 8 only in r5c9 -> no 3 in r5c9For reference, here's the near-solution I was talking about above:
Code:
.-------------.-------------.------.-------------.-------------.
| 2689 29 | 16 128 | 1689 | 5 4 | 3 7 |
:------. :------. | | .------'------. |
| 4689 | 349 | 36 | 8 | 3689 | 7 | 5 1 | 2 |
| '------: '------: :------'------. :------:
| 28 235 | 37 258 | 38 | 6 9 | 4 | 1 |
:-------------'------.------'------: .------'------: |
| 469 459 1 | 15 16 | 8 | 7 2 | 3 |
:-------------.------+------. :------'------. | |
| 2 23 | 5 | 7 | 13 | 4 6 | 9 | 8 |
| .------' | '------: .------+------'------:
| 7 | 8 9 | 3 4 | 2 | 1 | 5 6 |
:------'------.------'------.------'------: '------. |
| 1 7 | 2 6 | 5 9 | 3 8 | 4 |
| .------: .------+------. :------.------'------:
| 3 | 6 | 4 | 9 | 2 | 1 | 8 | 7 5 |
:------' :------' | '------: '------. |
| 5 1 | 8 4 | 7 3 | 2 6 | 9 |
'-------------'-------------'-------------'-------------'------'
Hopefully, someone can prove me wrong. Otherwise I'll be considering having "TJK18" engraved on my tombstone!
R.I.P.
ParaHi
Just a little bit more. Only 2 digits eliminated in three steps.
66. 18(3) at R1C5 = {189/369/459/567}: {378/468} blocked by 16(3) at R1C6
67. Hidden13(3) at R78C6 + R9C6 = [913]/{15}[7]/[256]/[625]: [526] blocked by h15(3) at R7C789(needs one of {58}): R78C6 = [52] -> R7C5 = 8
68. LOL R89: R8C6789 + R9C789 = R5C3 + R6C23 + R7C1234: all different digits outies are in same house
68a. 21(3) at R8C8 = {579} -> 16(3) at R8C7 = {268} - > R7C7 = 1 -> R7C56 = {59}
68b. 21(3) at R8C8 = {678} -> h 15(3) in R7C789 = {19}[5]
68c. Conclusion: 5 in R7 locked for R7C569: R7C12: no 5
Mike (mhparker)Another tiny increment:
65b. sub-step added (elimination of 3 in r5c9) - see corrected walkthrough above
...
69. r7c123456 = h30(6)r7 = {125679/234678}
69a. {59} only in r7c56
69b. -> no 1 in r7c6
ParaWith this pace i think we are gonna go on till step 200.
But here's a bit more again.
70. 12(3) at R8C5 = {138/147/156/237/246/345}
70a. {345} blocked, this is how:
70aa. R9C6 = 3 -> R89C5 = {45} -> R7C5 = 5: 2 5's in C5
70ab. R9C6 = 5 -> R89C5 = {34} -> R7C5 = 7 -> 18(3) at R1C5 = {189} -> 16(3) at R1C6 = {457} -> R12C6 = {57}: 2 5's in C6
70b. 12(3) at R8C5 = {138/147/156/237/246}: only place for 1 is R9C5 -> R9C5: no 5
70c. 12(3) at R8C5 = {138/147/156/237/246}: {1/2...}
71. 12(3) at R8C2: {129} blocked by 12(3) at R8C5 -> no 9 in 12(3) at R8C2
71a. 9 in N9 locked in 21(3) at R8C4 = {489/579}: no 6; {4/5...}/{4/7...}
71b. 12(3) at R8C2 = {138/156/237/246}: {147/345} blocked by 21(3) at R8C4
71c. 12(3) at R8C5 = {138/156/237/246}: {147} blocked by 21(3) at R8C4
Richard (rcbroughton)I share Mike's pessimism. This one is a stinker.
72. 45 rule on c9 - innies total 33
72a. 2 in r6c9 means r7c9=4 - r1289c9=27 = {37}{89} or {57}{69}
72b. {37}{69} - blocked because can't make cage sum in 21(3)r8c8
72c. {57}{69} - blocked because can't make cage sum in 12(3)r1c8
73. 15(3)r6c8 - only combo with 9 is {249} - no 9 at r6c8
74. 45 rule on r1234 r5c58 = r34c9 + 5
74a. Innies total 10,8,7,6,5,4,3 - outies total 15,13,12,11,10,9,8
74b. 10 - 15 - requires 2 9's in nonet r3c9
74c. 8 - 13 - can't have 13=[67] in outies
74d. 7 - 12 - can't have {66} in outies
74e. 6 - 11 - can't have 6 in outies because need 6 in r5c9
74f. 5 - 10 - no 6 at r5c5 (missing 4 at r5c8)
74g. 4 - 9 - outies can't be [63] as it makes two 3's in nonet r3c9
74h. 3 - 8 - outies can't be [62] as it makes two 2's in nonet r39
74i. (phew) no 6 at r5c5
Lots of work for not very much
ParaJust a little bit....
75. 15(3) in R6C8 = {249/348/357/456}(needs 4 or 5 in R7C9): {4/7...}
75a. 12(3) in R3C9 = {129/138/156}({3/6/9}: {147} blocked by 15(3) -->> no 4,7
75b. 18(3) in R4C7 = {279/378/468/567}: {369} blocked by 12(3)
76. LOL R789: R5C467 + R6C4567 = R7C12349 + R8C13: All cells in innies in same house except R7C9, which contains only {45} so only {45} can appear twice in the outies.
76a. 12(3) at R5C6 = {246/345} = {3/6..}
76b. 14(3) at R5C4 = {158/167/347}: {356} blocked by LOL R789 + 12(3) at R5C6
77. R5C4: no 5, this is how.
77a. R5C4 = 5 -> R6C45 = {18} -> R6C7 = 2 -> 12(3) at R5C6 = {345} except no room left for 5 in 12(3)
Mike (mhparker)TJK18: The next action-packed episodeMore candidates than usual gone this time. Fun, isn't it?
.
78. 18(3)r2c1 = {189/369/378/459/468}
78a. {459} blocked. Here's how:
78b. LoL r123: r2c1+r3c129 = r4c456+r5c5
78c. outies include 11(3) cage
78d. -> 3 of the digits in innies must add up to 11
78e. -> if r3c9 = 1, 2 of 18(3)r2c1 must sum to 10 and...
78f. ...if r3c9 = 2, 2 of 18(3) must sum to 9
78g. now, if 18(3) = {459}, then 14(3)r4c1 = {167} (only non-conflicting combo)
78h. -> r3c9 = 1 (hidden single c9)
78i. but this contradicts assertion in step 78e
78j. -> 18(3)r2c1 <> {459}
78k. -> 18(3)r2c1 = {189/369/378/468} (no 5) = {(3/8)..}
78l. -> {238} combo blocked from 13(3)r5c1
79. LoL r123 (see step 78b): no 5 in innies -> no 5 in outies
79a. -> no 5 in 11(3)r4c4, no 7 in r6c5 (step 17)
79b. -> 11(3)r4c4 = {128/137/146/236} = {(1/6)..}
79c. -> {169} combo blocked for 16(3)r2c3
80. no 4 in r2c1 (requires {68} in r3c12 -> conflict w/ r3c67)
81. r3c679 (innies r123) = h16(3)r3 = {169/268} = {(1/8)..}
81a. -> r3c12 <> {18}
81b. -> no 9 in r2c1
82. LoL r12: r1c89+r2c1789 = r3c345+r4c45+r5c5
82a. no 9 in innies -> no 9 in outies r3c345
83. 9 in c4 locked in n9
83a. -> no 9 in r9c3
84. 18(3)r1c5 = {189/369/459/567} (step 66)
84a. {69} only in r12c5
84b. -> no 3 in r12c5
85. no 2 in r2c3 (would require one of {69} in r3c34 - unavailable)
86. CPE: r7c4 sees all 7's in n7(r5c4)
86a. -> no 7 in r7c4
87. no 1 in r7c3 (would require 8 in r7c4 -> clash w/ r7c789, which needs 1 of {18} (step 61))
88. 14(3)r5c4 = {158/167/347} (step 45b)
88a. {17} only in r56c4
88b. -> no 6 in r56c4
89. {345} combo blocked from r456c4 (innies c1234) = h(12)c4. Here's how:
89a. 5 only within 14(3)r5c4 -> 14(3) = {158}
89b. -> can't get 2 of {345} in r56c4
89c. -> h(12)c4 = {138/147/156/237} ({246} blocked because {26} only in r4c4)
89d. -> h(12)c4 = {(1/2)..}
89e. -> r12c4 <> {12}
89f. -> no 8 in r1c3
New marks pic after step 89f:
Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789 123456789 | 123456 1234568 | 1456789 | 134579 489 | 123457 23457 |
:-----------. :-----------. | | .-----------'-----------. |
| 3678 | 123456789 | 13456789 | 1234568 | 1456789 | 134579 | 13457 123457 | 23457 |
| '-----------: '-----------: :-----------'-----------. :-----------:
| 134789 134789 | 1234578 1234578 | 134578 | 689 69 | 123457 | 12 |
:-----------------------'-----------.-----------'-----------: .-----------'-----------: |
| 123456789 123456789 12345 | 12346 1234678 | 89 | 3457 2356789 | 123569 |
:-----------------------.-----------+-----------. :-----------'-----------. | |
| 123456789 123456789 | 56789 | 13478 | 123478 | 2346 456 | 2356789 | 25689 |
| .-----------' | '-----------: .-----------+-----------'-----------:
| 123456789 | 56789 56789 | 134578 34568 | 2346 | 12 | 234567 3456789 |
:-----------'-----------.-----------'-----------.-----------'-----------: '-----------. |
| 1234678 1234678 | 234678 123468 | 5789 2569 | 139 189 | 45 |
| .-----------: .-----------+-----------. :-----------.-----------'-----------:
| 12345 | 2345678 | 12345 | 45789 | 2345678 | 125 | 23489 | 56789 56789 |
:-----------' :-----------' | '-----------: '-----------. |
| 12345678 12345678 | 4578 45789 | 12347 3567 | 23489 3469 | 56789 |
'-----------------------'-----------------------'-----------------------'-----------------------'-----------'
ParaMorning all, here's last nights moves from when internet went down here. That's 4 digits in 6 moves.
90. 18(3) at R2C1 = {189/369/378/468} = {1/6/7..}
90a. 14(3) at R4C1: {167} blocked by 18(3)
91. 14(3) at R4C1: {356} blocked; Here's how:
91a. 14(3) = {356}: R4C45 and R4C78 need {47} but can't contain both
91aa. 11(3) at R4C7 = {137}({146 blocked cause no 6 available) -> R5C5 = 3; R4C4 = 7; R4C3 = 1-> R6C5 = 3(step 17): 2 3's in C5
91b. 14(3) = {149/158/239/248/257/347}: no 6
92. 14(3) at R4C1: {347} blocked; here's how
92a. 14(3) = {347} -->> R2C7 = 7(hidden single) -->> R23C8 = {12} -->> naked pair {12} in R3C89(nowhere else in R3), which leaves no options for 18(3) at R2C1
92b. 14(3) = {149/158/239/248/257}: {1/2..}
93. R5C5: no 8
93a. R5C5 = 8 -> R4C45 = {12}: clashes with 14(3) cage at R4C1
94. outies R1234: R5C589 = 17: R8C59 = 15/13/12/11/10/9/8, so R8C8: no 3
95. 14(3) at R4C1: {158} blocked; this is how
a.14(3) = {158} -> R4C6 = 9 -> R3C9 = 2("45" R123): no place for 1 in C9
b. 14(3) = {149/239/248/257} = {2/4..}
c. 13(3) at R5C1: {247} blocked by 14(3)
So at a pace of eliminating an average of 1 digit per move how many moves do we have to make before we are done?
sudokuEdFirst: a very big thankyou to Mike for getting around my mistake way back forever ago. A really neat move it was too. Para noticed the same mistake. Thanks to you both.
I admire everyones perserverence with this. I'm glad i can finally add some more.
96. no 6 r6c5. Here's how.
96a. "45" c1234: 3 outies r456c5 = 13 = h13(3)r4c5
96b. = {148}/{17}[5]/{238}/[625]/[634]/[643] ({{27}[4]/{34}[6} blocked by combo's in 11(3))
96c. -> no 6 r6c5
96d.-> no 4 r4c4 (I/O c1234)
97. 14(3)r5c4 = {158/347}
98. {258} combo. blocked from 15(3)r7c5. Forces 3 into both 14(3) and 16(3) in this nonet.
98a. 15(3)r7c5 = {159/267}(no 8)
98b. -> no 6 r9c6 (I/O c6789)
98c. 15(3)r7c5:6 only in r7c6 -> no 2 r7c6
99. 12(3)r8c5 = {138/156/237}(no 4)({246} blocked by r9c6)
99a. 1 only in r9c5 -> no 5 r8c5
100. from step 67. Hidden13(3) at R78C6 + R9C6 = [913]/[517]/[625]
100a. -> r7c5 + r9c6 =
i.[5][3]
ii.[9][7]
iii.[7][5]
100b. -> r789c5 =
i.[581]/[5]{27}
ii.[9]{23}
iii.[761]
100c. = [2/5/6..]
101. from step 96b. h(13)r456c5 = {148}/{17}[5]/{238}/[634]/[643] ([625] blocked by r789c5)(step 100c.)
102. {17}[5] blocked from r456c5. Here's how.
102a. r456c5 = {17}[5] forces 9 into both r789c5 (step 100b.) and 18(3)r1c5
102a. h(13)r456c5 = {148}/{238}/[634]/[643] (no 5 or 7 r456c5)
102b. -> no 3 r4c4 (I/O c1234)
103. 14(3)r5c4 = {158/347}.
103a. {15} only in r56c4 -> no 8 r56c4
104. 12(3)r8c5 = {138/156/237} = [1/3..]
104a. -> 12(3)r8c2 = {156/237/246}(no 8) ({138} blocked by other 12(3))
105. 11(3)r4c4 = {128/146/236} = [6/8..]
105a. -> {268} blocked from 16(3)r2c3
105b. -> {468} blocked from 18(3)r1c1
106.from step 89c. h(12)r456c4 = [1]{47}/[615]/[2]{37}
106a. no 1 r6c4
107. weak links on 1s in r7 & 12(3)r6c7
107a. -> no 1 r8c1 (1 in r6c7 -> 1 in r7 in n6r4c3 -> no 1 in 8c1: 1 in r7c1 -> no 1 in r8c1))
108. 11(3)r7c1 {128} blocked: r7c12 = {18} -> 12(3)r6c7 = {138}:but 2 8s r7
108a. = {137/146/236/245}(no 8) = [3/4..]
109. 12(3)r7c3 = {138/147/237/246}(no 5)({345} clashes with 11(3) step 108a)
i. {138}
ii. [714] only. 7 in r7c3 -> 15(3) r7c5 = {159} with 1 in r8c6 -> no 1 in r8c3
iii. [7]{23}
iv. {26}[4]. 6 in r7 -> 15(3)r7c5 = {59}[1] -> r7c9 = 4 -> no 4 possible in r7c34
109a. -> no 4 r7c34
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 123456789 123456789 123456 | 1234568 1456789 134579 | 489 123457 23457 |
| 3678 123456789 13456789 | 1234568 1456789 134579 | 13457 123457 23457 |
| 134789 134789 1234578 | 1234578 134578 689 | 69 123457 12 |
:-------------------------------+-------------------------------+-------------------------------:
| 12345789 12345789 12345 | 126 123468 89 | 3457 2356789 123569 |
| 123456789 123456789 56789 | 1347 1234 2346 | 456 256789 25689 |
| 123456789 56789 56789 | 3457 348 2346 | 12 234567 3456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 123467 123467 23678 | 12368 579 569 | 139 189 45 |
| 2345 234567 1234 | 45789 23678 125 | 23489 56789 56789 |
| 1234567 1234567 4578 | 45789 1237 357 | 23489 3469 56789 |
'-------------------------------.-------------------------------.-------------------------------'
Mike (mhparker)Light at the end of the tunnel Thanks Ed, that made a big difference.
A couple of overlooked moves first...
110. no 5 in r8c6 (from permutations for h13(3) listed in step 100)
111. 2 in r7 locked in n6(r5c3)
111a. -> no 2 in r8c13
Now to get down to business...
112. LoL r123 (see step 78b): no 7 in outies -> no 7 in innies r2c1+r3c12
112a. -> 18(3)r2c1 = {189/369/468} = {(4/9)..}
112b. 6 only in r2c1 -> no 3 in r2c1
113. 14(3)r4c1 = {149/239/248/257} (step 95b)
113a. {149} blocked by 18(3)r2c1 (step 112a)
113b. -> 14(3) = {239/248/257} (no 1)
113c. 2 locked for r4 and n4
114. h12(3)r456c4 (step 106) = {147/156} (no 3)
114a. 1 locked for c4
115. CPE: r5c5 sees all 1's in c4
115a. -> no 1 in r5c5
116. LoL r1234: r2c1+r3c12+r4c123 = r5c589+r6c89+r7c9
116a. no 1 in outies -> no 1 in innies r3c12
117. 18(3)r2c1 = {369/468}
117a. 6 locked, only in r2c1
117b. -> r2c1 = 6 \:D/
117 moves to make a placement! (never would have thought first to go would be a cell in the top-left of the grid). Time for a handover (marks pic to follow).
ParaOk a bit of overlap with Mike. Here is what he left out that i did get.
118.First some clean up: R6C2: no 5(i/o C12); R6C5: no 4(I/O c1234)
119. 11(3) in R4C4 = {128/146/236}: 2 only in R5C5 -> R5C5: no 3
119a. Needs one of {24}: has to go in R5C5 -> R4C5: no 4
120. 14(3) at R5C4 = {158/347}; R6C5 needs {3/8} so nowhere else in 14(3) -> R56C4: no 3
More later
ParaHere's some more. I can't see that 6 opening things up but i might be overlooking something.
121. 6 in N2 locked for R1
121a. 6 in N1 locked for R4
121b. 6 in N1 locked in 11(3) at R4C3 -->> 11(3) = {164/632}: no 8; {3/4..}
121c. Clean up: R5C9: no 5
122. R3C12 = {39/48}: {8/9..}
122. Killer Triple {689} in R3C1267: locked for R3
123. 18(3) at R1C5 = {189/369/459/567}
123a. {89} only in R12C5 -> R12C5: no 1
123b. 6 only in R1C5 -> R1C5: no 7
124. 16(3) at R2C3 = {178/259/358/457}
124a. {89} only in R2C3 -> R2C3: no 1,3
125. colouring on 1's from C4: R3C5 <> 1
125a. R4C4 = 1 -> R3C9 = 1: R3C5 <> 1
125b. R5C4 = 1 -> R1/2C6 = 1: R3C5 <> 1
126. one more colouring 1's from C4: R9C1 <> 1
126a. R4C4 = 1 -> R9C5 = 1: R9C1 <> 1
126b. R5C4 = 1 -> R6C1 = 1: R9C1 <> 1
127. 1 in 12(3) at R8C2 only in R9C2 -->> R9C2: no 5
128. "45" R1234 : R5C589 = 17 = [2]{69}/[278]/[458]/[476]: R5C8: no 2,8; R5C9: no 2
128a. 12(3) at R3C9 = [219/156/138]: R4C9: no 9
Time for other things right now. Maybe later tonight some more. Leave something for me
Richard (rcbroughton)A couple of quick ones
129. 2 in n5 (r3c9) only in r3c9/r6c8 - > no 2 in r3c8
130. from 125b. 18(3) r1c5 - no 1, so {189} no longer valid. No 8 r12c5
131. 8 in c5 locked at r6r8 -> CPE no 8 at r8c7
132. 10(3) ar r2c7 = {127}/{145}/{235} (6 has gone)
132a. 2 only at r2c8 -> no 3,7 r2c8
133. 12(3) r3c9 = [219]/[138]/[156] - > no 9 at r4c9
134. 18(3)r4c7 ={378}/{468}/{567} - no 9
134a. 8 only at r4c8 -> no 3 at r4c8
134b. 6 only at r5c8 -> no 5 at r4c8
135. 9 now locked at r56c9 for c9 - nowhere else in c9
Richard (rcbroughton)Just had to post this one - might just have cracked it!!
136. 45 on r4. Innies r4c456789 = 31
only combinations are:
{135679}, {145678}. {134689}
(can't place {235678}, {234679}. {234589}, {125689}. {124789})
136a. {135679}/{134689} - 9 must be at r4c6
136b. {145678} - r4c45={16} r4c6={8} r4c9={5} - so r4c78={47} but it can't be {47} as you can't make 18(3).
136c. r4c6 = 9
136d. r3c7= 6
136e. r3c6 = 8
Mike (mhparker)Thanks, Richard!
Unfortunately, you beat me to it with your last move. Here's another way of peeling the proverbial onion:
136. r4c789 cannot contain both of {45} due to r7c9
136a. only other place for {45} on r4 is 14(3)r4c1
136b. -> 14(3)r4c1 = {(4/5)..} = {248/257} (no 3,9)
136c. -> hidden single in r4 at r4c6 = 9
136d. -> r3c67 = [86]
As requested, I think we should leave the rest for Para...
ParaYou could at least have provided me with a marks pic
.
ParaI get to do all singles, i am so happy. I think i can handle that.
137. I/O dif R123: R3C9 = 2 -> R45C9 = [19]
137a. R4C45 = [63]; R5C5 = 2; R6C5 = 8
137b. R56C4 = [15](last possible combi); R789C6 = [625]; R7C5 = 7
137c. R89C5 = [61]; R7C13 = [51](hidden 8(3) cage); R6C1 = 1(hidden)
137d. R7C7 = 2; R7C9 = 5(hidden); R9C9 = 6(hidden); R5C7 = 5(hidden)
137e. R1C6 = 8(hidden 19(3) in C7); R3C8 = 1(hidden); R7C7 = 1(hidden); R7C8 = 9
137f. R1C3 = 6; R6C2 = 6; R5C8 = 6; R4C8 = 8; R8C9 = 8(all hidden)
137g. R4C7 = 4; R8C8 = 7; R6C89 = [37]; R56C6 = [34]; R56C3 = [79]
137h. R9C8 = 4; R9C3 = 8
137i. R2C2 = 8; R5C1 = 8; R7C4 = 8(all hidden); R5C2 = 4; R7C123 = [423]
137j. R8C247 = [349]; R9C12 = [27]; R9C47 = [93]; R4C123 = [752]
137k. R3C12 = [39]; R1C12 = [91]; R12C6 = [71]; R2C78 = [72]
137l. R12C4 = [23]; R12C9 = [34]; R1C8 = 5; R123C5 = [495]; R23C3 = [54]; R3C4 = 7
And we have this:
Code:
.-------.-------.---.-------.-------.
| 9 1 | 6 2 | 4 | 7 8 | 5 3 |
:---. :---. | | .---'---. |
| 6 | 8 | 5 | 3 | 9 | 1 | 7 2 | 4 |
| '---: '---: :---'---. :---:
| 3 9 | 4 7 | 5 | 8 6 | 1 | 2 |
:-------'---.---'---: .---'---: |
| 7 5 2 | 6 3 | 9 | 4 8 | 1 |
:-------.---+---. :---'---. | |
| 8 4 | 7 | 1 | 2 | 3 5 | 6 | 9 |
| .---' | '---: .---+---'---:
| 1 | 6 9 | 5 8 | 4 | 2 | 3 7 |
:---'---.---'---.---'---: '---. |
| 4 2 | 3 8 | 7 6 | 1 9 | 5 |
| .---: .---+---. :---.---'---:
| 5 | 3 | 1 | 4 | 6 | 2 | 9 | 7 8 |
:---' :---' | '---: '---. |
| 2 7 | 8 9 | 1 5 | 3 4 | 6 |
'-------'-------'-------'-------'---'