Ed: Para wrote "TJK 31V2 This one is a lot harder."
Oh silly me. Nice one Para.
Here is the start. Haven't looked at any combination crunching yet. Will have to work on this one over the week. Anyone is welcome to join in
.
TJK 031V20. 10(2)r2c6 - no 5
0a. 26(4)r4c9 - no 1
0b. 9(2)r7c4 - no 9
0c. 20(3)r7c5 - no 12
0d. 6(3)r7c8 ={123}
0e. 19(3)r8c6 - no 1
1. 6(3)r7c8 = {123}: all locked for n8
2. "45" n8(r7c7): r79c7 = 15 = h15(2)n8
2a. = {69/78}
3. 24(4)r8c7 must have 4 and 5 for n8 = 45{69/78}
4. "45" n1: r13c3 = 7 = h7(2)n1
4a. ={16/25/34}(no 789)
5. "45" c123: (remembering the h7(2)n1):r456c4 = 15
6. LoL c123: 3 outies r456c4 = 3 innies r8c3 + r9c23
6a. 3 outies = 15 (step 5) -> 3 innies = 15
6b. -> r7c23 = 15 (same cage as 3 innies)
6b r7c23 = h15(2)r7 = {69/78} = [7/9,8/9..]
7. 20(3)r7c5 = {569/578} ({389/479} blocked by h15(2)r7 step 6b)
7a. = 5{69/78}(no 1..4)
7b. 5 locked for r7 and n4(r3c4)
7c. no 4 r8c4
8. Killer quad {6789} in 20(3)r7c5 and h15(2)r7
8a. {6789} locked for r7
8b. no 123 r8c4
9. LoL r789: 3 innies r7c456 = 3 outies r6c234
9a. 3 innies must have 5 -> 3 outies must have 5
9b. -> 15(3)r6c2 must have 5 = 5{19/28/37/46}
9c. 5 locked for r6 & n7(r6c2)
10. Common Peer Elimination (CPE): no 4 in r6c4 since it can 'see' both 4's in r7
11. LoL r123: 3 innies r3c456 = 3 outies r4c678
11a. no 5 in innies (from step 7b) -> no 5 in outies
11b. 15(3)r4c6 = {168/249/267/348}
12. "45" n3(r1c9): 2 innies r3c78 = 13 = h13(2)n3
12a. = {49/58/67}
13. rest of 24(5)r1c7 = 24 - 13 = 11 = h11(3)n2
13a. no 9 r1c78 or r2c7
14. LoL c789: 3 innies r1c78 + r2c7 = 3 outies r456c6
14a. no 9 in innies -> no 9 in outies r456c6
15. "45" c6789: r1c6 = r7c5
15a. -> r1c6 = {56789}
16. 5 in c6 only in r17c6. Here's how.
16a. 2 5's in r7 in c56.
16b. 5 in r7c5 -> 5 in r1c6 (step 15)
16c. or 5 in r7c6
16d. 5 locked for c7
17. LoL c789: 3 innies r1c78 + r2c7 = 3 outies r456c6
17a. no 5 in outies -> no 5 in innies
18. "45" n2: (remembering h11(3)n2): r1c3 = r2c6 = {12346}
18a. no 123 r3c6
18b. no 2 r3c3 (h7(2)n1)
19. LoLr89: 3 outies r7c789 = 3 innies r8c12 + r9c1
19a. no 4 in outies -> no 4 in innies
19b. 15(4)r7c1 = {1239/1248/1347/2346}
20. CPE: no 4 in r6c1 since it sees all 4's in n7(r6c2)
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 123456789 123456789 12346 | 123456789 123456789 56789 | 1234678 1234678 123456789 |
| 123456789 123456789 123456789 | 123456789 123456789 12346 | 1234678 123456789 123456789 |
| 123456789 123456789 13456 | 12346789 12346789 46789 | 456789 456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 123456789 123456789 | 123456789 12346789 1234678 | 12346789 12346789 23456789 |
| 123456789 123456789 123456789 | 123456789 12346789 1234678 | 123456789 123456789 23456789 |
| 1236789 123456789 123456789 | 12356789 12346789 1234678 | 12346789 2346789 2346789 |
:-------------------------------+-------------------------------+-------------------------------:
| 1234 6789 6789 | 1234 56789 56789 | 6789 123 123 |
| 1236789 1236789 123456789 | 5678 123456789 2346789 | 456789 456789 123 |
| 1236789 123456789 123456789 | 123456789 123456789 2346789 | 6789 456789 456789 |
'-------------------------------.-------------------------------.-------------------------------'
Richard: I'll jump in on this one - I think there is going to be some significant crunching on this one. I'm struggling to find a few moves to build on your start.
21. LOL on c6-9 - r3789c6 contains no 1 - so no 1 in r12c45 (just as well I got my Jigsaw highlighting working again!)
21a. 18(3) r1c5 now has no 1 - {189} no longer valid
22. 45 rule on c 1-4 r3c5=r9c4 (Let's make a note of this one - could be useful later)
22a. no 5 at r9c4
Couple of extra moves on the train this morning.
23. 45 Rule on n4 - innies r3c456 r7c456 total 30
Cage 20(3) at r7c5 limits r7c56 = 11,12(no 8),13(no 7),14(no 6) = {56}/{57}/{58}/{59}
Cage 12(3) at r3c3 limits r3c45 = 11,9(no 3),8,7,6={29}/{38}/{47}/{18}/{27}/{17}/{26}/{16}/{34}/{24}
23a. combinations = {234579}/{135678}/{125679}/{134589} (must use a 5)
23b. {234579} - r7c56={57} - > r3c345={29}4/{34}9/{24}9
23c. {234579} - r7c56={59} - > r3c345={27}4/{34}7/{24}7
23d. {134589} - r7c56={58} -> r3c345={34}9
23e. {134589} - r7c56={59} -> r3c345={34}8
23f. No other combo with a 4 - > no 4 at r7c4
23g cleanup - no 5 at r8c4
24. Hidden single 4 at r7c1 for r7
24a. 15(4)r7c1 = {1248}/{1347}/{2346} - no 9
25. 15(3)r6c2 - no {168}/{267} - blocked by 15(4)r7c1
25a. no 6 in 15(3)r6c2
26. LOL on r89 - no 9 in r8c12, r9c1 - > no 9 at r7c7
26a. innies on n9 r7c7+r9c7 = 15 - > no 6 at r9c7
27. LOL on r789 - no 6 in r6c
234 -> no 6 in r7c456
27a. (from step 22) - no 6 at r1c6
Ed: Nice one Richard. First placement already. This is going to be a breeze.
First up, alternate step 23, then a bit of combo crunching then finally a couple of eliminations to make the post worthwhile.
Alternative step 23.
23. no [45] in 9(2)r7c4. Here's how.
23a. from step 6b: r7c23 = h15(2)r7 = {69/78} = [6/8,6/7..]
23b. -> r8c3 + r9c23 = 15 = h15(3)r8c3
23c. = {159/249/258/348/357/456} ({168/267} clash with h15(2))
23d. = [4/5..]
23e. from LoL c123: 3 outies r456c4 = 3 innies r8c3 + r9c23
23f. -> 3 outies r456c4 = [4/5..]
23g. -> [45] blocked from 9(2)r7c4
Now some combo. work.
28. r3c78 = h13(2) = {49/58/67}
28a.-> r1c78 + r2c7 = h11(3) = {128/137/146/236}
29. 15(3)r4c5 = {168/249/267/348}
30. "45" c6789: r127c5 = 18 = h18(3)c5
30a. = {279/378/459/567} ({369/468} blocked by 15(3)r4c5 step 29)
30b. since r7c5 = r1c6 (i/oc6789) -> {369/468} also blocked from 18(3)r1c5
30c. 18(3)r1c5 = {279/378/459/567}
A few eliminations! Hope these are correct.
31. no 8 in r8c78, Here's how. (This might be easier to see if they were written as xy chains: might have to edit)
31a. r7c456 = same combinations as 15(3)r6c2 (from LoL r789)
31b. = [1]{59}/[2]{58}/[3]{57}
31c. -> r7c4 + r7c56 + r7c7 = [1]{59}[6]/[2]{58}[7]/[3]{57}[8]
31d. -> r7c7 + r8c4 = [68/77/86]
i. 8 is in r8c4 when 6 is in r7c7 -> no 8 in r8c78
ii. or 8 is in r9c7 when r7c7 = 7 -> no 8 in r8c78
iii. or 8 is in r7c7 -> no 8 in r8c78
32. no 7 in r8c12. Here's how.
32a. from LoL r89: 3 outies r7c789 = 3 innies r8c12 + r9c1
32b. 7 in outies in r7c7 -> 7 in r8c4 (step 31d) -> no 7 in r8c12
-> 7 in innies only fits in r9c1.
32c. if 7 is not in r7c7 -> from LoL r89, no 7 is possible in 8c12
Para: sudokuEd wrote "Nice one Richard. First placement already. This is going to be a breeze.
"
Look who's getting cocky. I never said it was going to be like TJK 18. But this was the easy bit. It get's a bit more challenging from now on. Took me a few days(well mostly nights) to solve it.
ps.
sudokuEd wrote "5. "45" c123: (remembering the h7(2)n1):r456c4 = 15"
Read my walkthrough for V1?
Richard: 33. 45 on n9 r8c3. outies = 25, but r7c23 = 15 so r7c4+r9c7 = 10.
33a. but, since r79c7=15, when r7c4=1 -> r7c7=6, 2->7, 3->8
33b. r7c456=h15(3)
33c. r3c456=h15(3)
34. placement for h15(3)r3c456 and h15(3)r7c456 -
34a. no 2 at r7c4, no 8 at r7c56 because:
{234579} -> needs r7c456=3{57},
{135678} -> needs r7c456=3{57},
{125679} -> needs r7c456=1{59},
{134589} -> needs r7c456=1{59},
34b. (from 21) no 8 at r1c6
35. from 33 - > no 8 at r9c7, no 7 at r7c7
35a. no 7 at r8c4
36. 2 locked in r7c89 for r7 - no 2 at r8c9
37. LOL on r89
37a. No 7 in outies r7c789 - so no 7 at r9c1
37b. 15(4) at r7c1 now = 4{128}/4{236} - must use 2, no 2 in 15(3)r6c2
37c. {258} no longer valid in 15(3) - no 8
[edit - a couple more for Ed to work on overnight]
38. 45 rule on n8 r7c7 - outies total 24.
38a. r7c56=12 -> r89c6 = 12, no 7 = {39}/{84}
38b. r7c56=14 -> r89c9=10, no 8,9 = {37}/{64}
38c - > no 2 in r89c6
Archive note. As alternative way to eliminate 2 from r89c6 is 45 rule on n79 3 innies r8c4+r89c6 1=18 cannot be {279}39. LOL on
c6789 - no 2 in r3789c6 - so no 2 in r12c45
40. outies of c1-4 = r389c6 = h12(3) ={129}/{138}/{147}/{156}/{237}/{246}/{345}
40a. so r127c6=h18(3) = {459}/{567}/{369}/{378}
40b. 15(3) in c5 = {168}/{249}/{267}/{348}
combining 40a/40b. = 33(6)={459}{168}/{459}{267}/{567}{249}/{567}{348}/{378}{249}
={145689}/{245679}/{345678}/{234789} = must use 4, blocked by 1/2/9, 1/4/7, 2/4/6, 3/4/5
40c so h12(3)={138}/{156}/{237} - no 4
41. 45 on c1-4 r9c4 = r3c5 - no 4 at r9c4
Ed: Good going Richard. Step 34 has made a big difference. Here's the next batch of steps.
Think there is a typo in step 40c, so will give an alternate step 40 first.
Alternative step 40. Trying to work out what happened to {129} combo in h12(3)
40. Updating step 30. r127c5 = 18 = h18(3)c5 = {378/459/567} & 15(3)r4c5 = {168/249/267/348}
40a. combining the two cages = {378-249/459-168/459-267/567-249/567-348}
40b. -> 4 locked for c5
40c. "45" c5: r389c5 = 12 = h12(3)c5= {
129/138/156/237}
More
42. 3 innies n9(r8c3): r8c4 + r89c6 = 18 = h18(3)n9
42a. = [6]{39/48}(from step 38a)
42b. = [8]{37/46}(from step 38b)
42c. = {369/378/468} = [3/8..]
43. 12(3)r8c5 = {129/156/237}(no 8)({138} blocked by h18(3)n9 step 42c)
43. ->no 8 r3c5 (I/Oc1234)
44. h12(3)c5 (alt.step 40c) = {129/156/237} = [2/6/7..]
45. 15(3)r4c5 = {168/249/348}(no 7) ({267} blocked by h12(3) step 44)
46.from alt. step 23b,c: r8c3 + r9c23 = h15(3)r8c3
46a. = {159/249/357/456}(no 8) ({258} blocked by 12(3)r8c5;{348} blocked by h18(3)n9 step 42)
47. LoL c123: 3 outies r456c4 = 3 innies r8c3 + r9c23
47a. no 8 in innies -> no 8 in outies
48. {159} blocked from h15(3)(r8c3 + r9c23 step 46a). Here's how.
48a. {159} in h15(3) -> r7c23 = {78} -> r7c7 = 6 -> r7c4 = 1 (step 33a)
48b. {159} in h15(3) -> from LoLc123: outies r456c4 = {159}
48c. but this means 2 1's in c4
48d. -> {159} blocked from h15(3)n9
49. updating step 46a. h15(3)n9 = {249/357/456} (no 1)
49a. -> r456c4 (LoLc123) = {249/357/456}(no 1)
49b. -> r456c4:no 9 r45c4 ({249} combo, 9 only can go in r6c4)
50. 1 in n9 now only in 12(3)r8c5
50a. = {129/156}(no 3,7)
50b. -> no 3 or 7 in r3c5 (i/oc1234)
50c. 12(3) = [6/9..]
51. from step 42. 3 innies n9 = h18(3)n9
51a. = [6]{48} ([6]{39} blocked by 12(3)n9 step 50c.)
52b. = [8]{37/46}
52c. = {378/468}(no 9)
53. no 1 in 15(3)r4c5. Here's how.
53a. 1 in 12(3)r8c5 in r9c4 -> 1 in r3c5 (i/oc1234) -> no 1 elsewhere in c5
53b. 1 in 12(3) in r89c5 -> no 1 elsewhere in c5
53c. 1 in c5 only in r389c5.
54. 15(3)r4c5 = {249/348} = 4{29/38}
54a. 4 locked for c5 & n4(r2c4)
54b. no 6 r2c6
Over to you Richard. Should be here.
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 12356789 123456789 12346 | 3456789 356789 579 | 1234678 1234678 123456789 |
| 12356789 123456789 123456789 | 3456789 356789 1234 | 1234678 123456789 123456789 |
| 12356789 123456789 13456 | 1236789 1269 6789 | 456789 456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 12356789 123456789 123456789 | 234567 23489 1234678 | 12346789 12346789 23456789 |
| 12356789 123456789 123456789 | 234567 23489 1234678 | 123456789 123456789 23456789 |
| 1236789 13579 13579 | 3579 23489 1234678 | 12346789 2346789 2346789 |
:-------------------------------+-------------------------------+-------------------------------:
| 4 6789 6789 | 13 579 579 | 68 123 123 |
| 12368 12368 2345679 | 68 12569 34678 | 45679 45679 13 |
| 12368 2345679 2345679 | 1269 12569 34678 | 79 456789 456789 |
'-------------------------------.-------------------------------.-------------------------------'
Richard: Sorry - but the train journey this evening provided just enough time to finish it.
weren't really any other tricky moves from where you'd left it.
55. 6 Locked in r3c456 in nonet at r3c4. Locked for r3
56. 18(3)r1c5 = {378}/{567} - must use 7. - nowhere else in nonet
57. LOL on r123 - no 4 in r3c456 - so no 4 in r4c678
57a. no 4 in 15(3) r4c6 = 6{18}/{27} - no 3, 9
57b. 6 locked for n3 and r4
58. LOL on c789 - no 7 in r1c78 r2c7 - so no 7 in r456c6
59. LOL on r123 - no 3,9 in r4c678 - so no 3,9 in r3c456
60. 12(3)r3c3 = 4{26}/[381]/[471]/5{16}/[372] - no 1 at r3c3
61. 45 Rule on n2r1c4 - outies r1c3 r3c6 total 10
61a. r1c3 - no 1,6
62. 9 locked in r12c4, 16(3) for c4 = 9{25}/9{34} - no 8
63. Hidden single 9 at r7c6 for c6
63a. 20(3)r7c5 = [596]
64. Hidden single 5 at r1c6 for c6
64a. 18(3)r1c5=5{67}
64b. {67} locked for c5
65. 16(3)r1c3 = {349}
65a. Cleanup - no 3,4 at r1c78
66. 10(2)r23c6 = no 1 at r2c6
66a. 1 locked in r1c78+r2c7 for n2 -> h11(3) = {128}
67. 10(2)r23c6 - no 8 at r3c6
68. 9 locked in 12(3) r8c5 for c5 - 12(3)={129}
69. h15(2) r7c23 = naked pair {78}
70. 15(4) r7c1 = 4{236}
70a. Naked single 5 at r6c4 -> 15(3)r6c2={19}5
70b. {19} locked at c23 for r6
71. 30(5)r7c2 = {78}{456} - no 2,3
71a {456} locked for nonet
71b. naked single 8 at r8c4 - > 9(2) = [18]
72. naked single 2 at r9c4 and r3c5
73. 19(3) r8c6 = {73}9
73a naked single 1 at r9c5 -> r8c5=9
74. Naked single 1 at c9 for r8
75 Naked pair {76} at r3c46
75a. 12(3)r3c3=[462][372] - no 5
76. 24(5)r1c7={128}[49]
76a. Naked single 3 at r3c3 - > r3c4=7, r1c3=4 -> r3c6=6 -> r2c6=4
77. hidden single 4 at r9c2 for nonet
78. hidden single 4 at r8c8 for r8 and nonet
79. hidden single 6 at r4c8 for nonet
80. naked pair {56} at r89c3
81. naked pair {39} at r12c4
81a. r4c4=4
81b. r5c4=6
82. hidden single 6 at r6c9 for row, col and nonet
83. 1 locked in r5c678 for nonet - locked for row5
83a. 1 locked in r4c123 for nonet - locked for row 4
83b. hidden single 1 at r2c8 for nonet
84. 17(4)r1c9 = 1{358} - {358} locked for nonet and col 9
84a.
naked single 2 at r4c6 - 15(3) = [276]
84b. r8c7 = 5
84c. r8c3=6, r9c3=5
84d. r7c9=2, r7c8=3
84e r9c9 = 7, r9c8 = 8
84f. more singles:
3 at r9c6,7 at r8c6,6 at r9c1,9 at r4c9,4 at r5c9,2 at r1c8,8 at r2c7,7 at r6c8,5 at r5c8,1 at r1c7,8 at r6c6,1 at r5c6
85. hidden single 4 at r6c5 for row, col, nonet
86. 25(4)r4c1 = {268}9/{358}9/{367}9 -
86a. 9 locked at r5c1 - only leaves {358}9 - 3 locked at r6c1
86b. more singles
2 at r6c7,3 at r5c7,2 at r8c1,3 at r8c2,8 at r5c5,3 at r4c5
87. Hidden single 1 at r4c3 for ror4
87a. more singles: 9 at r6c3, 1 at r6c2
88. hidden single 1 at r3c1
88a. 14(3)r2c1=[518]
88b naked singles to the end
Archive Note. Typos corrected and an alternative way added for step 38.