Analysis of zz-www.sudokuwiki.org-0054-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=54
level: hard
position: 9...53....4.....65..67..1..3..2......6..4..8......1..6..2..87..48.....1.....9...8 initial
Autosolve
position: 9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D9: 3,5 => CTR => D9: 1,4 * CNT 1 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D9: 3,5 => CTR => D9: 1,4 * STA D9: 1,4 * CNT 1 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:56.198861
The following important HDP chains were detected:
* DIS # C4: 4,5,7,9 # H6: 4,7 => CTR => H6: 2,3,9 * DIS # C4: 4,5,7,9 + H6: 2,3,9 # H6: 3,9 => CTR => H6: 2 * DIS # C4: 4,5,7,9 + H6: 2,3,9 + H6: 2 => CTR => C4: 1,8 * PRF C4: 1,8 # E2: 1 # A3: 5 => SOL * STA C4: 1,8 # E2: 1 + A3: 5 * CNT 4 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9...53....4.....65..67..1..3..2......6..4..8......1..6..2..87..48.....1.....9...8 | initial |
| 9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 | autosolve |
| 9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 | pair_reduction |
| 921653874847912365536784192378265941165349287294871536612438759489527613753196428 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (5) B1: 1,2 C1: 1,8 F2: 2,9 E3: 2,8 D8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 0 pairs (X) / C1 = 1 => 9 pairs (_) D2,E2: 1.. / D2 = 1 => 23 pairs (_) / E2 = 1 => 9 pairs (_) I4,I5: 1.. / I4 = 1 => 5 pairs (_) / I5 = 1 => 7 pairs (_) E2,E7: 1.. / E2 = 1 => 9 pairs (_) / E7 = 1 => 23 pairs (_) C2,B3: 3.. / C2 = 3 => 9 pairs (_) / B3 = 3 => 14 pairs (_) C2,G2: 3.. / C2 = 3 => 9 pairs (_) / G2 = 3 => 14 pairs (_) C4,C6: 4.. / C4 = 4 => 17 pairs (_) / C6 = 4 => 5 pairs (_) D7,D9: 4.. / D7 = 4 => 8 pairs (_) / D9 = 4 => 6 pairs (_) A3,B3: 5.. / A3 = 5 => 14 pairs (_) / B3 = 5 => 9 pairs (_) E4,F4: 6.. / E4 = 6 => 13 pairs (_) / F4 = 6 => 6 pairs (_) A7,A9: 6.. / A7 = 6 => 7 pairs (_) / A9 = 6 => 11 pairs (_) G8,G9: 6.. / G8 = 6 => 5 pairs (_) / G9 = 6 => 8 pairs (_) A7,E7: 6.. / A7 = 6 => 7 pairs (_) / E7 = 6 => 11 pairs (_) A2,C2: 7.. / A2 = 7 => 6 pairs (_) / C2 = 7 => 14 pairs (_) H1,I1: 7.. / H1 = 7 => 8 pairs (_) / I1 = 7 => 6 pairs (_) G1,G2: 8.. / G1 = 8 => 9 pairs (_) / G2 = 8 => 0 pairs (X) C1,G1: 8.. / C1 = 8 => 0 pairs (X) / G1 = 8 => 9 pairs (_) A3,E3: 8.. / A3 = 8 => 15 pairs (_) / E3 = 8 => 14 pairs (_) C4,E4: 8.. / C4 = 8 => 11 pairs (_) / E4 = 8 => 17 pairs (_) D2,D6: 8.. / D2 = 8 => 16 pairs (_) / D6 = 8 => 13 pairs (_) D2,F2: 9.. / D2 = 9 => 0 pairs (*) / F2 = 9 => 0 pairs (X) H3,I3: 9.. / H3 = 9 => 6 pairs (_) / I3 = 9 => 8 pairs (_) B7,C8: 9.. / B7 = 9 => 6 pairs (_) / C8 = 9 => 6 pairs (_) * DURATION: 0:00:26.832596 START: 18:33:06.771822 END: 18:33:33.604418 2017-04-30 * CP COUNT: (23) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:55.864938 START: 18:34:08.959223 END: 18:35:04.824161 2017-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0054-base-pr-002.dot * REASONING * DIS # C4: 4,5,7,9 # H6: 4,7 => CTR => H6: 2,3,9 * DIS # C4: 4,5,7,9 + H6: 2,3,9 # H6: 3,9 => CTR => H6: 2 * DIS # C4: 4,5,7,9 + H6: 2,3,9 + H6: 2 => CTR => C4: 1,8 * PRF C4: 1,8 # E2: 1 # A3: 5 => SOL * STA C4: 1,8 # E2: 1 + A3: 5 * CNT 4 HDP CHAINS / 54 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=54
Solution
position: 921653874847912365536784192378265941165349287294871536612438759489527613753196428 solved
See section Deep Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # C4: 1,8 => UNS * INC # C4: 4,5,7,9 => UNS * INC # E2: 2,8 => UNS * INC # E2: 1 => UNS * INC # A3: 2,8 => UNS * INC # A3: 5 => UNS * INC # D7: 3,5 => UNS * DIS # D9: 3,5 => CTR => D9: 1,4 * INC # D9: 1,4 => UNS * INC # C8: 3,5 => UNS * INC # G8: 3,5 => UNS * INC # D5: 3,5 => UNS * INC # D6: 3,5 => UNS * CNT 13 HDP CHAINS / 13 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 1,8 => UNS * INC # C4: 4,5,7,9 => UNS * INC # E2: 2,8 => UNS * INC # E2: 1 => UNS * INC # A3: 2,8 => UNS * INC # A3: 5 => UNS * INC # D7: 3,5 => UNS * DIS # D9: 3,5 => CTR => D9: 1,4 * INC D9: 1,4 # D7: 3,5 => UNS * INC D9: 1,4 # D7: 1,4 => UNS * INC D9: 1,4 # C8: 3,5 => UNS * INC D9: 1,4 # G8: 3,5 => UNS * INC D9: 1,4 # D5: 3,5 => UNS * INC D9: 1,4 # D6: 3,5 => UNS * INC D9: 1,4 # C4: 1,8 => UNS * INC D9: 1,4 # C4: 4,5,7,9 => UNS * INC D9: 1,4 # E2: 2,8 => UNS * INC D9: 1,4 # E2: 1 => UNS * INC D9: 1,4 # A3: 2,8 => UNS * INC D9: 1,4 # A3: 5 => UNS * INC D9: 1,4 # D7: 3,5 => UNS * INC D9: 1,4 # D7: 1,4 => UNS * INC D9: 1,4 # C8: 3,5 => UNS * INC D9: 1,4 # G8: 3,5 => UNS * INC D9: 1,4 # D5: 3,5 => UNS * INC D9: 1,4 # D6: 3,5 => UNS * INC D9: 1,4 # D7: 1,4 => UNS * INC D9: 1,4 # D7: 3,5 => UNS * STA D9: 1,4 * CNT 28 HDP CHAINS / 28 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 1,8 => UNS * INC # C4: 4,5,7,9 => UNS * INC # E2: 2,8 => UNS * INC # E2: 1 => UNS * INC # A3: 2,8 => UNS * INC # A3: 5 => UNS * INC # D7: 3,5 => UNS * INC # D7: 1,4 => UNS * INC # C8: 3,5 => UNS * INC # G8: 3,5 => UNS * INC # D5: 3,5 => UNS * INC # D6: 3,5 => UNS * INC # D7: 1,4 => UNS * INC # D7: 3,5 => UNS * INC # C4: 1,8 # C8: 3,7 => UNS * INC # C4: 1,8 # C9: 3,7 => UNS * INC # C4: 1,8 # E2: 2,8 => UNS * INC # C4: 1,8 # E2: 1 => UNS * INC # C4: 1,8 # A3: 2,8 => UNS * INC # C4: 1,8 # A3: 5 => UNS * INC # C4: 1,8 # D7: 3,5 => UNS * INC # C4: 1,8 # D7: 1,4 => UNS * INC # C4: 1,8 # C8: 3,5 => UNS * INC # C4: 1,8 # G8: 3,5 => UNS * INC # C4: 1,8 # D5: 3,5 => UNS * INC # C4: 1,8 # D6: 3,5 => UNS * INC # C4: 1,8 # D7: 1,4 => UNS * INC # C4: 1,8 # D7: 3,5 => UNS * INC # C4: 1,8 => UNS * DIS # C4: 4,5,7,9 # H6: 4,7 => CTR => H6: 2,3,9 * DIS # C4: 4,5,7,9 + H6: 2,3,9 # H6: 3,9 => CTR => H6: 2 * DIS # C4: 4,5,7,9 + H6: 2,3,9 + H6: 2 => CTR => C4: 1,8 * INC C4: 1,8 # C8: 3,7 => UNS * INC C4: 1,8 # C9: 3,7 => UNS * INC C4: 1,8 # E2: 2,8 => UNS * INC C4: 1,8 # E2: 1 => UNS * INC C4: 1,8 # A3: 2,8 => UNS * INC C4: 1,8 # A3: 5 => UNS * INC C4: 1,8 # D7: 3,5 => UNS * INC C4: 1,8 # D7: 1,4 => UNS * INC C4: 1,8 # C8: 3,5 => UNS * INC C4: 1,8 # G8: 3,5 => UNS * INC C4: 1,8 # D5: 3,5 => UNS * INC C4: 1,8 # D6: 3,5 => UNS * INC C4: 1,8 # D7: 1,4 => UNS * INC C4: 1,8 # D7: 3,5 => UNS * INC C4: 1,8 # E2: 2,8 => UNS * INC C4: 1,8 # E2: 1 # C8: 3,7 => UNS * INC C4: 1,8 # E2: 1 # C9: 3,7 => UNS * INC C4: 1,8 # E2: 1 # D6: 8,9 => UNS * INC C4: 1,8 # E2: 1 # D6: 3,5 => UNS * INC C4: 1,8 # E2: 1 # A3: 2,8 => UNS * PRF C4: 1,8 # E2: 1 # A3: 5 => SOL * STA C4: 1,8 # E2: 1 + A3: 5 * CNT 53 HDP CHAINS / 54 HYP OPENED