Analysis of xx-top500-424-base.sdk
Contents
Original Sudoku
level: medium
position: .6....3....89.................56..7.12.......3...7..........6.3..94..........12.. initial
Autosolve
position: .6....3....89................45631721278..536356172.........6.3..94..........12.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E9: 3,5 => CTR => E9: 8,9 * DIS # C3: 1,2 => CTR => C3: 3,5 * DIS # B8: 7,8 => CTR => B8: 1,3 * DIS # F8: 7,8 => CTR => F8: 5,6 * CNT 4 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E9: 3,5 => CTR => E9: 8,9 * DIS E9: 8,9 # C3: 1,2 => CTR => C3: 3,5 * DIS E9: 8,9 + C3: 3,5 # A7: 2,7 => CTR => A7: 4,5,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 # B8: 7,8 => CTR => B8: 1,3 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 # F8: 7,8 => CTR => F8: 5,6 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # E1: 1,2 => CTR => E1: 4,5,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 # H1: 1,2 => CTR => H1: 4,5,8,9 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 # E3: 3,5 => CTR => E3: 1,2,4,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 # A1: 2,7 => CTR => A1: 4,5,9 * PRF E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 + A1: 4,5,9 # I1: 4,7 => SOL * STA E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 + A1: 4,5,9 + I1: 4,7 * CNT 10 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6....3....89.................56..7.12.......3...7..........6.3..94..........12.. | initial |
| .6....3....89................45631721278..536356172.........6.3..94..........12.. | autosolve |
| 961287354248935761573614928894563172127849536356172489412758693739426815685391247 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D1: 2,7 D3: 3,6 G2: 4,7 A4: 8,9 B4: 8,9 E5: 4,9 F5: 4,9 C9: 3,5 D7: 2,7 D9: 3,6 G8: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,E8: 2.. / A8 = 2 => 0 pairs (X) / E8 = 2 => 12 pairs (_) D1,D7: 2.. / D1 = 2 => 12 pairs (_) / D7 = 2 => 0 pairs (X) B2,E2: 3.. / B2 = 3 => 0 pairs (X) / E2 = 3 => 12 pairs (_) B8,E8: 3.. / B8 = 3 => 12 pairs (_) / E8 = 3 => 0 pairs (X) C3,C9: 3.. / C3 = 3 => 12 pairs (_) / C9 = 3 => 0 pairs (X) D3,D9: 3.. / D3 = 3 => 0 pairs (X) / D9 = 3 => 12 pairs (_) E5,F5: 4.. / E5 = 4 => 9 pairs (_) / F5 = 4 => 9 pairs (_) H2,H3: 6.. / H2 = 6 => 11 pairs (_) / H3 = 6 => 0 pairs (X) A8,A9: 6.. / A8 = 6 => 0 pairs (X) / A9 = 6 => 12 pairs (_) F8,D9: 6.. / F8 = 6 => 12 pairs (_) / D9 = 6 => 0 pairs (X) F2,H2: 6.. / F2 = 6 => 0 pairs (X) / H2 = 6 => 11 pairs (_) A8,F8: 6.. / A8 = 6 => 0 pairs (X) / F8 = 6 => 12 pairs (_) A9,D9: 6.. / A9 = 6 => 12 pairs (_) / D9 = 6 => 0 pairs (X) D3,D9: 6.. / D3 = 6 => 12 pairs (_) / D9 = 6 => 0 pairs (X) D1,D7: 7.. / D1 = 7 => 0 pairs (X) / D7 = 7 => 12 pairs (_) A4,B4: 8.. / A4 = 8 => 9 pairs (_) / B4 = 8 => 11 pairs (_) A4,B4: 9.. / A4 = 9 => 11 pairs (_) / B4 = 9 => 9 pairs (_) E5,F5: 9.. / E5 = 9 => 9 pairs (_) / F5 = 9 => 9 pairs (_) B3,B4: 9.. / B3 = 9 => 11 pairs (_) / B4 = 9 => 9 pairs (_) F5,F7: 9.. / F5 = 9 => 9 pairs (_) / F7 = 9 => 9 pairs (_) G3,G6: 9.. / G3 = 9 => 10 pairs (_) / G6 = 9 => 13 pairs (_) * DURATION: 0:00:27.201566 START: 17:17:33.564090 END: 17:18:00.765656 2017-05-04 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B4,C9,D1,D3,D7,D9,E5,F5,G2,G8) * .6....3....89................45631721278..536356172.........6.3..94..........12.. * PAIR D1: 2,7 ROW 1 A1: 2,7,4,5,9 # reduction candidate for 2,7 A1: 2,7 # 17 pairs A1: 4,5,9 # 11 pairs * PAIR G2: 4,7 BLK 3 I1: 4,7,1,5,8,9 # reduction candidate for 4,7 I1: 4,7 # 14 pairs I2: 4,7,1,5 # reduction candidate for 4,7 I2: 4,7 # 16 pairs G3: 4,7,8,9 # reduction candidate for 4,7 G3: 4,7 # 15 pairs I3: 4,7,1,5,8,9 # reduction candidate for 4,7 I3: 4,7 # 14 pairs * PAIR G2: 4,7 ROW 2 A2: 4,7,2,5 # reduction candidate for 4,7 A2: 4,7 # 15 pairs B2: 4,7,1,3 # reduction candidate for 4,7 B2: 4,7 # 12 pairs F2: 4,7,5,6 # reduction candidate for 4,7 F2: 4,7 # 15 pairs * PAIR C9: 3,5 ROW 9 E9: 3,5,8,9 # reduction candidate for 3,5 E9: 3,5 => CTR * .6....3....89........3.......45631721278..536356172.........6.36.942......36512.. E9: 8,9 # 12 pairs * PAIR C9: 3,5 COL C C3: 3,5,1,2 # reduction candidate for 3,5 C3: 1,2 => CTR * .6....3....89........3.......45631721278..536356172.........6.36.94.......36.12.. C3: 3,5 # 14 pairs * PAIR D7: 2,7 ROW 7 A7: 2,7,4,5,8 # reduction candidate for 2,7 A7: 2,7 # 13 pairs A7: 4,5,8 # 11 pairs * PAIR G8: 7,8 BLK 9 I8: 7,8,1,5 # reduction candidate for 7,8 I8: 7,8 # 15 pairs I9: 7,8,4,5,9 # reduction candidate for 7,8 I9: 7,8 # 18 pairs * PAIR G8: 7,8 ROW 8 A8: 7,8,2,5,6 # reduction candidate for 7,8 A8: 7,8 # 12 pairs B8: 7,8,1,3 # reduction candidate for 7,8 B8: 7,8 => CTR * .6....3....89................45631721278..536356172.........6.3..943.......6.12.. B8: 1,3 # 12 pairs F8: 7,8,5,6 # reduction candidate for 7,8 F8: 7,8 => CTR * .6.2..3...389........3.......45631721278..536356172......7..6.36.94287....56312.. F8: 5,6 # 12 pairs * PAIR G8: 7,8 COL G G3: 7,8,4,9 # reduction candidate for 7,8 G3: 7,8 # 13 pairs G3: 4,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-424-base-pr-000.dot * REASONING * DIS # E9: 3,5 => CTR => E9: 8,9 * DIS # C3: 1,2 => CTR => C3: 3,5 * DIS # B8: 7,8 => CTR => B8: 1,3 * DIS # F8: 7,8 => CTR => F8: 5,6 * CNT 4 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B4,C9,D1,D3,D7,D9,E5,F5,G2,G8) * .6....3....89................45631721278..536356172.........6.3..94..........12.. * PAIR D1: 2,7 ROW 1 A1: 2,7,4,5,9 # reduction candidate for 2,7 A1: 2,7 # 17 pairs A1: 4,5,9 # 11 pairs * PAIR G2: 4,7 BLK 3 I1: 4,7,1,5,8,9 # reduction candidate for 4,7 I1: 4,7 # 14 pairs I2: 4,7,1,5 # reduction candidate for 4,7 I2: 4,7 # 16 pairs G3: 4,7,8,9 # reduction candidate for 4,7 G3: 4,7 # 15 pairs I3: 4,7,1,5,8,9 # reduction candidate for 4,7 I3: 4,7 # 14 pairs * PAIR G2: 4,7 ROW 2 A2: 4,7,2,5 # reduction candidate for 4,7 A2: 4,7 # 15 pairs B2: 4,7,1,3 # reduction candidate for 4,7 B2: 4,7 # 12 pairs F2: 4,7,5,6 # reduction candidate for 4,7 F2: 4,7 # 15 pairs * PAIR C9: 3,5 ROW 9 E9: 3,5,8,9 # reduction candidate for 3,5 E9: 3,5 => CTR * .6....3....89........3.......45631721278..536356172.........6.36.942......36512.. * PAIR C9: 3,5 COL C C3: 3,5,1,2 # reduction candidate for 3,5 C3: 1,2 => CTR * .6....3....89........3.......45631721278..536356172.........6.36.94.......36.12.. * PAIR RESTART * PAIR D7: 2,7 ROW 7 A7: 2,7,4,5,8 # reduction candidate for 2,7 A7: 2,7 => CTR * .627..3....89................45631721278..536356172...7.12..6.32.94..........12.. * PAIR RESTART * PAIR G8: 7,8 BLK 9 I8: 7,8,1,5 # reduction candidate for 7,8 I8: 7,8 # 19 pairs I9: 7,8,4,5,9 # reduction candidate for 7,8 I9: 7,8 # 23 pairs * PAIR G8: 7,8 ROW 8 A8: 7,8,2,5,6 # reduction candidate for 7,8 A8: 7,8 # 12 pairs B8: 7,8,1,3 # reduction candidate for 7,8 B8: 7,8 => CTR * .6....3....89................45631721278..536356172.........6.3..943.......6.12.. F8: 7,8,5,6 # reduction candidate for 7,8 F8: 7,8 => CTR * .6....3....89................45631721278..536356172.........6.36.942.........12.. * RESTART * PAIR G8: 7,8 ROW 8 A8: 7,8,2,5,6 # reduction candidate for 7,8 A8: 2,5,6 # 17 pairs A8: 7,8 # 12 pairs * PAIR G8: 7,8 COL G G3: 7,8,4,9 # reduction candidate for 7,8 G3: 7,8 # 19 pairs G3: 4,9 # 18 pairs * PAIR RESTART * PAIR G8: 7,8 BLK 9 I8: 7,8,1,5 # reduction candidate for 7,8 I8: 7,8 # 19 pairs I9: 7,8,4,5,9 # reduction candidate for 7,8 I9: 7,8 # 17 pairs * PAIR G8: 7,8 ROW 8 A8: 7,8,2,5,6 # reduction candidate for 7,8 A8: 2,5,6 # 17 pairs A8: 7,8 # 12 pairs * PAIR G8: 7,8 COL G G3: 7,8,4,9 # reduction candidate for 7,8 G3: 7,8 # 19 pairs G3: 4,9 # 18 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,B4,B8,C1,C3,C7,C9,D1,D3,D7,D9,E5,E9,F5,F8,G2,G8) * .6....3....89................45631721278..536356172.........6.3..94..........12.. * PAIR C1: 1,2 ROW 1 E1: 1,2,4,5,8 # reduction candidate for 1,2 E1: 1,2 => CTR * .6271.3....89...6...36.......45631721278..536356172......2.76.32.94.6...67.3.12.. H1: 1,2,4,5,8,9 # reduction candidate for 1,2 H1: 1,2 => CTR * .627..31...89...6...36.......45631721278..536356172......2.76.32.94.6...67.3.12.. * RESTART * PAIR RESTART * PAIR C3: 3,5 ROW 3 E3: 3,5,1,2,4,8 # reduction candidate for 3,5 E3: 3,5 => CTR * .6.2..3...3891......5.3......45631721278..536356172.....27..6.3.1942......36.12.. * PAIR RESTART * PAIR D1: 2,7 ROW 1 A1: 2,7,4,5,9 # reduction candidate for 2,7 A1: 2,7 => CTR * 7612..3..248935761593617428..45631721278..5363561729....27..6.3.39426.1.6753.12.. * PAIR RESTART * PAIR G2: 4,7 BLK 3 I1: 4,7,1,5,8,9 # reduction candidate for 4,7 I1: 4,7 => SOLVED * 961287354248935761573614928894563172127849536356172489412758693739426815685391247 * DURATION: 0:00:31.969409 START: 17:18:17.177439 END: 17:18:49.146848 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-424-base-pr-001.dot * REASONING * DIS # E9: 3,5 => CTR => E9: 8,9 * DIS E9: 8,9 # C3: 1,2 => CTR => C3: 3,5 * DIS E9: 8,9 + C3: 3,5 # A7: 2,7 => CTR => A7: 4,5,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 # B8: 7,8 => CTR => B8: 1,3 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 # F8: 7,8 => CTR => F8: 5,6 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # E1: 1,2 => CTR => E1: 4,5,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 # H1: 1,2 => CTR => H1: 4,5,8,9 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 # E3: 3,5 => CTR => E3: 1,2,4,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 # A1: 2,7 => CTR => A1: 4,5,9 * PRF E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 + A1: 4,5,9 # I1: 4,7 => SOL * STA E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 + A1: 4,5,9 + I1: 4,7 * CNT 10 HDP CHAINS / 33 HYP OPENED
Header Info
Top 500 Minimum 17 424 solution: 961287354248935761573614928894563172127849536356172489412758693739426815685391247 info: 95139 FNBTHWXYK S8.f 41317 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 961287354248935761573614928894563172127849536356172489412758693739426815685391247 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 # A1: 2,7 => UNS * INC # A1: 4,5,9 => UNS * INC # I1: 4,7 => UNS * INC # I2: 4,7 => UNS * INC # G3: 4,7 => UNS * INC # I3: 4,7 => UNS * INC # A2: 4,7 => UNS * INC # B2: 4,7 => UNS * INC # F2: 4,7 => UNS * DIS # E9: 3,5 => CTR => E9: 8,9 * INC # E9: 8,9 => UNS * INC # C3: 3,5 => UNS * DIS # C3: 1,2 => CTR => C3: 3,5 * INC # A7: 2,7 => UNS * INC # A7: 4,5,8 => UNS * INC # I8: 7,8 => UNS * INC # I9: 7,8 => UNS * INC # A8: 7,8 => UNS * DIS # B8: 7,8 => CTR => B8: 1,3 * INC # B8: 1,3 => UNS * DIS # F8: 7,8 => CTR => F8: 5,6 * INC # F8: 5,6 => UNS * INC # G3: 7,8 => UNS * INC # G3: 4,9 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,7 => UNS * INC # A1: 4,5,9 => UNS * INC # I1: 4,7 => UNS * INC # I2: 4,7 => UNS * INC # G3: 4,7 => UNS * INC # I3: 4,7 => UNS * INC # A2: 4,7 => UNS * INC # B2: 4,7 => UNS * INC # F2: 4,7 => UNS * DIS # E9: 3,5 => CTR => E9: 8,9 * INC E9: 8,9 # C3: 3,5 => UNS * DIS E9: 8,9 # C3: 1,2 => CTR => C3: 3,5 * DIS E9: 8,9 + C3: 3,5 # A7: 2,7 => CTR => A7: 4,5,8 * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 # I8: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 # I9: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 # A8: 7,8 => UNS * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 # B8: 7,8 => CTR => B8: 1,3 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 # F8: 7,8 => CTR => F8: 5,6 * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # A8: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # A8: 2,5,6 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # G3: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # G3: 4,9 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # I8: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # I9: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # A8: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # A8: 2,5,6 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # G3: 7,8 => UNS * INC E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # G3: 4,9 => UNS * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 # E1: 1,2 => CTR => E1: 4,5,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 # H1: 1,2 => CTR => H1: 4,5,8,9 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 # E3: 3,5 => CTR => E3: 1,2,4,8 * DIS E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 # A1: 2,7 => CTR => A1: 4,5,9 * PRF E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 + A1: 4,5,9 # I1: 4,7 => SOL * STA E9: 8,9 + C3: 3,5 + A7: 4,5,8 + B8: 1,3 + F8: 5,6 + E1: 4,5,8 + H1: 4,5,8,9 + E3: 1,2,4,8 + A1: 4,5,9 + I1: 4,7 * CNT 33 HDP CHAINS / 33 HYP OPENED