Analysis of xx-top500-452-base.sdk
Contents
Original Sudoku
level: medium
position: .51..........6.4...........4...3...16......8........59.8.5.1...7.....6.....2..... initial
Autosolve
position: .51...8.6....6541..64.1.5..4.5.3..616..15..841.86...59.865.19..71..8.6.554.2.61.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 2,3 => CTR => A3: 8,9 * DIS # D3: 8,9 => CTR => D3: 3,7 * DIS # F3: 8,9 => CTR => F3: 2,3,7 * DIS # H3: 2,3 => CTR => H3: 7,9 * PRF # I3: 2,3 => SOL * PRF # I7: 7 => SOL * DIS # F6: 7 => CTR => F6: 2,4 * DIS # E1: 2,4 => CTR => E1: 9 * PRF # E1: 9 => SOL * DIS # F4: 2,7 => CTR => F4: 8,9 * PRF # H7: 2,3 => SOL * DIS # A3: 2,3 => CTR => A3: 8,9 * PRF # H7: 2,3 => SOL * DIS # H7: 3,7 => CTR => H7: 2,4 * DIS # H7: 3,7 => CTR => H7: 2,4 * DIS # H3: 3,7 => CTR => H3: 2,9 * CNT 16 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:
* DIS # A3: 2,3 => CTR => A3: 8,9 * DIS A3: 8,9 # D3: 8,9 => CTR => D3: 3,7 * DIS A3: 8,9 + D3: 3,7 # F3: 8,9 => CTR => F3: 2,3,7 * PRF A3: 8,9 + D3: 3,7 + F3: 2,3,7 # I3: 2,3 => SOL * STA A3: 8,9 + D3: 3,7 + F3: 2,3,7 + I3: 2,3 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .51..........6.4...........4...3...16......8........59.8.5.1...7.....6.....2..... | initial |
| .51...8.6....6541..64.1.5..4.5.3..616..15..841.86...59.865.19..71..8.6.554.2.61.8 | autosolve |
| 251493876937865412864712593425938761693157284178624359386541927712389645549276138 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 8,9 D2: 8,9 I2: 2,3 E6: 2,4 G4: 2,7 A7: 2,3 C8: 2,9 C9: 3,9 E7: 4,7 E9: 7,9 H8: 2,4 H9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,C8: 2.. / A7 = 2 => 0 pairs (X) / C8 = 2 => 0 pairs (_) C8,H8: 2.. / C8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) E1,E6: 2.. / E1 = 2 => 0 pairs (X) / E6 = 2 => 16 pairs (_) G5,G6: 3.. / G5 = 3 => 15 pairs (_) / G6 = 3 => 14 pairs (_) A7,C9: 3.. / A7 = 3 => 0 pairs (*) / C9 = 3 => 0 pairs (X) D8,F8: 3.. / D8 = 3 => 14 pairs (_) / F8 = 3 => 13 pairs (_) B6,G6: 3.. / B6 = 3 => 15 pairs (_) / G6 = 3 => 14 pairs (_) C9,H9: 3.. / C9 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) E6,F6: 4.. / E6 = 4 => 0 pairs (X) / F6 = 4 => 16 pairs (_) H7,H8: 4.. / H7 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) E7,H7: 4.. / E7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) D1,D8: 4.. / D1 = 4 => 14 pairs (_) / D8 = 4 => 0 pairs (X) B2,C2: 7.. / B2 = 7 => 17 pairs (_) / C2 = 7 => 14 pairs (_) E7,E9: 7.. / E7 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) E9,H9: 7.. / E9 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) C2,C5: 7.. / C2 = 7 => 14 pairs (_) / C5 = 7 => 17 pairs (_) I3,I7: 7.. / I3 = 7 => 14 pairs (_) / I7 = 7 => 0 pairs (*) A2,A3: 8.. / A2 = 8 => 0 pairs (X) / A3 = 8 => 12 pairs (_) D4,F4: 8.. / D4 = 8 => 0 pairs (X) / F4 = 8 => 13 pairs (_) A2,D2: 8.. / A2 = 8 => 0 pairs (X) / D2 = 8 => 12 pairs (_) F3,F4: 8.. / F3 = 8 => 0 pairs (X) / F4 = 8 => 13 pairs (_) H1,H3: 9.. / H1 = 9 => 0 pairs (X) / H3 = 9 => 12 pairs (_) B4,B5: 9.. / B4 = 9 => 14 pairs (_) / B5 = 9 => 18 pairs (_) C8,C9: 9.. / C8 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) A2,D2: 9.. / A2 = 9 => 12 pairs (_) / D2 = 9 => 0 pairs (X) B5,F5: 9.. / B5 = 9 => 18 pairs (_) / F5 = 9 => 14 pairs (_) C9,E9: 9.. / C9 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) E1,E9: 9.. / E1 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) * DURATION: 0:00:48.871381 START: 18:11:07.526017 END: 18:11:56.397398 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C8,C9,D2,E6,E7,E9,G4,H8,H9,I2) * .51...8.6....6541..64.1.5..4.5.3..616..15..841.86...59.865.19..71..8.6.554.2.61.8 * PAIR A2: 8,9 BLK 1 A3: 8,9,2,3 # reduction candidate for 8,9 A3: 2,3 => CTR * 951...836837965412264.1.5974.5.3..616..15..841.86...59.86571943719.8.625543296178 A3: 8,9 # 14 pairs * PAIR D2: 8,9 BLK 2 D3: 8,9,3,7 # reduction candidate for 8,9 D3: 8,9 => CTR * .51.278.6.3..6541..64.1.5.74957382616..159.841.86...59286571943719.8.625543296178 D3: 3,7 # 13 pairs F3: 8,9,2,3,7 # reduction candidate for 8,9 F3: 8,9 => CTR * .51...8.6....6541..64.1.5.74.5.3..616..15..841.86...59286571943719.8.625543296178 F3: 2,3,7 # 13 pairs * PAIR D2: 8,9 COL D D4: 8,9,7 # reduction candidate for 8,9 D4: 7 # 16 pairs D4: 8,9 # 15 pairs * PAIR I2: 2,3 BLK 3 H1: 2,3,7,9 # reduction candidate for 2,3 H1: 2,3 # 16 pairs H3: 2,3,7,9 # reduction candidate for 2,3 H3: 2,3 => CTR * .51...896.37.65412.64.1.5374.5.3..616.215.3841786..259286571943719.8.625543296178 H3: 7,9 # 13 pairs I3: 2,3,7 # reduction candidate for 2,3 I3: 2,3 => SOLVED * 251493876937865412864712593425938761693157284178624359386541927712389645549276138 I3: 7 # 14 pairs * PAIR I2: 2,3 ROW 2 B2: 2,3,7 # reduction candidate for 2,3 B2: 2,3 # 14 pairs C2: 2,3,7 # reduction candidate for 2,3 C2: 2,3 # 17 pairs * PAIR I2: 2,3 COL I I7: 2,3,7 # reduction candidate for 2,3 I7: 7 => SOLVED * 251493876937865412864712593425938761693157284178624359386541927712389645549276138 I7: 2,3 # 14 pairs * PAIR E6: 2,4 BLK 5 F6: 2,4,7 # reduction candidate for 2,4 F6: 7 => CTR * .517248.6....6541..64.1.5.74.5.3..616..15..841.8647.59286571943719483625543296178 F6: 2,4 # 16 pairs * PAIR E6: 2,4 COL E E1: 2,4,9 # reduction candidate for 2,4 E1: 2,4 => CTR * .51...8.6.37.65412.64.1.5.74.5.3..616.215.3841786..259286571943719.8.625543296178 E1: 9 => SOLVED * 251493876937865412864712593425938761693157284178624359386541927712389645549276138 * PAIR G4: 2,7 BLK 6 G5: 2,7,3 # reduction candidate for 2,7 G5: 2,7 # 14 pairs G6: 2,7,3 # reduction candidate for 2,7 G6: 2,7 # 15 pairs * PAIR G4: 2,7 ROW 4 B4: 2,7,9 # reduction candidate for 2,7 B4: 2,7 # 18 pairs F4: 2,7,8,9 # reduction candidate for 2,7 F4: 2,7 => CTR * .51...8.68..96541..64.185.749583..616..159.841.86...59286571943719.8.625543296178 F4: 8,9 # 13 pairs * PAIR A7: 2,3 ROW 7 H7: 2,3,4,7 # reduction candidate for 2,3 H7: 2,3 => SOLVED * 251493876937865412864712593425938761693157284178624359386541927712389645549276138 H7: 4,7 # 14 pairs I7: 2,3,7 # reduction candidate for 2,3 I7: 2,3 # 14 pairs * PAIR A7: 2,3 COL A A1: 2,3,9 # reduction candidate for 2,3 A1: 2,3 # 14 pairs A3: 2,3,8,9 # reduction candidate for 2,3 A3: 2,3 => CTR * 951...836837965412264.1.5974.5.3..616..15..841.86...59.86571943719.8.625543296178 A3: 8,9 # 14 pairs * PAIR E7: 4,7 ROW 7 H7: 4,7,2,3 # reduction candidate for 4,7 H7: 2,3 => SOLVED * 251493876937865412864712593425938761693157284178624359386541927712389645549276138 H7: 4,7 # 14 pairs * PAIR H8: 2,4 BLK 9 H7: 2,4,3,7 # reduction candidate for 2,4 H7: 3,7 => CTR * .5149.8.69..86541.864.1.59.4.5.38.616..15..841.8624.59386541972712.8.645549276138 H7: 2,4 # 14 pairs * PAIR H9: 3,7 BLK 9 H7: 3,7,2,4 # reduction candidate for 3,7 H7: 3,7 => CTR * .5149.8.69..86541.864.1.59.4.5.38.616..15..841.8624.59386541972712.8.645549276138 H7: 2,4 # 14 pairs I7: 3,7,2 # reduction candidate for 3,7 I7: 3,7 # 14 pairs * PAIR H9: 3,7 COL H H1: 3,7,2,9 # reduction candidate for 3,7 H1: 3,7 # 15 pairs H3: 3,7,2,9 # reduction candidate for 3,7 H3: 3,7 => CTR * 351...896....65412264.1.5374.5.3..616..15..841.86...59.86571943719.8.625543296178 H3: 2,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-452-base-pr-000.dot * REASONING * DIS # A3: 2,3 => CTR => A3: 8,9 * DIS # D3: 8,9 => CTR => D3: 3,7 * DIS # F3: 8,9 => CTR => F3: 2,3,7 * DIS # H3: 2,3 => CTR => H3: 7,9 * PRF # I3: 2,3 => SOL * PRF # I7: 7 => SOL * DIS # F6: 7 => CTR => F6: 2,4 * DIS # E1: 2,4 => CTR => E1: 9 * PRF # E1: 9 => SOL * DIS # F4: 2,7 => CTR => F4: 8,9 * PRF # H7: 2,3 => SOL * DIS # A3: 2,3 => CTR => A3: 8,9 * PRF # H7: 2,3 => SOL * DIS # H7: 3,7 => CTR => H7: 2,4 * DIS # H7: 3,7 => CTR => H7: 2,4 * DIS # H3: 3,7 => CTR => H3: 2,9 * CNT 16 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C8,C9,D2,E6,E7,E9,G4,H8,H9,I2) * .51...8.6....6541..64.1.5..4.5.3..616..15..841.86...59.865.19..71..8.6.554.2.61.8 * PAIR A2: 8,9 BLK 1 A3: 8,9,2,3 # reduction candidate for 8,9 A3: 2,3 => CTR * 951...836837965412264.1.5974.5.3..616..15..841.86...59.86571943719.8.625543296178 * PAIR D2: 8,9 BLK 2 D3: 8,9,3,7 # reduction candidate for 8,9 D3: 8,9 => CTR * 351427896....65413.64.1.5..4.57382616..159.841.86...59.8657194.719.8.625543296178 F3: 8,9,2,3,7 # reduction candidate for 8,9 F3: 8,9 => CTR * 351...8.6....65413.6431.5..4.5.3..616..15..841.86...592865.193771..8.6.554.2.61.8 * PAIR I2: 2,3 BLK 3 H1: 2,3,7 # reduction candidate for 2,3 H1: 2,3 # 20 pairs I3: 2,3,7 # reduction candidate for 2,3 I3: 2,3 => SOLVED * 251493876937865412864712593425938761693157284178624359386541927712389645549276138 * DURATION: 0:00:07.788768 START: 18:12:37.806126 END: 18:12:45.594894 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-452-base-pr-001.dot * REASONING * DIS # A3: 2,3 => CTR => A3: 8,9 * DIS A3: 8,9 # D3: 8,9 => CTR => D3: 3,7 * DIS A3: 8,9 + D3: 3,7 # F3: 8,9 => CTR => F3: 2,3,7 * PRF A3: 8,9 + D3: 3,7 + F3: 2,3,7 # I3: 2,3 => SOL * STA A3: 8,9 + D3: 3,7 + F3: 2,3,7 + I3: 2,3 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 452 solution: 251493876937865412864712593425938761693157284178624359386541927712389645549276138 info: 95454 FNBHYK S8.f 20431 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 251493876937865412864712593425938761693157284178624359386541927712389645549276138 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 # A3: 8,9 => UNS * DIS # A3: 2,3 => CTR => A3: 8,9 * DIS # D3: 8,9 => CTR => D3: 3,7 * INC # D3: 3,7 => UNS * DIS # F3: 8,9 => CTR => F3: 2,3,7 * INC # F3: 2,3,7 => UNS * INC # D4: 8,9 => UNS * INC # D4: 7 => UNS * INC # H1: 2,3 => UNS * DIS # H3: 2,3 => CTR => H3: 7,9 * INC # H3: 7,9 => UNS * PRF # I3: 2,3 => SOL * INC # I3: 7 => UNS * INC # B2: 2,3 => UNS * INC # C2: 2,3 => UNS * INC # I7: 2,3 => UNS * PRF # I7: 7 => SOL * INC # F6: 2,4 => UNS * DIS # F6: 7 => CTR => F6: 2,4 * DIS # E1: 2,4 => CTR => E1: 9 * PRF # E1: 9 => SOL * INC # G5: 2,7 => UNS * INC # G6: 2,7 => UNS * INC # B4: 2,7 => UNS * DIS # F4: 2,7 => CTR => F4: 8,9 * INC # F4: 8,9 => UNS * PRF # H7: 2,3 => SOL * INC # H7: 4,7 => UNS * INC # I7: 2,3 => UNS * INC # A1: 2,3 => UNS * DIS # A3: 2,3 => CTR => A3: 8,9 * INC # A3: 8,9 => UNS * INC # H7: 4,7 => UNS * PRF # H7: 2,3 => SOL * INC # H7: 2,4 => UNS * DIS # H7: 3,7 => CTR => H7: 2,4 * DIS # H7: 3,7 => CTR => H7: 2,4 * INC # H7: 2,4 => UNS * INC # I7: 3,7 => UNS * INC # H1: 3,7 => UNS * DIS # H3: 3,7 => CTR => H3: 2,9 * INC # H3: 2,9 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 8,9 => UNS * DIS # A3: 2,3 => CTR => A3: 8,9 * DIS A3: 8,9 # D3: 8,9 => CTR => D3: 3,7 * DIS A3: 8,9 + D3: 3,7 # F3: 8,9 => CTR => F3: 2,3,7 * INC A3: 8,9 + D3: 3,7 + F3: 2,3,7 # H1: 2,3 => UNS * PRF A3: 8,9 + D3: 3,7 + F3: 2,3,7 # I3: 2,3 => SOL * STA A3: 8,9 + D3: 3,7 + F3: 2,3,7 + I3: 2,3 * CNT 6 HDP CHAINS / 6 HYP OPENED