Analysis of xx-top500-312-base.sdk
Contents
Original Sudoku
level: medium
position: 4...5.1...3.6..............5.1...7.....3.4....6.8...........2861...............3. initial
Autosolve
position: 4.8.5316..356.18.461.48.3.5581...743...314658364875912.5314.2861.6.38...8......31 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 2,9 => CTR => D1: 7 * PRF # H2: 2,9 => SOL * PRF # H3: 7,9 => SOL * DIS # B1: 7,9 => CTR => B1: 2 * DIS # D1: 2,9 => CTR => D1: 7 * DIS # D9: 2,9 => CTR => D9: 5,7 * DIS # C9: 7,9 => CTR => C9: 2 * DIS # A5: 7,9 => CTR => A5: 2 * DIS # B9: 2,4 => CTR => B9: 7,9 * DIS # D9: 7,9 => CTR => D9: 2,5 * PRF # F9: 7,9 => SOL * PRF # F3: 2 => SOL * DIS # D9: 7,9 => CTR => D9: 2,5 * PRF # H3: 7,9 => SOL * CNT 14 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 2,9 => CTR => D1: 7 * PRF D1: 7 # F9: 7,9 => SOL * STA D1: 7 + F9: 7,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4...5.1...3.6..............5.1...7.....3.4....6.8...........2861...............3. | initial |
| 4.8.5316..356.18.461.48.3.5581...743...314658364875912.5314.2861.6.38...8......31 | autosolve |
| 428753169735691824619482375581926743297314658364875912953147286146238597872569431 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) E2: 2,9 I1: 7,9 D4: 2,9 A7: 7,9 B8: 2,4 F7: 7,9 D8: 2,5 G8: 4,5 H8: 7,9 I8: 7,9 G9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 2.. / H2 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) B1,D1: 2.. / B1 = 2 => 14 pairs (_) / D1 = 2 => 0 pairs (X) B8,D8: 2.. / B8 = 2 => 0 pairs (X) / D8 = 2 => 14 pairs (_) A2,A5: 2.. / A2 = 2 => 0 pairs (X) / A5 = 2 => 14 pairs (_) B8,B9: 4.. / B8 = 4 => 14 pairs (_) / B9 = 4 => 0 pairs (X) G8,G9: 4.. / G8 = 4 => 0 pairs (X) / G9 = 4 => 14 pairs (_) B8,G8: 4.. / B8 = 4 => 14 pairs (_) / G8 = 4 => 0 pairs (X) B9,G9: 4.. / B9 = 4 => 0 pairs (X) / G9 = 4 => 14 pairs (_) D8,D9: 5.. / D8 = 5 => 0 pairs (X) / D9 = 5 => 14 pairs (_) G8,G9: 5.. / G8 = 5 => 14 pairs (_) / G9 = 5 => 0 pairs (X) D8,G8: 5.. / D8 = 5 => 0 pairs (X) / G8 = 5 => 14 pairs (_) D9,G9: 5.. / D9 = 5 => 14 pairs (_) / G9 = 5 => 0 pairs (X) E4,F4: 6.. / E4 = 6 => 13 pairs (_) / F4 = 6 => 12 pairs (_) E9,F9: 6.. / E9 = 6 => 12 pairs (_) / F9 = 6 => 13 pairs (_) E4,E9: 6.. / E4 = 6 => 13 pairs (_) / E9 = 6 => 12 pairs (_) F4,F9: 6.. / F4 = 6 => 12 pairs (_) / F9 = 6 => 13 pairs (_) D1,F3: 7.. / D1 = 7 => 14 pairs (_) / F3 = 7 => 0 pairs (X) H8,I8: 7.. / H8 = 7 => 0 pairs (X) / I8 = 7 => 12 pairs (_) A2,H2: 7.. / A2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) A7,F7: 7.. / A7 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) D1,D9: 7.. / D1 = 7 => 14 pairs (_) / D9 = 7 => 0 pairs (X) I1,I8: 7.. / I1 = 7 => 0 pairs (X) / I8 = 7 => 12 pairs (_) H8,I8: 9.. / H8 = 9 => 12 pairs (_) / I8 = 9 => 0 pairs (X) A7,F7: 9.. / A7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) I1,I8: 9.. / I1 = 9 => 12 pairs (_) / I8 = 9 => 0 pairs (X) * DURATION: 0:00:50.837543 START: 13:38:53.812573 END: 13:39:44.650116 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,D4,D8,E2,F7,G8,G9,H8,I1,I8) * 4.8.5316..356.18.461.48.3.5581...743...314658364875912.5314.2861.6.38...8......31 * PAIR E2: 2,9 BLK 2 D1: 2,9,7 # reduction candidate for 2,9 D1: 2,9 => CTR * 478253169.356918746194873255819..74392.3146583648759127531492861.6.38...8..7..531 D1: 7 # 14 pairs F3: 2,9,7 # reduction candidate for 2,9 F3: 2,9 # 14 pairs * PAIR E2: 2,9 ROW 2 A2: 2,9,7 # reduction candidate for 2,9 A2: 2,9 # 15 pairs H2: 2,9,7 # reduction candidate for 2,9 H2: 2,9 => SOLVED * 428753169735691824619482375581926743297314658364875912953147286146238597872569431 H2: 7 # 15 pairs * PAIR E2: 2,9 COL E E4: 2,9,6 # reduction candidate for 2,9 E4: 2,9 # 12 pairs E9: 2,9,6 # reduction candidate for 2,9 E9: 2,9 # 13 pairs * PAIR I1: 7,9 BLK 3 H2: 7,9,2 # reduction candidate for 7,9 H2: 7,9 # 16 pairs H3: 7,9,2 # reduction candidate for 7,9 H3: 7,9 => SOLVED * 428753169735691824619482375581926743297314658364875912953147286146238597872569431 H3: 2 # 16 pairs * PAIR I1: 7,9 ROW 1 B1: 7,9,2 # reduction candidate for 7,9 B1: 7,9 => CTR * 4.825316..356918.461.4873.55819..743...3146583648759127531492861265384..8497..531 B1: 2 # 14 pairs D1: 7,9,2 # reduction candidate for 7,9 D1: 7,9 # 14 pairs * PAIR D4: 2,9 BLK 5 E4: 2,9,6 # reduction candidate for 2,9 E4: 2,9 # 12 pairs F4: 2,9,6 # reduction candidate for 2,9 F4: 2,9 # 13 pairs * PAIR D4: 2,9 COL D D1: 2,9,7 # reduction candidate for 2,9 D1: 2,9 => CTR * 478253169.356918746194873255819..74392.3146583648759127531492861.6.38...8..7..531 D1: 7 # 14 pairs D9: 2,9,5,7 # reduction candidate for 2,9 D9: 2,9 => CTR * 4.8753169.356.18.461.48.3.5581...743...314658364875912.5314.2861.653849784....531 D9: 5,7 # 12 pairs * PAIR A7: 7,9 BLK 7 B9: 7,9,2,4 # reduction candidate for 7,9 B9: 7,9 # 14 pairs C9: 7,9,2 # reduction candidate for 7,9 C9: 7,9 => CTR * 4.825316..356918.461.4873.55819..743...3146583648759127531492861265384..8497..531 C9: 2 # 14 pairs * PAIR A7: 7,9 COL A A2: 7,9,2 # reduction candidate for 7,9 A2: 7,9 # 14 pairs A5: 7,9,2 # reduction candidate for 7,9 A5: 7,9 => CTR * 4.82531692356918746194873255819..743...314658364875912753149286126.38.978......31 A5: 2 # 14 pairs * PAIR B8: 2,4 BLK 7 B9: 2,4,7,9 # reduction candidate for 2,4 B9: 2,4 => CTR * 4.825316..356918.461.4873.55819..743...3146583648759127531492861265384..8497..531 B9: 7,9 # 14 pairs * PAIR F7: 7,9 BLK 8 D9: 7,9,2,5 # reduction candidate for 7,9 D9: 7,9 => CTR * 4.825316..356918.461.4873.55819..743...3146583648759127531492861265384..8497..531 D9: 2,5 # 14 pairs F9: 7,9,2,6 # reduction candidate for 7,9 F9: 7,9 => SOLVED * 428753169735691824619482375581926743297314658364875912953147286146238597872569431 F9: 2,6 # 12 pairs * PAIR F7: 7,9 COL F F3: 7,9,2 # reduction candidate for 7,9 F3: 2 => SOLVED * 428753169735691824619482375581926743297314658364875912953147286146238597872569431 F3: 7,9 # 14 pairs * PAIR D8: 2,5 BLK 8 D9: 2,5,7,9 # reduction candidate for 2,5 D9: 7,9 => CTR * 4.825316..356918.461.4873.55819..743...3146583648759127531492861265384..8497..531 D9: 2,5 # 14 pairs * PAIR H8: 7,9 COL H H2: 7,9,2 # reduction candidate for 7,9 H2: 7,9 # 16 pairs H3: 7,9,2 # reduction candidate for 7,9 H3: 7,9 => SOLVED * 428753169735691824619482375581926743297314658364875912953147286146238597872569431 H3: 2 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-312-base-pr-000.dot * REASONING * DIS # D1: 2,9 => CTR => D1: 7 * PRF # H2: 2,9 => SOL * PRF # H3: 7,9 => SOL * DIS # B1: 7,9 => CTR => B1: 2 * DIS # D1: 2,9 => CTR => D1: 7 * DIS # D9: 2,9 => CTR => D9: 5,7 * DIS # C9: 7,9 => CTR => C9: 2 * DIS # A5: 7,9 => CTR => A5: 2 * DIS # B9: 2,4 => CTR => B9: 7,9 * DIS # D9: 7,9 => CTR => D9: 2,5 * PRF # F9: 7,9 => SOL * PRF # F3: 2 => SOL * DIS # D9: 7,9 => CTR => D9: 2,5 * PRF # H3: 7,9 => SOL * CNT 14 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,D4,D8,E2,F7,G8,G9,H8,I1,I8) * 4.8.5316..356.18.461.48.3.5581...743...314658364875912.5314.2861.6.38...8......31 * PAIR E2: 2,9 BLK 2 D1: 2,9,7 # reduction candidate for 2,9 D1: 2,9 => CTR * 478253169.356918746194873255819..74392.3146583648759127531492861.6.38...8..7..531 * RESTART * PAIR F7: 7,9 BLK 8 F9: 7,9,6 # reduction candidate for 7,9 F9: 7,9 => SOLVED * 428753169735691824619482375581926743297314658364875912953147286146238597872569431 * DURATION: 0:00:03.665965 START: 13:40:29.955464 END: 13:40:33.621429 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-312-base-pr-001.dot * REASONING * DIS # D1: 2,9 => CTR => D1: 7 * PRF D1: 7 # F9: 7,9 => SOL * STA D1: 7 + F9: 7,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 312 solution: 428753169735691824619482375581926743297314658364875912953147286146238597872569431 info: 2844 FNBWXY S8.f 30721 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 428753169735691824619482375581926743297314658364875912953147286146238597872569431 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:
* DIS # D1: 2,9 => CTR => D1: 7 * INC # D1: 7 => UNS * INC # F3: 2,9 => UNS * INC # A2: 2,9 => UNS * PRF # H2: 2,9 => SOL * INC # H2: 7 => UNS * INC # E4: 2,9 => UNS * INC # E9: 2,9 => UNS * INC # H2: 7,9 => UNS * PRF # H3: 7,9 => SOL * INC # H3: 2 => UNS * DIS # B1: 7,9 => CTR => B1: 2 * INC # B1: 2 => UNS * INC # D1: 7,9 => UNS * INC # E4: 2,9 => UNS * INC # F4: 2,9 => UNS * DIS # D1: 2,9 => CTR => D1: 7 * INC # D1: 7 => UNS * DIS # D9: 2,9 => CTR => D9: 5,7 * INC # D9: 5,7 => UNS * INC # B9: 7,9 => UNS * DIS # C9: 7,9 => CTR => C9: 2 * INC # C9: 2 => UNS * INC # A2: 7,9 => UNS * DIS # A5: 7,9 => CTR => A5: 2 * INC # A5: 2 => UNS * DIS # B9: 2,4 => CTR => B9: 7,9 * INC # B9: 7,9 => UNS * DIS # D9: 7,9 => CTR => D9: 2,5 * INC # D9: 2,5 => UNS * PRF # F9: 7,9 => SOL * INC # F9: 2,6 => UNS * INC # F3: 7,9 => UNS * PRF # F3: 2 => SOL * INC # D9: 2,5 => UNS * DIS # D9: 7,9 => CTR => D9: 2,5 * INC # H2: 7,9 => UNS * PRF # H3: 7,9 => SOL * INC # H3: 2 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 2,9 => CTR => D1: 7 * PRF D1: 7 # F9: 7,9 => SOL * STA D1: 7 + F9: 7,9 * CNT 2 HDP CHAINS / 2 HYP OPENED