Analysis of zz-www.sudokuwiki.org-0140-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=140
level: medium
position: 2....47....8..1.9.9...2...14..8...3...1...9...3...5..73...6...9.2.4..3....47....8 initial
Autosolve
position: 21...47....8..1.9.9...2...14..8...3...1...9...3...5..73...6...9.2.4..3....47....8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B7: 5,7 => CTR => B7: 8 * DIS # C3: 5,7 => CTR => C3: 3,6 * DIS # C4: 5,7 => CTR => C4: 2,6,9 * DIS # H8: 5,6 => CTR => H8: 1,7 * DIS # I1: 5,6 => CTR => I1: 3 * DIS # I2: 5,6 => CTR => I2: 2,3,4 * CNT 6 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B7: 5,7 => CTR => B7: 8 * DIS B7: 8 # C3: 5,7 => CTR => C3: 3,6 * DIS B7: 8 + C3: 3,6 # C4: 5,7 => CTR => C4: 2,6,9 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 # E8: 1,5 => CTR => E8: 8,9 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 # H8: 5,6 => CTR => H8: 1,7 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 # A8: 5,6 => CTR => A8: 1 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 # I1: 5,6 => CTR => I1: 3 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 # I2: 5,6 => CTR => I2: 2,4 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 # I5: 5,6 => CTR => I5: 2,4 * PRF B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 + I5: 2,4 # G9: 5,6 => SOL * STA B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 + I5: 2,4 + G9: 5,6 * CNT 10 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2....47....8..1.9.9...2...14..8...3...1...9...3...5..73...6...9.2.4..3....47....8 | initial |
| 21...47....8..1.9.9...2...14..8...3...1...9...3...5..73...6...9.2.4..3....47....8 | autosolve |
| 216984753748351692953627841462879135571236984839145267387562419125498376694713528 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A6: 6,8 C7: 5,7 F7: 2,8 F8: 8,9 I8: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,A9: 1.. / A8 = 1 => 7 pairs (_) / A9 = 1 => 8 pairs (_) E4,G4: 1.. / E4 = 1 => 7 pairs (_) / G4 = 1 => 6 pairs (_) D6,D7: 1.. / D6 = 1 => 9 pairs (_) / D7 = 1 => 6 pairs (_) G2,I2: 2.. / G2 = 2 => 5 pairs (_) / I2 = 2 => 9 pairs (_) C4,C6: 2.. / C4 = 2 => 12 pairs (_) / C6 = 2 => 6 pairs (_) C1,C3: 3.. / C1 = 3 => 0 pairs (X) / C3 = 3 => 7 pairs (_) I1,I2: 3.. / I1 = 3 => 7 pairs (_) / I2 = 3 => 0 pairs (X) E9,F9: 3.. / E9 = 3 => 12 pairs (_) / F9 = 3 => 5 pairs (_) B2,B3: 4.. / B2 = 4 => 6 pairs (_) / B3 = 4 => 13 pairs (_) E5,E6: 4.. / E5 = 4 => 18 pairs (_) / E6 = 4 => 6 pairs (_) G7,H7: 4.. / G7 = 4 => 5 pairs (_) / H7 = 4 => 5 pairs (_) I2,I5: 4.. / I2 = 4 => 11 pairs (_) / I5 = 4 => 6 pairs (_) E2,F3: 7.. / E2 = 7 => 8 pairs (_) / F3 = 7 => 9 pairs (_) H7,H8: 7.. / H7 = 7 => 8 pairs (_) / H8 = 7 => 5 pairs (_) E1,F3: 8.. / E1 = 8 => 6 pairs (_) / F3 = 8 => 0 pairs (X) B7,A8: 8.. / B7 = 8 => 6 pairs (_) / A8 = 8 => 0 pairs (X) E1,H1: 8.. / E1 = 8 => 6 pairs (_) / H1 = 8 => 0 pairs (X) B7,F7: 8.. / B7 = 8 => 6 pairs (_) / F7 = 8 => 0 pairs (X) B5,B7: 8.. / B5 = 8 => 0 pairs (X) / B7 = 8 => 6 pairs (_) E1,E8: 8.. / E1 = 8 => 6 pairs (_) / E8 = 8 => 0 pairs (X) G3,G6: 8.. / G3 = 8 => 6 pairs (_) / G6 = 8 => 9 pairs (_) D1,E1: 9.. / D1 = 9 => 5 pairs (_) / E1 = 9 => 0 pairs (X) C8,B9: 9.. / C8 = 9 => 0 pairs (X) / B9 = 9 => 8 pairs (_) B4,B9: 9.. / B4 = 9 => 0 pairs (X) / B9 = 9 => 8 pairs (_) D1,D6: 9.. / D1 = 9 => 5 pairs (_) / D6 = 9 => 0 pairs (X) * DURATION: 0:00:27.730144 START: 06:06:25.293699 END: 06:06:53.023843 2017-05-01 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C7,F7,F8,I8) * 21...47....8..1.9.9...2...14..8...3...1...9...3...5..73...6...9.2.4..3....47....8 * PAIR A6: 6,8 BLK 4 A5: 6,8,5,7 # reduction candidate for 6,8 A5: 6,8 # 13 pairs B5: 6,8,5,7 # reduction candidate for 6,8 B5: 6,8 # 8 pairs * PAIR A6: 6,8 ROW 6 G6: 6,8,1,2,4 # reduction candidate for 6,8 G6: 6,8 # 7 pairs H6: 6,8,1,2,4 # reduction candidate for 6,8 H6: 6,8 # 9 pairs * PAIR A6: 6,8 COL A A8: 6,8,1,5,7 # reduction candidate for 6,8 A8: 6,8 # 11 pairs A8: 1,5,7 # 6 pairs * PAIR C7: 5,7 BLK 7 B7: 5,7,8 # reduction candidate for 5,7 B7: 5,7 => CTR * 2159847637.8..1.9.9...2...14..8..13..81...95.63.1.5..73..268419826419375194753..8 B7: 8 # 6 pairs A8: 5,7,1,6,8 # reduction candidate for 5,7 A8: 5,7 # 11 pairs C8: 5,7,6,9 # reduction candidate for 5,7 C8: 5,7 # 21 pairs * PAIR C7: 5,7 ROW 7 H7: 5,7,1,2,4 # reduction candidate for 5,7 H7: 5,7 # 7 pairs H7: 1,2,4 # 5 pairs * PAIR C7: 5,7 COL C C3: 5,7,3,6 # reduction candidate for 5,7 C3: 5,7 => CTR * 213.9478..48..12939...28..14..81..32..12..9.4.3294581738.162..912.4893...94753128 C3: 3,6 # 6 pairs C4: 5,7,2,6,9 # reduction candidate for 5,7 C4: 5,7 => CTR * 216984753..83512949436278.149.876132..12439...32195..7387562419.2941837.1.4739.28 C4: 2,6,9 # 5 pairs * PAIR F8: 8,9 BLK 8 E8: 8,9,1,5 # reduction candidate for 8,9 E8: 8,9 # 10 pairs E8: 1,5 # 7 pairs * PAIR I8: 5,6 BLK 9 H8: 5,6,1,7 # reduction candidate for 5,6 H8: 5,6 => CTR * 2169847537.8.316929.352.8.14.28.9536.61..798.8396.5..7385162479127498365694753..8 H8: 1,7 # 6 pairs G9: 5,6,1,2 # reduction candidate for 5,6 G9: 5,6 # 8 pairs H9: 5,6,1,2 # reduction candidate for 5,6 H9: 5,6 # 8 pairs * PAIR I8: 5,6 ROW 8 A8: 5,6,1,7,8 # reduction candidate for 5,6 A8: 5,6 # 10 pairs C8: 5,6,7,9 # reduction candidate for 5,6 C8: 5,6 # 10 pairs * PAIR I8: 5,6 COL I I1: 5,6,3 # reduction candidate for 5,6 I1: 5,6 => CTR * 21..9478..48..12939...28..14..81..32..12..9.4.3294581738.162..912.4893...94753128 I1: 3 # 7 pairs I2: 5,6,2,3,4 # reduction candidate for 5,6 I2: 5,6 => CTR * 21..94783.48..129.9.3.28..14..81..32..12..9.4.3294581738.162..912.4893...94753128 I2: 2,3,4 # 5 pairs I4: 5,6,2 # reduction candidate for 5,6 I4: 5,6 # 10 pairs I5: 5,6,2,4 # reduction candidate for 5,6 I5: 5,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0140-base-pr-000.dot * REASONING * DIS # B7: 5,7 => CTR => B7: 8 * DIS # C3: 5,7 => CTR => C3: 3,6 * DIS # C4: 5,7 => CTR => C4: 2,6,9 * DIS # H8: 5,6 => CTR => H8: 1,7 * DIS # I1: 5,6 => CTR => I1: 3 * DIS # I2: 5,6 => CTR => I2: 2,3,4 * CNT 6 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C7,F7,F8,I8) * 21...47....8..1.9.9...2...14..8...3...1...9...3...5..73...6...9.2.4..3....47....8 * PAIR A6: 6,8 BLK 4 A5: 6,8,5,7 # reduction candidate for 6,8 A5: 6,8 # 13 pairs B5: 6,8,5,7 # reduction candidate for 6,8 B5: 6,8 # 8 pairs * PAIR A6: 6,8 ROW 6 G6: 6,8,1,2,4 # reduction candidate for 6,8 G6: 6,8 # 7 pairs H6: 6,8,1,2,4 # reduction candidate for 6,8 H6: 6,8 # 9 pairs * PAIR A6: 6,8 COL A A8: 6,8,1,5,7 # reduction candidate for 6,8 A8: 6,8 # 11 pairs A8: 1,5,7 # 6 pairs * PAIR C7: 5,7 BLK 7 B7: 5,7,8 # reduction candidate for 5,7 B7: 5,7 => CTR * 2159847637.8..1.9.9...2...14..8..13..81...95.63.1.5..73..268419826419375194753..8 A8: 5,7,1,6 # reduction candidate for 5,7 A8: 5,7 # 11 pairs C8: 5,7,6,9 # reduction candidate for 5,7 C8: 5,7 # 21 pairs * PAIR C7: 5,7 ROW 7 H7: 5,7,1,4 # reduction candidate for 5,7 H7: 5,7 # 7 pairs H7: 1,4 # 6 pairs * PAIR C7: 5,7 COL C C3: 5,7,3,6 # reduction candidate for 5,7 C3: 5,7 => CTR * 213.9478..48..12939..328..14..81..328.12..9.463294581738.162..912648937...47...28 C4: 5,7,2,6,9 # reduction candidate for 5,7 C4: 5,7 => CTR * 21.9847.3..8351294943627..1495876132..12439...32195..7387562419.2941837.1.4739.28 * RESTART * PAIR RESTART * PAIR C7: 5,7 BLK 7 C8: 5,7,6,9 # reduction candidate for 5,7 C8: 5,7 # 21 pairs C8: 6,9 # 10 pairs * PAIR C7: 5,7 ROW 7 H7: 5,7,1,4 # reduction candidate for 5,7 H7: 5,7 # 8 pairs H7: 1,4 # 7 pairs * PAIR F8: 8,9 BLK 8 E8: 8,9,1,5 # reduction candidate for 8,9 E8: 1,5 => CTR * 215984763..83.1.94943.27..149.876135..1243986.3..95..7387.62..9.294.837...4739..8 * PAIR I8: 5,6 BLK 9 H8: 5,6,1,7 # reduction candidate for 5,6 H8: 5,6 => CTR * 2169847537.8.316929.352.8.14.28.9536.61..798.8396.5..7385162479127498365694753..8 G9: 5,6,1,2 # reduction candidate for 5,6 G9: 5,6 # 14 pairs H9: 5,6,1,2 # reduction candidate for 5,6 H9: 5,6 # 16 pairs * PAIR I8: 5,6 ROW 8 A8: 5,6,1 # reduction candidate for 5,6 A8: 5,6 => CTR * 2169847537.8.31.9.9...2.8.14.2819536.61..798.839645127385162479627498315194753268 * RESTART * PAIR I8: 5,6 COL I I1: 5,6,3 # reduction candidate for 5,6 I1: 5,6 => CTR * 21..9478..48.7129397..28..14.98...32..123.9.4.32945..7387162..912.4.937..94753.28 I2: 5,6,2,4 # reduction candidate for 5,6 I2: 5,6 => CTR * 21..94783.4837129.973.28..14.98...32..123.9.4.32945..7387162..912.4.937..94753128 I4: 5,6,2 # reduction candidate for 5,6 I4: 5,6 # 16 pairs I5: 5,6,2,4 # reduction candidate for 5,6 I5: 5,6 => CTR * 21...47.3..8..1.94943.27..14..8...32..1236945.32.45..7387.624.91254.83766947.3.28 * RESTART * PAIR RESTART * PAIR I8: 5,6 BLK 9 G9: 5,6,1,2 # reduction candidate for 5,6 G9: 5,6 => SOLVED * 216984753748351692953627841462879135571236984839145267387562419125498376694713528 * DURATION: 0:00:24.367126 START: 06:07:12.208112 END: 06:07:36.575238 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0140-base-pr-001.dot * REASONING * DIS # B7: 5,7 => CTR => B7: 8 * DIS B7: 8 # C3: 5,7 => CTR => C3: 3,6 * DIS B7: 8 + C3: 3,6 # C4: 5,7 => CTR => C4: 2,6,9 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 # E8: 1,5 => CTR => E8: 8,9 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 # H8: 5,6 => CTR => H8: 1,7 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 # A8: 5,6 => CTR => A8: 1 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 # I1: 5,6 => CTR => I1: 3 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 # I2: 5,6 => CTR => I2: 2,4 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 # I5: 5,6 => CTR => I5: 2,4 * PRF B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 + I5: 2,4 # G9: 5,6 => SOL * STA B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 + I5: 2,4 + G9: 5,6 * CNT 10 HDP CHAINS / 28 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=140
Solution
position: 216984753748351692953627841462879135571236984839145267387562419125498376694713528 solved
See section 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 # A5: 6,8 => UNS * INC # B5: 6,8 => UNS * INC # G6: 6,8 => UNS * INC # H6: 6,8 => UNS * INC # A8: 6,8 => UNS * INC # A8: 1,5,7 => UNS * DIS # B7: 5,7 => CTR => B7: 8 * INC # B7: 8 => UNS * INC # A8: 5,7 => UNS * INC # C8: 5,7 => UNS * INC # H7: 5,7 => UNS * INC # H7: 1,2,4 => UNS * DIS # C3: 5,7 => CTR => C3: 3,6 * INC # C3: 3,6 => UNS * DIS # C4: 5,7 => CTR => C4: 2,6,9 * INC # C4: 2,6,9 => UNS * INC # E8: 8,9 => UNS * INC # E8: 1,5 => UNS * DIS # H8: 5,6 => CTR => H8: 1,7 * INC # H8: 1,7 => UNS * INC # G9: 5,6 => UNS * INC # H9: 5,6 => UNS * INC # A8: 5,6 => UNS * INC # C8: 5,6 => UNS * DIS # I1: 5,6 => CTR => I1: 3 * INC # I1: 3 => UNS * DIS # I2: 5,6 => CTR => I2: 2,3,4 * INC # I2: 2,3,4 => UNS * INC # I4: 5,6 => UNS * INC # I5: 5,6 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A5: 6,8 => UNS * INC # B5: 6,8 => UNS * INC # G6: 6,8 => UNS * INC # H6: 6,8 => UNS * INC # A8: 6,8 => UNS * INC # A8: 1,5,7 => UNS * DIS # B7: 5,7 => CTR => B7: 8 * INC B7: 8 # A8: 5,7 => UNS * INC B7: 8 # C8: 5,7 => UNS * INC B7: 8 # H7: 5,7 => UNS * INC B7: 8 # H7: 1,4 => UNS * DIS B7: 8 # C3: 5,7 => CTR => C3: 3,6 * DIS B7: 8 + C3: 3,6 # C4: 5,7 => CTR => C4: 2,6,9 * INC B7: 8 + C3: 3,6 + C4: 2,6,9 # C8: 5,7 => UNS * INC B7: 8 + C3: 3,6 + C4: 2,6,9 # C8: 6,9 => UNS * INC B7: 8 + C3: 3,6 + C4: 2,6,9 # H7: 5,7 => UNS * INC B7: 8 + C3: 3,6 + C4: 2,6,9 # H7: 1,4 => UNS * INC B7: 8 + C3: 3,6 + C4: 2,6,9 # E8: 8,9 => UNS * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 # E8: 1,5 => CTR => E8: 8,9 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 # H8: 5,6 => CTR => H8: 1,7 * INC B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 # G9: 5,6 => UNS * INC B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 # H9: 5,6 => UNS * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 # A8: 5,6 => CTR => A8: 1 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 # I1: 5,6 => CTR => I1: 3 * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 # I2: 5,6 => CTR => I2: 2,4 * INC B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 # I4: 5,6 => UNS * DIS B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 # I5: 5,6 => CTR => I5: 2,4 * PRF B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 + I5: 2,4 # G9: 5,6 => SOL * STA B7: 8 + C3: 3,6 + C4: 2,6,9 + E8: 8,9 + H8: 1,7 + A8: 1 + I1: 3 + I2: 2,4 + I5: 2,4 + G9: 5,6 * CNT 28 HDP CHAINS / 28 HYP OPENED