Analysis of xx-top500-110-base.sdk
Contents
Original Sudoku
level: medium
position: 4...2............1.......6.....4.27..16......8..........76.3....5....4.....8..3.. initial
Autosolve
position: 46.7218......6...11......6....146278.16......8.4...61..476.318.3582174966.18.43.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * DIS # C2: 5,9 => CTR => C2: 2,3 * DIS # C3: 5,9 => CTR => C3: 2,3 * DIS # I1: 3 => CTR => I1: 5,9 * DIS # C4: 3 => CTR => C4: 5,9 * DIS # H5: 3,5 => CTR => H5: 4 * PRF # H5: 4 => SOL * DIS # C4: 3 => CTR => C4: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * DIS # C4: 5 => CTR => C4: 3,9 * DIS # B2: 3,9 => CTR => B2: 7,8 * PRF # B3: 3,9 => SOL * DIS # I5: 5,9 => CTR => I5: 3,4 * DIS # D5: 3 => CTR => D5: 5,9 * DIS # G3: 5,9 => CTR => G3: 7 * CNT 17 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 5,9 => CTR => A2: 7 * PRF A2: 7 => SOL * STA A2: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4...2............1.......6.....4.27..16......8..........76.3....5....4.....8..3.. | initial |
| 46.7218......6...11......6....146278.16......8.4...61..476.318.3582174966.18.43.7 | autosolve |
| 465721839783469521192385764539146278216578943874932615947653182358217496621894357 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C1: 5,9 E3: 3,8 H1: 3,5 H2: 2,4 I3: 2,4 A4: 5,9 B4: 3,9 A5: 2,7 B6: 2,7 E5: 7,8 F5: 2,8 E6: 3,7 G5: 5,9 A7: 2,9 B9: 2,9 E7: 5,9 E9: 5,9 I7: 2,5 H9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 2.. / C2 = 2 => 0 pairs (X) / C3 = 2 => 0 pairs (_) H2,I3: 2.. / H2 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) A5,B6: 2.. / A5 = 2 => 0 pairs (*) / B6 = 2 => 0 pairs (X) F5,F6: 2.. / F5 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) A7,B9: 2.. / A7 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) I7,H9: 2.. / I7 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) C2,H2: 2.. / C2 = 2 => 0 pairs (X) / H2 = 2 => 0 pairs (_) C3,I3: 2.. / C3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) A5,F5: 2.. / A5 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) B6,F6: 2.. / B6 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) A7,I7: 2.. / A7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) B9,H9: 2.. / B9 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) A5,A7: 2.. / A5 = 2 => 0 pairs (*) / A7 = 2 => 0 pairs (X) B6,B9: 2.. / B6 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) H2,H9: 2.. / H2 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) I3,I7: 2.. / I3 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) H1,I1: 3.. / H1 = 3 => 20 pairs (_) / I1 = 3 => 0 pairs (X) B4,C4: 3.. / B4 = 3 => 22 pairs (_) / C4 = 3 => 0 pairs (X) E3,E6: 3.. / E3 = 3 => 0 pairs (X) / E6 = 3 => 0 pairs (_) H1,H5: 3.. / H1 = 3 => 20 pairs (_) / H5 = 3 => 0 pairs (X) D2,D3: 4.. / D2 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) H2,I3: 4.. / H2 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) H5,I5: 4.. / H5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) D2,H2: 4.. / D2 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) D3,I3: 4.. / D3 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) H2,H5: 4.. / H2 = 4 => 0 pairs (X) / H5 = 4 => 0 pairs (_) I3,I5: 4.. / I3 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) A4,C4: 5.. / A4 = 5 => 20 pairs (_) / C4 = 5 => 0 pairs (X) E7,E9: 5.. / E7 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) I7,H9: 5.. / I7 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) E7,I7: 5.. / E7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) E9,H9: 5.. / E9 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) A2,A4: 5.. / A2 = 5 => 0 pairs (X) / A4 = 5 => 20 pairs (_) G2,G3: 7.. / G2 = 7 => 0 pairs (X) / G3 = 7 => 20 pairs (_) A5,B6: 7.. / A5 = 7 => 0 pairs (X) / B6 = 7 => 0 pairs (_) E5,E6: 7.. / E5 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) B3,G3: 7.. / B3 = 7 => 0 pairs (X) / G3 = 7 => 20 pairs (_) A5,E5: 7.. / A5 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) B6,E6: 7.. / B6 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) A2,A5: 7.. / A2 = 7 => 0 pairs (*) / A5 = 7 => 0 pairs (X) B2,B3: 8.. / B2 = 8 => 22 pairs (_) / B3 = 8 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) B2,F2: 8.. / B2 = 8 => 22 pairs (_) / F2 = 8 => 0 pairs (X) E3,E5: 8.. / E3 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) A7,B9: 9.. / A7 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) E7,E9: 9.. / E7 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) C1,I1: 9.. / C1 = 9 => 25 pairs (_) / I1 = 9 => 22 pairs (_) A7,E7: 9.. / A7 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) B9,E9: 9.. / B9 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) * DURATION: 0:01:34.877266 START: 06:31:14.777106 END: 06:32:49.654372 2017-05-04 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A7,B4,B6,B9,C1,E3,E5,E6,E7,E9,F5,G5,H1,H2,H9,I3,I7) * 46.7218......6...11......6....146278.16......8.4...61..476.318.3582174966.18.43.7 * PAIR C1: 5,9 BLK 1 A2: 5,9,7 # reduction candidate for 5,9 A2: 5,9 => CTR * 46.7218....2.6..411..43..62.3.146278716.82..4824.7.61.247693185358217496691854327 A2: 7 => SOLVED * 465721839783469521192385764539146278216578943874932615947653182358217496621894357 C2: 5,9,2,3 # reduction candidate for 5,9 C2: 5,9 => CTR * 46.72183....46..211.2....64593146278216.78.4.874...61..476.3182358217496621894357 C2: 2,3 # 20 pairs C3: 5,9,2,3 # reduction candidate for 5,9 C3: 5,9 => CTR * 46.7218....2.6..411..4...62..3146278.16.....48.4...61.2476931853582174966918.43.7 C3: 2,3 # 20 pairs * PAIR C1: 5,9 ROW 1 I1: 5,9,3 # reduction candidate for 5,9 I1: 3 => CTR * 469721853..256..411.543..62...146278.169..534824.75619247693185358217496691854327 I1: 5,9 # 20 pairs * PAIR C1: 5,9 COL C C4: 5,9,3 # reduction candidate for 5,9 C4: 3 => CTR * 46.72183.78..6..211.2...764593146278216.78.4.874.3261.947653182358217496621894357 C4: 5,9 # 22 pairs * PAIR E3: 3,8 ROW 3 B3: 3,8,7,9 # reduction candidate for 3,8 B3: 7,9 # 24 pairs B3: 3,8 # 22 pairs * PAIR H1: 3,5 BLK 3 I1: 3,5,9 # reduction candidate for 3,5 I1: 3,5 # 25 pairs I1: 9 # 22 pairs * PAIR H1: 3,5 COL H H5: 3,5,4 # reduction candidate for 3,5 H5: 3,5 => CTR * 46.7218....236..411..4...62.3.146278716.82..4824.7.61.247693185358217496691854327 H5: 4 => SOLVED * 465721839783469521192385764539146278216578943874932615947653182358217496621894357 * PAIR A4: 5,9 BLK 4 C4: 5,9,3 # reduction candidate for 5,9 C4: 3 => CTR * 46.72183.78..6..211.2...764593146278216.78.4.874.3261.947653182358217496621894357 C4: 5,9 # 22 pairs * PAIR A4: 5,9 COL A A2: 5,9,7 # reduction candidate for 5,9 A2: 5,9 => CTR * 46.7218....2.6..411..43..62.3.146278716.82..4824.7.61.247693185358217496691854327 A2: 7 => SOLVED * 465721839783469521192385764539146278216578943874932615947653182358217496621894357 * PAIR B4: 3,9 BLK 4 C4: 3,9,5 # reduction candidate for 3,9 C4: 5 => CTR * 4697218535.236...11......6.935146278716.82...824.7.61.247693185358217496691854327 C4: 3,9 # 20 pairs * PAIR B4: 3,9 COL B B2: 3,9,7,8 # reduction candidate for 3,9 B2: 3,9 => CTR * 46.7218......68..118..3.76....146278.16.82...8.4...61..476.318.3582174966.18.43.7 B2: 7,8 # 22 pairs B3: 3,9,7,8 # reduction candidate for 3,9 B3: 3,9 => SOLVED * 465721839783469521192385764539146278216578943874932615947653182358217496621894357 B3: 7,8 # 20 pairs * PAIR G5: 5,9 BLK 6 I5: 5,9,3,4 # reduction candidate for 5,9 I5: 5,9 => CTR * 46.7218......6...11......64...146278.16....4.8.4...613.476.3182358217496621894357 I5: 3,4 # 20 pairs I6: 5,9,3 # reduction candidate for 5,9 I6: 5,9 # 23 pairs * PAIR G5: 5,9 ROW 5 D5: 5,9,3 # reduction candidate for 5,9 D5: 3 => CTR * 4657218399.2.6...11...3..6....146278716382...824.7.613247693185358217496691854327 D5: 5,9 # 23 pairs * PAIR G5: 5,9 COL G G2: 5,9,7 # reduction candidate for 5,9 G2: 5,9 # 20 pairs G3: 5,9,7 # reduction candidate for 5,9 G3: 5,9 => CTR * 46.7218...8236.7.117.....6....146278716.82...824.7.61.247693185358217496691854327 G3: 7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-110-base-pr-000.dot * REASONING * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * DIS # C2: 5,9 => CTR => C2: 2,3 * DIS # C3: 5,9 => CTR => C3: 2,3 * DIS # I1: 3 => CTR => I1: 5,9 * DIS # C4: 3 => CTR => C4: 5,9 * DIS # H5: 3,5 => CTR => H5: 4 * PRF # H5: 4 => SOL * DIS # C4: 3 => CTR => C4: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * DIS # C4: 5 => CTR => C4: 3,9 * DIS # B2: 3,9 => CTR => B2: 7,8 * PRF # B3: 3,9 => SOL * DIS # I5: 5,9 => CTR => I5: 3,4 * DIS # D5: 3 => CTR => D5: 5,9 * DIS # G3: 5,9 => CTR => G3: 7 * CNT 17 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A7,B4,B6,B9,C1,E3,E5,E6,E7,E9,F5,G5,H1,H2,H9,I3,I7) * 46.7218......6...11......6....146278.16......8.4...61..476.318.3582174966.18.43.7 * PAIR C1: 5,9 BLK 1 A2: 5,9,7 # reduction candidate for 5,9 A2: 5,9 => CTR * 46.7218....2.6..411..43..62.3.146278716.82..4824.7.61.247693185358217496691854327 A2: 7 => SOLVED * 465721839783469521192385764539146278216578943874932615947653182358217496621894357 * DURATION: 0:00:01.943864 START: 06:33:26.059203 END: 06:33:28.003067 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-110-base-pr-001.dot * REASONING * DIS # A2: 5,9 => CTR => A2: 7 * PRF A2: 7 => SOL * STA A2: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 110 solution: 465721839783469521192385764539146278216578943874932615947653182358217496621894357 info: 1630 FNBTHY S8.f 30636 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 465721839783469521192385764539146278216578943874932615947653182358217496621894357 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 # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * DIS # C2: 5,9 => CTR => C2: 2,3 * INC # C2: 2,3 => UNS * DIS # C3: 5,9 => CTR => C3: 2,3 * INC # C3: 2,3 => UNS * INC # I1: 5,9 => UNS * DIS # I1: 3 => CTR => I1: 5,9 * INC # C4: 5,9 => UNS * DIS # C4: 3 => CTR => C4: 5,9 * INC # B3: 3,8 => UNS * INC # B3: 7,9 => UNS * INC # I1: 3,5 => UNS * INC # I1: 9 => UNS * DIS # H5: 3,5 => CTR => H5: 4 * PRF # H5: 4 => SOL * INC # C4: 5,9 => UNS * DIS # C4: 3 => CTR => C4: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * INC # C4: 3,9 => UNS * DIS # C4: 5 => CTR => C4: 3,9 * DIS # B2: 3,9 => CTR => B2: 7,8 * INC # B2: 7,8 => UNS * PRF # B3: 3,9 => SOL * INC # B3: 7,8 => UNS * DIS # I5: 5,9 => CTR => I5: 3,4 * INC # I5: 3,4 => UNS * INC # I6: 5,9 => UNS * INC # D5: 5,9 => UNS * DIS # D5: 3 => CTR => D5: 5,9 * INC # G2: 5,9 => UNS * DIS # G3: 5,9 => CTR => G3: 7 * INC # G3: 7 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 5,9 => CTR => A2: 7 * PRF A2: 7 => SOL * STA A2: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED