Analysis of xx-top500-041-base.sdk
Contents
Original Sudoku
level: medium
position: 5......79...6.1...4............9.3..7...5.....8....6...623............5..1....... initial
Autosolve
position: 536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 2,8 => CTR => D8: 9 * DIS # D9: 2,8 => CTR => D9: 4,9 * PRF # E9: 2,8 => SOL * DIS # H9: 6,8,9 => CTR => H9: 3,4 * DIS # I9: 3,4 => CTR => I9: 2,6,8 * DIS # I3: 6 => CTR => I3: 2,8 * DIS # G9: 2,8 => CTR => G9: 4,9 * DIS # I3: 6,8 => CTR => I3: 2 * DIS # H9: 6,8 => CTR => H9: 3,4,9 * PRF # E9: 2,4 => SOL * DIS # D9: 8,9 => CTR => D9: 2,4 * DIS # H9: 8,9 => CTR => H9: 3,4,6 * DIS # D8: 2,8 => CTR => D8: 9 * DIS # D9: 2,8 => CTR => D9: 4,9 * PRF # E9: 2,8 => SOL * DIS # G8: 9 => CTR => G8: 2,8 * CNT 16 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 2,8 => CTR => D8: 9 * DIS D8: 9 # D9: 2,8 => CTR => D9: 4 * DIS D8: 9 + D9: 4 # D4: 1 => CTR => D4: 2,8 * PRF D8: 9 + D9: 4 + D4: 2,8 # I9: 2,6 => SOL * STA D8: 9 + D9: 4 + D4: 2,8 + I9: 2,6 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5......79...6.1...4............9.3..7...5.....8....6...623............5..1....... | initial |
| 536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7... | autosolve |
| 536284179298671543471539862654892317723156498189743625962315784347968251815427936 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) D1: 2,8 E1: 2,8 H2: 3,4 I2: 3,4 G3: 2,8 H3: 6,8 F4: 2,8 E6: 2,4 H6: 2,4 A7: 8,9 A9: 8,9 E8: 1,6 F8: 2,8 I8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,D5: 1.. / D4 = 1 => 16 pairs (_) / D5 = 1 => 18 pairs (_) E7,E8: 1.. / E7 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) D4,H4: 1.. / D4 = 1 => 16 pairs (_) / H4 = 1 => 18 pairs (_) E8,I8: 1.. / E8 = 1 => 13 pairs (_) / I8 = 1 => 0 pairs (*) D1,E1: 2.. / D1 = 2 => 15 pairs (_) / E1 = 2 => 0 pairs (X) G3,I3: 2.. / G3 = 2 => 0 pairs (X) / I3 = 2 => 16 pairs (_) H4,H6: 2.. / H4 = 2 => 0 pairs (X) / H6 = 2 => 17 pairs (_) E6,H6: 2.. / E6 = 2 => 0 pairs (X) / H6 = 2 => 17 pairs (_) F4,F8: 2.. / F4 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) I3,I9: 2.. / I3 = 2 => 16 pairs (_) / I9 = 2 => 0 pairs (X) H2,I2: 3.. / H2 = 3 => 0 pairs (X) / I2 = 3 => 16 pairs (_) H9,I9: 3.. / H9 = 3 => 16 pairs (_) / I9 = 3 => 0 pairs (X) H2,H9: 3.. / H2 = 3 => 0 pairs (X) / H9 = 3 => 16 pairs (_) I2,I9: 3.. / I2 = 3 => 16 pairs (_) / I9 = 3 => 0 pairs (X) H2,I2: 4.. / H2 = 4 => 16 pairs (_) / I2 = 4 => 0 pairs (X) D5,E6: 4.. / D5 = 4 => 0 pairs (X) / E6 = 4 => 17 pairs (_) E6,H6: 4.. / E6 = 4 => 17 pairs (_) / H6 = 4 => 0 pairs (X) D5,D9: 4.. / D5 = 4 => 0 pairs (X) / D9 = 4 => 17 pairs (_) G5,G9: 4.. / G5 = 4 => 17 pairs (_) / G9 = 4 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 14 pairs (_) / I3 = 6 => 0 pairs (X) E8,E9: 6.. / E8 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) E8,I8: 6.. / E8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) H3,H9: 6.. / H3 = 6 => 14 pairs (_) / H9 = 6 => 0 pairs (X) D1,E1: 8.. / D1 = 8 => 0 pairs (X) / E1 = 8 => 15 pairs (_) A7,A9: 8.. / A7 = 8 => 0 pairs (X) / A9 = 8 => 12 pairs (_) F4,F8: 8.. / F4 = 8 => 17 pairs (_) / F8 = 8 => 0 pairs (*) G5,H5: 9.. / G5 = 9 => 0 pairs (X) / H5 = 9 => 13 pairs (_) A7,A9: 9.. / A7 = 9 => 12 pairs (_) / A9 = 9 => 0 pairs (X) D8,D9: 9.. / D8 = 9 => 17 pairs (_) / D9 = 9 => 0 pairs (X) A7,H7: 9.. / A7 = 9 => 12 pairs (_) / H7 = 9 => 0 pairs (X) D8,G8: 9.. / D8 = 9 => 17 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:00:57.597408 START: 04:04:12.444390 END: 04:05:10.041798 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,D1,E1,E6,E8,F4,F8,G3,H2,H3,H6,I2,I8) * 536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7... * PAIR D1: 2,8 COL D D4: 2,8,1 # reduction candidate for 2,8 D4: 2,8 # 18 pairs D8: 2,8,9 # reduction candidate for 2,8 D8: 2,8 => CTR * 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743. D8: 9 # 17 pairs D9: 2,8,4,9 # reduction candidate for 2,8 D9: 2,8 => CTR * 536..41792986715..471539...654.9.3.7723456...189723645.623.57..3479.285..158.74.2 D9: 4,9 # 15 pairs * PAIR E1: 2,8 COL E E9: 2,8,4,6 # reduction candidate for 2,8 E9: 2,8 => SOLVED * 536284179298671543471539862654892317723156498189743625962315784347968251815427936 E9: 4,6 # 15 pairs * PAIR H2: 3,4 COL H H9: 3,4,6,8,9 # reduction candidate for 3,4 H9: 6,8,9 => CTR * 536284179298671534471539862654.9.3.7723.56...189723645.623457..347.12956.15.67..3 H9: 3,4 # 16 pairs * PAIR I2: 3,4 COL I I9: 3,4,2,6,8 # reduction candidate for 3,4 I9: 3,4 => CTR * 5362841792986715..471539862654.9.3.7723.56...189723645.623457..347.12956.15.67... I9: 2,6,8 # 16 pairs * PAIR G3: 2,8 BLK 3 I3: 2,8,6 # reduction candidate for 2,8 I3: 6 => CTR * 536..41792986715..471539286654.9.3.7723.56...1897.36.5.623.57..347.6..51.15..7.6. I3: 2,8 # 14 pairs * PAIR G3: 2,8 COL G G8: 2,8,9 # reduction candidate for 2,8 G8: 2,8 # 17 pairs G9: 2,8,4,9 # reduction candidate for 2,8 G9: 2,8 => CTR * 536..41792986715..471539...654.9.3.7723.5649.1897436259623.57..347...95.815..7... G9: 4,9 # 15 pairs * PAIR H3: 6,8 BLK 3 I3: 6,8,2 # reduction candidate for 6,8 I3: 6,8 => CTR * 536.24179298671543471539268654.9.3.7723.56491189743625962385714347912856815467932 I3: 2 # 16 pairs * PAIR H3: 6,8 COL H H9: 6,8,3,4,9 # reduction candidate for 6,8 H9: 6,8 => CTR * 536..4179298671534471539862654.9.3.7723.56..81897.36.58623.5791347918256915267483 H9: 3,4,9 # 14 pairs * PAIR F4: 2,8 BLK 5 D4: 2,8,1 # reduction candidate for 2,8 D4: 2,8 # 18 pairs D4: 1 # 16 pairs * PAIR F4: 2,8 ROW 4 H4: 2,8,1 # reduction candidate for 2,8 H4: 1 # 18 pairs H4: 2,8 # 16 pairs * PAIR E6: 2,4 COL E E9: 2,4,6,8 # reduction candidate for 2,4 E9: 2,4 => SOLVED * 536284179298671543471539862654892317723156498189743625962315784347968251815427936 E9: 6,8 # 15 pairs * PAIR A7: 8,9 ROW 7 H7: 8,9,1,4 # reduction candidate for 8,9 H7: 8,9 # 18 pairs H7: 1,4 # 13 pairs * PAIR A9: 8,9 ROW 9 D9: 8,9,2,4 # reduction candidate for 8,9 D9: 8,9 => CTR * 536..41792986715..471539...654.9.3.7723456...189723645.623.57..347..2.5..15..74.2 D9: 2,4 # 18 pairs G9: 8,9,2,4 # reduction candidate for 8,9 G9: 8,9 # 17 pairs H9: 8,9,3,4,6 # reduction candidate for 8,9 H9: 8,9 => CTR * 536284179298671534471539862654.9.3.7723.56...189723645.623457..347.12956.15.67..3 H9: 3,4,6 # 14 pairs * PAIR F8: 2,8 BLK 8 D8: 2,8,9 # reduction candidate for 2,8 D8: 2,8 => CTR * 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743. D8: 9 # 17 pairs D9: 2,8,4,9 # reduction candidate for 2,8 D9: 2,8 => CTR * 536..41792986715..471539...654.9.3.7723456...189723645.623.57..3479.285..158.74.2 D9: 4,9 # 15 pairs E9: 2,8,4,6 # reduction candidate for 2,8 E9: 2,8 => SOLVED * 536284179298671543471539862654892317723156498189743625962315784347968251815427936 E9: 4,6 # 15 pairs * PAIR F8: 2,8 ROW 8 G8: 2,8,9 # reduction candidate for 2,8 G8: 9 => CTR * 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743. G8: 2,8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-041-base-pr-000.dot * REASONING * DIS # D8: 2,8 => CTR => D8: 9 * DIS # D9: 2,8 => CTR => D9: 4,9 * PRF # E9: 2,8 => SOL * DIS # H9: 6,8,9 => CTR => H9: 3,4 * DIS # I9: 3,4 => CTR => I9: 2,6,8 * DIS # I3: 6 => CTR => I3: 2,8 * DIS # G9: 2,8 => CTR => G9: 4,9 * DIS # I3: 6,8 => CTR => I3: 2 * DIS # H9: 6,8 => CTR => H9: 3,4,9 * PRF # E9: 2,4 => SOL * DIS # D9: 8,9 => CTR => D9: 2,4 * DIS # H9: 8,9 => CTR => H9: 3,4,6 * DIS # D8: 2,8 => CTR => D8: 9 * DIS # D9: 2,8 => CTR => D9: 4,9 * PRF # E9: 2,8 => SOL * DIS # G8: 9 => CTR => G8: 2,8 * CNT 16 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,D1,E1,E6,E8,F4,F8,G3,H2,H3,H6,I2,I8) * 536..41792986715..471539...654.9.3.7723.56...1897.36.5.623.57..347....5..15..7... * PAIR D1: 2,8 COL D D4: 2,8,1 # reduction candidate for 2,8 D4: 2,8 # 18 pairs D8: 2,8,9 # reduction candidate for 2,8 D8: 2,8 => CTR * 536..41792986715..471539...654.9.3.77234568911897236459623.571.347.1295681596743. D9: 2,8,4 # reduction candidate for 2,8 D9: 2,8 => CTR * 536..41792986715..471539...654.9.3.77234569..189723645.623.57..3479.285..158.74.2 * RESTART * PAIR D1: 2,8 COL D D4: 2,8,1 # reduction candidate for 2,8 D4: 1 => CTR * 5362841792986715..471539...65419238772385649118974362596231574834796..5.8154.79.. * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (D1,D4,E1,E7,E8,E9,F4,F8,G3,G8,H2,H3,H7,H9,I2,I3,I7,I8) * 536..41792986715..471539...654.9.3177231564981897436259623.57..3479...5.8154.79.. * PAIR I3: 2,6 COL I I9: 2,6,3 # reduction candidate for 2,6 I9: 2,6 => SOLVED * 536284179298671543471539862654892317723156498189743625962315784347968251815427936 * DURATION: 0:00:08.556199 START: 04:05:51.837363 END: 04:06:00.393562 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-041-base-pr-001.dot * REASONING * DIS # D8: 2,8 => CTR => D8: 9 * DIS D8: 9 # D9: 2,8 => CTR => D9: 4 * DIS D8: 9 + D9: 4 # D4: 1 => CTR => D4: 2,8 * PRF D8: 9 + D9: 4 + D4: 2,8 # I9: 2,6 => SOL * STA D8: 9 + D9: 4 + D4: 2,8 + I9: 2,6 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 041 solution: 536284179298671543471539862654892317723156498189743625962315784347968251815427936 info: 1372 FNBHWY S8.f 31992 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 536284179298671543471539862654892317723156498189743625962315784347968251815427936 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 # D4: 2,8 => UNS * DIS # D8: 2,8 => CTR => D8: 9 * INC # D8: 9 => UNS * DIS # D9: 2,8 => CTR => D9: 4,9 * INC # D9: 4,9 => UNS * PRF # E9: 2,8 => SOL * INC # E9: 4,6 => UNS * INC # H9: 3,4 => UNS * DIS # H9: 6,8,9 => CTR => H9: 3,4 * DIS # I9: 3,4 => CTR => I9: 2,6,8 * INC # I9: 2,6,8 => UNS * INC # I3: 2,8 => UNS * DIS # I3: 6 => CTR => I3: 2,8 * INC # G8: 2,8 => UNS * DIS # G9: 2,8 => CTR => G9: 4,9 * INC # G9: 4,9 => UNS * DIS # I3: 6,8 => CTR => I3: 2 * INC # I3: 2 => UNS * DIS # H9: 6,8 => CTR => H9: 3,4,9 * INC # H9: 3,4,9 => UNS * INC # D4: 2,8 => UNS * INC # D4: 1 => UNS * INC # H4: 2,8 => UNS * INC # H4: 1 => UNS * PRF # E9: 2,4 => SOL * INC # E9: 6,8 => UNS * INC # H7: 8,9 => UNS * INC # H7: 1,4 => UNS * DIS # D9: 8,9 => CTR => D9: 2,4 * INC # D9: 2,4 => UNS * INC # G9: 8,9 => UNS * DIS # H9: 8,9 => CTR => H9: 3,4,6 * INC # H9: 3,4,6 => UNS * DIS # D8: 2,8 => CTR => D8: 9 * INC # D8: 9 => UNS * DIS # D9: 2,8 => CTR => D9: 4,9 * INC # D9: 4,9 => UNS * PRF # E9: 2,8 => SOL * INC # E9: 4,6 => UNS * INC # G8: 2,8 => UNS * DIS # G8: 9 => CTR => G8: 2,8 * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D4: 2,8 => UNS * DIS # D8: 2,8 => CTR => D8: 9 * DIS D8: 9 # D9: 2,8 => CTR => D9: 4 * INC D8: 9 + D9: 4 # D4: 2,8 => UNS * DIS D8: 9 + D9: 4 # D4: 1 => CTR => D4: 2,8 * PRF D8: 9 + D9: 4 + D4: 2,8 # I9: 2,6 => SOL * STA D8: 9 + D9: 4 + D4: 2,8 + I9: 2,6 * CNT 6 HDP CHAINS / 6 HYP OPENED