Analysis of xx-top500-371-base.sdk
Contents
Original Sudoku
level: medium
position: 17.....4.2..8........6......38.....6....1..3...4......5.....2.8...3...........7.. initial
Autosolve
position: 17653.84.24.8..36.38.6......384..1.6652.1843..14.63.8.5631..2988.73..6144.1.86753 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I2: 5,9 => SOL * DIS # I2: 1,7 => CTR => I2: 5,9 * DIS # I2: 7,9 => CTR => I2: 1,5 * DIS # F3: 1,7 => CTR => F3: 4 * DIS # I2: 1,7 => CTR => I2: 5,9 * PRF # I2: 5,9 => SOL * DIS # I6: 2,9 => CTR => I6: 5,7 * PRF # I6: 5,7 => SOL * PRF # I2: 5,9 => SOL * DIS # I2: 1,7 => CTR => I2: 5,9 * DIS # I3: 2,7 => CTR => I3: 1 * DIS # E3: 4 => CTR => E3: 2,7 * DIS # D6: 7,9 => CTR => D6: 2 * PRF # D6: 2 => SOL * PRF # I6: 7,9 => SOL * DIS # D6: 7,9 => CTR => D6: 2 * PRF # D6: 2 => SOL * PRF # I6: 2,7 => SOL * DIS # I6: 5,9 => CTR => I6: 2,7 * PRF # I6: 7,9 => SOL * DIS # I2: 7,9 => CTR => I2: 1,5 * DIS # I6: 5,9 => CTR => I6: 2,7 * PRF # I6: 2,7 => SOL * DIS # E3: 4,7 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # F3: 1 => CTR => F3: 4,7 * PRF # D6: 2,9 => SOL * DIS # D6: 7 => CTR => D6: 2,9 * CNT 28 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I2: 5,9 => SOL * STA I2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 17.....4.2..8........6......38.....6....1..3...4......5.....2.8...3...........7.. | initial |
| 17653.84.24.8..36.38.6......384..1.6652.1843..14.63.8.5631..2988.73..6144.1.86753 | autosolve |
| 176539842249871365385624971738495126652718439914263587563147298897352614421986753 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C2: 5,9 C3: 5,9 F1: 2,9 E2: 7,9 F2: 1,7 I1: 2,9 G3: 5,9 H3: 2,7 A4: 7,9 A6: 7,9 D5: 7,9 H4: 2,7 I5: 7,9 G6: 5,9 B8: 2,9 B9: 2,9 E7: 4,7 F7: 4,7 D9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 1.. / F2 = 1 => 19 pairs (_) / F3 = 1 => 0 pairs (X) I2,I3: 1.. / I2 = 1 => 0 pairs (X) / I3 = 1 => 19 pairs (_) F2,I2: 1.. / F2 = 1 => 19 pairs (_) / I2 = 1 => 0 pairs (X) F3,I3: 1.. / F3 = 1 => 0 pairs (X) / I3 = 1 => 19 pairs (_) F1,E3: 2.. / F1 = 2 => 0 pairs (X) / E3 = 2 => 0 pairs (_) H4,I6: 2.. / H4 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) B8,B9: 2.. / B8 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) F1,I1: 2.. / F1 = 2 => 0 pairs (X) / I1 = 2 => 0 pairs (_) D6,I6: 2.. / D6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) B9,D9: 2.. / B9 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) D6,D9: 2.. / D6 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) H3,H4: 2.. / H3 = 2 => 0 pairs (X) / H4 = 2 => 0 pairs (_) E3,F3: 4.. / E3 = 4 => 0 pairs (X) / F3 = 4 => 17 pairs (_) E7,F7: 4.. / E7 = 4 => 17 pairs (_) / F7 = 4 => 0 pairs (X) E3,E7: 4.. / E3 = 4 => 0 pairs (X) / E7 = 4 => 17 pairs (_) F3,F7: 4.. / F3 = 4 => 17 pairs (_) / F7 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) I2,G3: 5.. / I2 = 5 => 0 pairs (*) / G3 = 5 => 0 pairs (X) E4,F4: 5.. / E4 = 5 => 21 pairs (_) / F4 = 5 => 21 pairs (_) G6,I6: 5.. / G6 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) E8,F8: 5.. / E8 = 5 => 21 pairs (_) / F8 = 5 => 21 pairs (_) C2,I2: 5.. / C2 = 5 => 0 pairs (X) / I2 = 5 => 0 pairs (_) C3,G3: 5.. / C3 = 5 => 0 pairs (*) / G3 = 5 => 0 pairs (X) E4,E8: 5.. / E4 = 5 => 21 pairs (_) / E8 = 5 => 21 pairs (_) F4,F8: 5.. / F4 = 5 => 21 pairs (_) / F8 = 5 => 21 pairs (_) G3,G6: 5.. / G3 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) I2,I6: 5.. / I2 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) A4,A6: 7.. / A4 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) D5,D6: 7.. / D5 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 0 pairs (X) / F7 = 7 => 17 pairs (_) A4,H4: 7.. / A4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) D5,I5: 7.. / D5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) H3,H4: 7.. / H3 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) C2,C3: 9.. / C2 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) F1,E2: 9.. / F1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) A4,A6: 9.. / A4 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) B8,B9: 9.. / B8 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) F1,I1: 9.. / F1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) C3,G3: 9.. / C3 = 9 => 0 pairs (X) / G3 = 9 => 0 pairs (_) D5,I5: 9.. / D5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) B9,D9: 9.. / B9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) G3,G6: 9.. / G3 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) * DURATION: 0:01:15.961645 START: 15:32:12.529171 END: 15:33:28.490816 2017-05-04 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B8,B9,C2,C3,D5,D9,E2,E7,F1,F2,F7,G3,G6,H3,H4,I1,I5) * 17653.84.24.8..36.38.6......384..1.6652.1843..14.63.8.5631..2988.73..6144.1.86753 * PAIR C2: 5,9 ROW 2 I2: 5,9,1,7 # reduction candidate for 5,9 I2: 5,9 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 I2: 1,7 => CTR * 17653284924589.36.3896..5.29384.51.6652.1843..14.639855631..2988.73..6144.1.86753 * PAIR F1: 2,9 COL F F4: 2,9,5 # reduction candidate for 2,9 F4: 2,9 # 21 pairs F8: 2,9,5 # reduction candidate for 2,9 F8: 2,9 # 21 pairs * PAIR E2: 7,9 ROW 2 I2: 7,9,1,5 # reduction candidate for 7,9 I2: 7,9 => CTR * 17653.8422458.1369389624571.384..1.6652.1843..14.639855631..2988.73..6144.1.86753 I2: 1,5 # 22 pairs * PAIR F2: 1,7 BLK 2 F3: 1,7,4 # reduction candidate for 1,7 F3: 1,7 => CTR * 17653284924.89.36.38964.5...384..1.6652918437.1476398.5631742988.73..6144.1.86753 F3: 4 # 17 pairs * PAIR F2: 1,7 ROW 2 I2: 1,7,5,9 # reduction candidate for 1,7 I2: 1,7 => CTR * 17653284924589.36.3896..5.29384.51.6652.1843..14.639855631..2988.73..6144.1.86753 I2: 5,9 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 * PAIR I1: 2,9 COL I I6: 2,9,5,7 # reduction candidate for 2,9 I6: 2,9 => CTR * 17653.84.24.8..3653856..9.1.384..1.6652.18437.1476358.5631..2988.73..6144.1.86753 I6: 5,7 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 * PAIR G3: 5,9 BLK 3 I2: 5,9,1,7 # reduction candidate for 5,9 I2: 5,9 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 I2: 1,7 => CTR * 17653284924589.36.3896..5.29384.51.6652.1843..14.639855631..2988.73..6144.1.86753 * PAIR H3: 2,7 BLK 3 I3: 2,7,1 # reduction candidate for 2,7 I3: 2,7 => CTR * 17653.8492458973613896415.29384..1.6652.1843..14.639855631.42988.73..6144.1.86753 I3: 1 # 19 pairs * PAIR H3: 2,7 ROW 3 E3: 2,7,4 # reduction candidate for 2,7 E3: 4 => CTR * 17653284924.89.36.38964.5...384..1.6652918437.1476398.5631..2988.73..6144.1.86753 E3: 2,7 # 17 pairs * PAIR A6: 7,9 ROW 6 D6: 7,9,2 # reduction candidate for 7,9 D6: 7,9 => CTR * 17653284924.89.36538.6......384..1.6652.1843..14.63.825631..2988.73..6144.1286753 D6: 2 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 I6: 7,9,2,5 # reduction candidate for 7,9 I6: 7,9 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 I6: 2,5 # 20 pairs * PAIR D5: 7,9 BLK 5 D6: 7,9,2 # reduction candidate for 7,9 D6: 7,9 => CTR * 17653284924.89.36538.6......384..1.6652.1843..14.63.825631..2988.73..6144.1286753 D6: 2 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 * PAIR H4: 2,7 BLK 6 I6: 2,7,5,9 # reduction candidate for 2,7 I6: 2,7 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 I6: 5,9 => CTR * 17653.84.24.8..36.38.6......384..126652.18437.14.63.8.5631..2988.73..6144.1.86753 * PAIR I5: 7,9 BLK 6 I6: 7,9,2,5 # reduction candidate for 7,9 I6: 7,9 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 I6: 2,5 # 20 pairs * PAIR I5: 7,9 COL I I2: 7,9,1,5 # reduction candidate for 7,9 I2: 7,9 => CTR * 17653.8422458.1369389624571.384..1.6652.1843..14.639855631..2988.73..6144.1.86753 I2: 1,5 # 22 pairs * PAIR G6: 5,9 BLK 6 I6: 5,9,2,7 # reduction candidate for 5,9 I6: 5,9 => CTR * 17653.84.24.8..36.38.6......384..126652.18437.14.63.8.5631..2988.73..6144.1.86753 I6: 2,7 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 * PAIR B8: 2,9 ROW 8 E8: 2,9,5 # reduction candidate for 2,9 E8: 2,9 # 21 pairs F8: 2,9,5 # reduction candidate for 2,9 F8: 2,9 # 21 pairs * PAIR E7: 4,7 COL E E3: 4,7,2 # reduction candidate for 4,7 E3: 4,7 => CTR * 17653284924.89.36.3896..5...384..1.6652918437.1476398.5631..2988.73..6144.1.86753 E3: 2 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 * PAIR F7: 4,7 COL F F3: 4,7,1 # reduction candidate for 4,7 F3: 1 => CTR * 17653284924.8973613896415...384..1.6652918437.1476398.5631742988.73..6144.1.86753 F3: 4,7 # 19 pairs * PAIR D9: 2,9 BLK 8 E8: 2,9,5 # reduction candidate for 2,9 E8: 2,9 # 21 pairs F8: 2,9,5 # reduction candidate for 2,9 F8: 2,9 # 21 pairs * PAIR D9: 2,9 COL D D6: 2,9,7 # reduction candidate for 2,9 D6: 2,9 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 D6: 7 => CTR * 17653284924.89.36538.6......384..1.6652.1843..14763.825631..2988.73..6144.1286753 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-371-base-pr-000.dot * REASONING * PRF # I2: 5,9 => SOL * DIS # I2: 1,7 => CTR => I2: 5,9 * DIS # I2: 7,9 => CTR => I2: 1,5 * DIS # F3: 1,7 => CTR => F3: 4 * DIS # I2: 1,7 => CTR => I2: 5,9 * PRF # I2: 5,9 => SOL * DIS # I6: 2,9 => CTR => I6: 5,7 * PRF # I6: 5,7 => SOL * PRF # I2: 5,9 => SOL * DIS # I2: 1,7 => CTR => I2: 5,9 * DIS # I3: 2,7 => CTR => I3: 1 * DIS # E3: 4 => CTR => E3: 2,7 * DIS # D6: 7,9 => CTR => D6: 2 * PRF # D6: 2 => SOL * PRF # I6: 7,9 => SOL * DIS # D6: 7,9 => CTR => D6: 2 * PRF # D6: 2 => SOL * PRF # I6: 2,7 => SOL * DIS # I6: 5,9 => CTR => I6: 2,7 * PRF # I6: 7,9 => SOL * DIS # I2: 7,9 => CTR => I2: 1,5 * DIS # I6: 5,9 => CTR => I6: 2,7 * PRF # I6: 2,7 => SOL * DIS # E3: 4,7 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # F3: 1 => CTR => F3: 4,7 * PRF # D6: 2,9 => SOL * DIS # D6: 7 => CTR => D6: 2,9 * CNT 28 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B8,B9,C2,C3,D5,D9,E2,E7,F1,F2,F7,G3,G6,H3,H4,I1,I5) * 17653.84.24.8..36.38.6......384..1.6652.1843..14.63.8.5631..2988.73..6144.1.86753 * PAIR C2: 5,9 ROW 2 I2: 5,9,1,7 # reduction candidate for 5,9 I2: 5,9 => SOLVED * 176539842249871365385624971738495126652718439914263587563147298897352614421986753 * DURATION: 0:00:02.252758 START: 15:34:16.784521 END: 15:34:19.037279 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-371-base-pr-001.dot * REASONING * PRF # I2: 5,9 => SOL * STA I2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 371 solution: 176539842249871365385624971738495126652718439914263587563147298897352614421986753 info: 5955 FNBTWXY S8.f 42030 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 176539842249871365385624971738495126652718439914263587563147298897352614421986753 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 # I2: 5,9 => SOL * DIS # I2: 1,7 => CTR => I2: 5,9 * INC # F4: 2,9 => UNS * INC # F8: 2,9 => UNS * DIS # I2: 7,9 => CTR => I2: 1,5 * INC # I2: 1,5 => UNS * DIS # F3: 1,7 => CTR => F3: 4 * INC # F3: 4 => UNS * DIS # I2: 1,7 => CTR => I2: 5,9 * PRF # I2: 5,9 => SOL * DIS # I6: 2,9 => CTR => I6: 5,7 * PRF # I6: 5,7 => SOL * PRF # I2: 5,9 => SOL * DIS # I2: 1,7 => CTR => I2: 5,9 * DIS # I3: 2,7 => CTR => I3: 1 * INC # I3: 1 => UNS * INC # E3: 2,7 => UNS * DIS # E3: 4 => CTR => E3: 2,7 * DIS # D6: 7,9 => CTR => D6: 2 * PRF # D6: 2 => SOL * PRF # I6: 7,9 => SOL * INC # I6: 2,5 => UNS * DIS # D6: 7,9 => CTR => D6: 2 * PRF # D6: 2 => SOL * PRF # I6: 2,7 => SOL * DIS # I6: 5,9 => CTR => I6: 2,7 * PRF # I6: 7,9 => SOL * INC # I6: 2,5 => UNS * DIS # I2: 7,9 => CTR => I2: 1,5 * INC # I2: 1,5 => UNS * DIS # I6: 5,9 => CTR => I6: 2,7 * PRF # I6: 2,7 => SOL * INC # E8: 2,9 => UNS * INC # F8: 2,9 => UNS * DIS # E3: 4,7 => CTR => E3: 2 * PRF # E3: 2 => SOL * INC # F3: 4,7 => UNS * DIS # F3: 1 => CTR => F3: 4,7 * INC # E8: 2,9 => UNS * INC # F8: 2,9 => UNS * PRF # D6: 2,9 => SOL * DIS # D6: 7 => CTR => D6: 2,9 * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I2: 5,9 => SOL * STA I2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED