Analysis of xx-top95-061-base.sdk
Contents
Original Sudoku
level: medium
position: .2......6....41.....78....1......7....37.....6..412....1..74..5..8.5..7......39.. initial
Autosolve
position: .2...7..6.35641..7.6782...1......7....37.....679412..831.974..5.98.56.7375..839.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 1,4 => SOL * DIS # A1: 8,9 => CTR => A1: 1,4 * DIS # A1: 8,9 => CTR => A1: 1,4 * PRF # A1: 1,4 => SOL * DIS # H2: 2 => CTR => H2: 8,9 * DIS # A1: 4,9 => CTR => A1: 1,8 * PRF # H3: 4,9 => SOL * PRF # E4: 3,9 => SOL * DIS # E4: 6 => CTR => E4: 3,9 * DIS # H3: 5,9 => CTR => H3: 3,4 * DIS # H2: 2,8 => CTR => H2: 9 * DIS # G7: 2,8 => CTR => G7: 6 * PRF # G7: 6 => SOL * DIS # A5: 1,2 => CTR => A5: 5 * DIS # H4: 1,2 => CTR => H4: 4,6 * DIS # E4: 6,9 => CTR => E4: 3 * PRF # E4: 3 => SOL * DIS # G3: 4 => CTR => G3: 3,5 * PRF # H3: 4,9 => SOL * PRF # C9: 2,6 => SOL * DIS # C9: 4 => CTR => C9: 2,6 * DIS # H7: 2,6 => CTR => H7: 8 * DIS # C9: 2,4 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # G8: 2,4 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # G8: 1,2 => SOL * DIS # G8: 4 => CTR => G8: 1,2 * PRF # H9: 1,2 => SOL * DIS # H9: 4,6 => CTR => H9: 1,2 * DIS # G8: 2,4 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # H9: 2,4 => SOL * DIS # C9: 2,4 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # I4: 2,4 => CTR => I4: 9 * CNT 36 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 1,4 => SOL * STA A1: 1,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2......6....41.....78....1......7....37.....6..412....1..74..5..8.5..7......39.. | initial |
| .2...7..6.35641..7.6782...1......7....37.....679412..831.974..5.98.56.7375..839.. | autosolve |
| 124397856835641297967825341241538769583769412679412538312974685498256173756183924 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C1: 1,4 A2: 8,9 A3: 4,9 D1: 3,5 E1: 3,9 F3: 5,9 G2: 2,8 B4: 4,8 C4: 1,2 B5: 4,8 D4: 3,5 E5: 6,9 G6: 3,5 H6: 3,5 C7: 2,6 A8: 2,4 D8: 1,2 D9: 1,2 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 0 pairs (*) / C1 = 1 => 0 pairs (X) D8,D9: 1.. / D8 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) G8,H9: 1.. / G8 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) D8,G8: 1.. / D8 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) D9,H9: 1.. / D9 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) C1,C4: 1.. / C1 = 1 => 0 pairs (X) / C4 = 1 => 0 pairs (_) G5,G8: 1.. / G5 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) G2,H2: 2.. / G2 = 2 => 21 pairs (_) / H2 = 2 => 0 pairs (X) D8,D9: 2.. / D8 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) D1,E1: 3.. / D1 = 3 => 0 pairs (*) / E1 = 3 => 0 pairs (X) G3,H3: 3.. / G3 = 3 => 18 pairs (_) / H3 = 3 => 18 pairs (_) D4,E4: 3.. / D4 = 3 => 0 pairs (X) / E4 = 3 => 0 pairs (_) G6,H6: 3.. / G6 = 3 => 18 pairs (_) / H6 = 3 => 18 pairs (_) D1,D4: 3.. / D1 = 3 => 0 pairs (*) / D4 = 3 => 0 pairs (X) E1,E4: 3.. / E1 = 3 => 0 pairs (X) / E4 = 3 => 0 pairs (_) G3,G6: 3.. / G3 = 3 => 18 pairs (_) / G6 = 3 => 18 pairs (_) H3,H6: 3.. / H3 = 3 => 18 pairs (_) / H6 = 3 => 18 pairs (_) B4,B5: 4.. / B4 = 4 => 19 pairs (_) / B5 = 4 => 22 pairs (_) A8,C9: 4.. / A8 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) A8,G8: 4.. / A8 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) C1,C9: 4.. / C1 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) D1,F3: 5.. / D1 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) A4,A5: 5.. / A4 = 5 => 0 pairs (X) / A5 = 5 => 23 pairs (_) G6,H6: 5.. / G6 = 5 => 18 pairs (_) / H6 = 5 => 18 pairs (_) A5,F5: 5.. / A5 = 5 => 23 pairs (_) / F5 = 5 => 0 pairs (X) D1,D4: 5.. / D1 = 5 => 0 pairs (X) / D4 = 5 => 0 pairs (_) E4,E5: 6.. / E4 = 6 => 0 pairs (X) / E5 = 6 => 0 pairs (_) C7,C9: 6.. / C7 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) E4,H4: 6.. / E4 = 6 => 0 pairs (X) / H4 = 6 => 0 pairs (_) C9,H9: 6.. / C9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) G5,G7: 6.. / G5 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) A1,A2: 8.. / A1 = 8 => 0 pairs (X) / A2 = 8 => 19 pairs (_) B4,B5: 8.. / B4 = 8 => 22 pairs (_) / B5 = 8 => 19 pairs (_) F4,F5: 8.. / F4 = 8 => 19 pairs (_) / F5 = 8 => 22 pairs (_) G7,H7: 8.. / G7 = 8 => 0 pairs (X) / H7 = 8 => 21 pairs (_) B4,F4: 8.. / B4 = 8 => 22 pairs (_) / F4 = 8 => 19 pairs (_) B5,F5: 8.. / B5 = 8 => 19 pairs (_) / F5 = 8 => 22 pairs (_) E1,F3: 9.. / E1 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) I4,I5: 9.. / I4 = 9 => 22 pairs (_) / I5 = 9 => 0 pairs (X) A2,H2: 9.. / A2 = 9 => 0 pairs (X) / H2 = 9 => 19 pairs (_) * DURATION: 0:01:14.995051 START: 00:10:36.440725 END: 00:11:51.435776 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,B4,B5,C1,C4,C7,D1,D4,D8,D9,E1,E5,F3,G2,G6,H6,I9) * .2...7..6.35641..7.6782...1......7....37.....679412..831.974..5.98.56.7375..839.. * PAIR C1: 1,4 BLK 1 A1: 1,4,8,9 # reduction candidate for 1,4 A1: 1,4 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 A1: 8,9 => CTR * .21..7..6.35641..746782...1..2...7....37.....679412..8316974..529815647375..839.. * PAIR A2: 8,9 BLK 1 A1: 8,9,1,4 # reduction candidate for 8,9 A1: 8,9 => CTR * .21..7..6.35641..746782...1..2...7....37.....679412..8316974..529815647375..839.. A1: 1,4 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 * PAIR A2: 8,9 ROW 2 H2: 8,9,2 # reduction candidate for 8,9 H2: 2 => CTR * .2...7..693564182746782...1......7....37.....679412..831.974.852981564737542839.. H2: 8,9 # 21 pairs * PAIR A3: 4,9 BLK 1 A1: 4,9,1,8 # reduction candidate for 4,9 A1: 4,9 => CTR * .21..7..6835641297.6782...1..2...7....37.....679412..831697482529815647375..839.. A1: 1,8 # 20 pairs * PAIR A3: 4,9 ROW 3 H3: 4,9,3,5 # reduction candidate for 4,9 H3: 4,9 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 H3: 3,5 # 20 pairs * PAIR E1: 3,9 COL E E4: 3,9,6 # reduction candidate for 3,9 E4: 3,9 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 E4: 6 => CTR * .2.537..6.35641..7467829..1...36.7.9..379....679412..831.974..52981564737542839.. * PAIR F3: 5,9 ROW 3 H3: 5,9,3,4 # reduction candidate for 5,9 H3: 5,9 => CTR * .2...7..6.35641..746782.3.1......7....37.....67941253831.974..52981564737542839.. H3: 3,4 # 20 pairs * PAIR F3: 5,9 COL F F4: 5,9,8 # reduction candidate for 5,9 F4: 5,9 # 22 pairs F5: 5,9,8 # reduction candidate for 5,9 F5: 5,9 # 19 pairs * PAIR G2: 2,8 BLK 3 H2: 2,8,9 # reduction candidate for 2,8 H2: 2,8 => CTR * .2...7..6935641..746782...1......7....37.....679412..831.974..52981564737542839.. H2: 9 # 19 pairs * PAIR G2: 2,8 COL G G7: 2,8,6 # reduction candidate for 2,8 G7: 2,8 => CTR * .24.37..6.35641..7967825..1....6.7....379.6..679412..831.974..549825617375.1839.. G7: 6 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 * PAIR C4: 1,2 BLK 4 A4: 1,2,5 # reduction candidate for 1,2 A4: 1,2 # 23 pairs A5: 1,2,5 # reduction candidate for 1,2 A5: 1,2 => CTR * .2.537..6.35641..7467829..154.3.87...837.5...679412..831.974..52981564737542839.. A5: 5 # 23 pairs * PAIR C4: 1,2 ROW 4 H4: 1,2,4,6 # reduction candidate for 1,2 H4: 1,2 => CTR * .2.537..6.35641..7467829..1.4.3687.9.83795...679412..831.974..52981564737542839.. H4: 4,6 # 21 pairs * PAIR E5: 6,9 BLK 5 E4: 6,9,3 # reduction candidate for 6,9 E4: 6,9 => CTR * .2.537..6.35641..7467829..1...3..7....37.....679412..831.974..52981564737542839.. E4: 3 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 * PAIR G6: 3,5 COL G G3: 3,5,4 # reduction candidate for 3,5 G3: 4 => CTR * .24..75.6.35641..7967825431..153.76.5.376....67941235831.974685498.56.73756.839.. G3: 3,5 # 21 pairs * PAIR H6: 3,5 COL H H3: 3,5,4,9 # reduction candidate for 3,5 H3: 4,9 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 H3: 3,5 # 20 pairs * PAIR C7: 2,6 BLK 7 C9: 2,6,4 # reduction candidate for 2,6 C9: 2,6 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 C9: 4 => CTR * .2...7..6.35641..7.6782...1......7....37.....679412..8316974..529815647375..839.. * PAIR C7: 2,6 ROW 7 G7: 2,6,8 # reduction candidate for 2,6 G7: 2,6 # 21 pairs H7: 2,6,8 # reduction candidate for 2,6 H7: 2,6 => CTR * .24.375.6.356412.7.6782...1....6.7....379.6..679412..831.9748.549825617375.1839.. H7: 8 # 21 pairs * PAIR A8: 2,4 BLK 7 C9: 2,4,6 # reduction candidate for 2,4 C9: 2,4 => CTR * .24.37..6.35641..7967825..1....6.7....379.6..679412..8316974..5.98.5617375.183964 C9: 6 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 * PAIR A8: 2,4 ROW 8 G8: 2,4,1 # reduction candidate for 2,4 G8: 2,4 => CTR * .24..7..6.35641..7967825431..153.76.5.376.14267941235831.974685.98156.73756283914 G8: 1 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 * PAIR D8: 1,2 ROW 8 G8: 1,2,4 # reduction candidate for 1,2 G8: 1,2 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 G8: 4 => CTR * .2...7..6.35641..7.6782...1......7....37..1..679412..831.974685.9815647375..839.. * PAIR D9: 1,2 ROW 9 H9: 1,2,4,6 # reduction candidate for 1,2 H9: 1,2 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 H9: 4,6 => CTR * .24..7..6.35641..7967825..1..153.76.5.376..1.679412..831.97468549825617375618394. * PAIR I9: 2,4 BLK 9 G8: 2,4,1 # reduction candidate for 2,4 G8: 2,4 => CTR * .24..7..6.35641..7967825431..153.76.5.376.14267941235831.974685.98156.73756283914 G8: 1 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 H9: 2,4,1,6 # reduction candidate for 2,4 H9: 2,4 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 H9: 1,6 # 20 pairs * PAIR I9: 2,4 ROW 9 C9: 2,4,6 # reduction candidate for 2,4 C9: 2,4 => CTR * .24.37..6.35641..7967825..1....6.7....379.6..679412..8316974..5.98.5617375.183964 C9: 6 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 * PAIR I9: 2,4 COL I I4: 2,4,9 # reduction candidate for 2,4 I4: 2,4 => CTR * 124397856835641297967825..12815397645437681.9679412..8312974685498.56.73756.839.. I4: 9 # 22 pairs I5: 2,4,9 # reduction candidate for 2,4 I5: 2,4 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-061-base-pr-000.dot * REASONING * PRF # A1: 1,4 => SOL * DIS # A1: 8,9 => CTR => A1: 1,4 * DIS # A1: 8,9 => CTR => A1: 1,4 * PRF # A1: 1,4 => SOL * DIS # H2: 2 => CTR => H2: 8,9 * DIS # A1: 4,9 => CTR => A1: 1,8 * PRF # H3: 4,9 => SOL * PRF # E4: 3,9 => SOL * DIS # E4: 6 => CTR => E4: 3,9 * DIS # H3: 5,9 => CTR => H3: 3,4 * DIS # H2: 2,8 => CTR => H2: 9 * DIS # G7: 2,8 => CTR => G7: 6 * PRF # G7: 6 => SOL * DIS # A5: 1,2 => CTR => A5: 5 * DIS # H4: 1,2 => CTR => H4: 4,6 * DIS # E4: 6,9 => CTR => E4: 3 * PRF # E4: 3 => SOL * DIS # G3: 4 => CTR => G3: 3,5 * PRF # H3: 4,9 => SOL * PRF # C9: 2,6 => SOL * DIS # C9: 4 => CTR => C9: 2,6 * DIS # H7: 2,6 => CTR => H7: 8 * DIS # C9: 2,4 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # G8: 2,4 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # G8: 1,2 => SOL * DIS # G8: 4 => CTR => G8: 1,2 * PRF # H9: 1,2 => SOL * DIS # H9: 4,6 => CTR => H9: 1,2 * DIS # G8: 2,4 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # H9: 2,4 => SOL * DIS # C9: 2,4 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # I4: 2,4 => CTR => I4: 9 * CNT 36 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,B4,B5,C1,C4,C7,D1,D4,D8,D9,E1,E5,F3,G2,G6,H6,I9) * .2...7..6.35641..7.6782...1......7....37.....679412..831.974..5.98.56.7375..839.. * PAIR C1: 1,4 BLK 1 A1: 1,4,8,9 # reduction candidate for 1,4 A1: 1,4 => SOLVED * 124397856835641297967825341241538769583769412679412538312974685498256173756183924 * DURATION: 0:00:02.383817 START: 00:12:51.229682 END: 00:12:53.613499 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-061-base-pr-001.dot * REASONING * PRF # A1: 1,4 => SOL * STA A1: 1,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 061 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 124397856835641297967825341241538769583769412679412538312974685498256173756183924 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:
* PRF # A1: 1,4 => SOL * DIS # A1: 8,9 => CTR => A1: 1,4 * DIS # A1: 8,9 => CTR => A1: 1,4 * PRF # A1: 1,4 => SOL * INC # H2: 8,9 => UNS * DIS # H2: 2 => CTR => H2: 8,9 * DIS # A1: 4,9 => CTR => A1: 1,8 * INC # A1: 1,8 => UNS * PRF # H3: 4,9 => SOL * INC # H3: 3,5 => UNS * PRF # E4: 3,9 => SOL * DIS # E4: 6 => CTR => E4: 3,9 * DIS # H3: 5,9 => CTR => H3: 3,4 * INC # H3: 3,4 => UNS * INC # F4: 5,9 => UNS * INC # F5: 5,9 => UNS * DIS # H2: 2,8 => CTR => H2: 9 * INC # H2: 9 => UNS * DIS # G7: 2,8 => CTR => G7: 6 * PRF # G7: 6 => SOL * INC # A4: 1,2 => UNS * DIS # A5: 1,2 => CTR => A5: 5 * INC # A5: 5 => UNS * DIS # H4: 1,2 => CTR => H4: 4,6 * INC # H4: 4,6 => UNS * DIS # E4: 6,9 => CTR => E4: 3 * PRF # E4: 3 => SOL * INC # G3: 3,5 => UNS * DIS # G3: 4 => CTR => G3: 3,5 * INC # H3: 3,5 => UNS * PRF # H3: 4,9 => SOL * PRF # C9: 2,6 => SOL * DIS # C9: 4 => CTR => C9: 2,6 * INC # G7: 2,6 => UNS * DIS # H7: 2,6 => CTR => H7: 8 * INC # H7: 8 => UNS * DIS # C9: 2,4 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # G8: 2,4 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # G8: 1,2 => SOL * DIS # G8: 4 => CTR => G8: 1,2 * PRF # H9: 1,2 => SOL * DIS # H9: 4,6 => CTR => H9: 1,2 * DIS # G8: 2,4 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # H9: 2,4 => SOL * INC # H9: 1,6 => UNS * DIS # C9: 2,4 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # I4: 2,4 => CTR => I4: 9 * INC # I4: 9 => UNS * INC # I5: 2,4 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 1,4 => SOL * STA A1: 1,4 * CNT 1 HDP CHAINS / 1 HYP OPENED