Analysis of xx-top500-459-base.sdk
Contents
Original Sudoku
level: medium
position: .7....81..4.5.9............6.1.........3..4..2........5......6.....1...2...48.... initial
Autosolve
position: .7....81.1485.9....2.....4.6.1......8.73..4..2.4......589...164463915782712486... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I1: 5,6 => CTR => I1: 3,9 * DIS # I1: 5,6 => CTR => I1: 3,9 * DIS # E1: 2,6 => CTR => E1: 3,4 * PRF # D6: 1,8 => SOL * DIS # D6: 6,7 => CTR => D6: 1,8 * DIS # F6: 1,8 => CTR => F6: 7 * PRF # F6: 7 => SOL * DIS # E5: 5,9 => CTR => E5: 2,6 * PRF # I5: 5,9 => SOL * DIS # F7: 2,7 => CTR => F7: 3 * PRF # D4: 2,7 => SOL * DIS # D4: 8 => CTR => D4: 2,7 * DIS # F7: 7 => CTR => F7: 2,3 * DIS # E1: 2,3 => CTR => E1: 4,6 * CNT 14 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I1: 5,6 => CTR => I1: 3,9 * PRF I1: 3,9 # D6: 1,8 => SOL * STA I1: 3,9 + D6: 1,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7....81..4.5.9............6.1.........3..4..2........5......6.....1...2...48.... | initial |
| .7....81.1485.9....2.....4.6.1......8.73..4..2.4......589...164463915782712486... | autosolve |
| 375642819148579236926138547651294378897361425234857691589723164463915782712486953 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 3,9 C1: 5,6 A3: 3,9 C3: 5,6 D1: 2,6 D3: 1,8 F3: 1,8 B5: 5,9 F5: 1,2 D7: 2,7 E7: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 10 pairs (_) / F3 = 1 => 0 pairs (X) I5,I6: 1.. / I5 = 1 => 0 pairs (X) / I6 = 1 => 0 pairs (_) F5,I5: 1.. / F5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D3,D6: 1.. / D3 = 1 => 10 pairs (_) / D6 = 1 => 0 pairs (X) G2,H2: 2.. / G2 = 2 => 12 pairs (_) / H2 = 2 => 19 pairs (_) G2,G4: 2.. / G2 = 2 => 12 pairs (_) / G4 = 2 => 19 pairs (_) A1,A3: 3.. / A1 = 3 => 12 pairs (_) / A3 = 3 => 10 pairs (_) B4,B6: 3.. / B4 = 3 => 12 pairs (_) / B6 = 3 => 12 pairs (_) E7,F7: 3.. / E7 = 3 => 0 pairs (X) / F7 = 3 => 11 pairs (_) F1,F7: 3.. / F1 = 3 => 0 pairs (X) / F7 = 3 => 11 pairs (_) E1,F1: 4.. / E1 = 4 => 12 pairs (_) / F1 = 4 => 0 pairs (X) E4,F4: 4.. / E4 = 4 => 0 pairs (X) / F4 = 4 => 12 pairs (_) E1,E4: 4.. / E1 = 4 => 12 pairs (_) / E4 = 4 => 0 pairs (X) F1,F4: 4.. / F1 = 4 => 0 pairs (X) / F4 = 4 => 12 pairs (_) C1,C3: 5.. / C1 = 5 => 10 pairs (_) / C3 = 5 => 0 pairs (X) C1,I1: 5.. / C1 = 5 => 10 pairs (_) / I1 = 5 => 0 pairs (X) C1,C3: 6.. / C1 = 6 => 0 pairs (X) / C3 = 6 => 10 pairs (_) E5,I5: 6.. / E5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) D1,D6: 6.. / D1 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) E2,E3: 7.. / E2 = 7 => 16 pairs (_) / E3 = 7 => 12 pairs (_) D7,F7: 7.. / D7 = 7 => 12 pairs (_) / F7 = 7 => 0 pairs (X) E3,I3: 7.. / E3 = 7 => 12 pairs (_) / I3 = 7 => 16 pairs (_) D3,F3: 8.. / D3 = 8 => 0 pairs (X) / F3 = 8 => 10 pairs (_) I4,I6: 8.. / I4 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) A1,A3: 9.. / A1 = 9 => 10 pairs (_) / A3 = 9 => 12 pairs (_) A1,I1: 9.. / A1 = 9 => 10 pairs (_) / I1 = 9 => 12 pairs (_) * DURATION: 0:00:38.319084 START: 18:25:48.837237 END: 18:26:27.156321 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,C1,C3,D1,D3,D7,E7,F3,F5) * .7....81.1485.9....2.....4.6.1......8.73..4..2.4......589...164463915782712486... * PAIR A1: 3,9 ROW 1 I1: 3,9,5,6 # reduction candidate for 3,9 I1: 5,6 => CTR * 9762..8151485.9...3251.8.4.6.18.....8.73.14.62.46.7..15897..164463915782712486... I1: 3,9 # 13 pairs * PAIR C1: 5,6 ROW 1 I1: 5,6,3,9 # reduction candidate for 5,6 I1: 5,6 => CTR * 9762..8151485.9...3251.8.4.6.18.....8.73.14.62.46.7..15897..164463915782712486... I1: 3,9 # 13 pairs * PAIR A3: 3,9 ROW 3 G3: 3,9,5,6 # reduction candidate for 3,9 G3: 3,9 # 14 pairs I3: 3,9,5,6,7 # reduction candidate for 3,9 I3: 3,9 # 15 pairs * PAIR C3: 5,6 ROW 3 G3: 5,6,3,9 # reduction candidate for 5,6 G3: 5,6 # 14 pairs I3: 5,6,3,7,9 # reduction candidate for 5,6 I3: 5,6 # 15 pairs * PAIR D1: 2,6 BLK 2 E1: 2,6,3,4 # reduction candidate for 2,6 E1: 2,6 => CTR * .7.26481.1485.9....26....4.6.184....8.73..4.62.46.....589723164463915782712486... E1: 3,4 # 12 pairs * PAIR D3: 1,8 COL D D6: 1,8,6,7 # reduction candidate for 1,8 D6: 1,8 => SOLVED * 375642819148579236926138547651294378897361425234857691589723164463915782712486953 D6: 6,7 => CTR * .7.6..81.1485.9..6.261.8.4.6.18.....8.73624.12.47.16.8589237164463915782712486... * PAIR F3: 1,8 COL F F6: 1,8,7 # reduction candidate for 1,8 F6: 1,8 => CTR * .7.62481.1485.9....26....4.6.1.47...8.73624.12.4......589...164463915782712486... F6: 7 => SOLVED * 375642819148579236926138547651294378897361425234857691589723164463915782712486953 * PAIR B5: 5,9 BLK 4 B4: 5,9,3 # reduction candidate for 5,9 B4: 5,9 # 12 pairs B6: 5,9,3 # reduction candidate for 5,9 B6: 5,9 # 12 pairs * PAIR B5: 5,9 ROW 5 E5: 5,9,2,6 # reduction candidate for 5,9 E5: 5,9 => CTR * .7....81.1485.9....2.1.8.4.6.1.....88.73.14262.4867..15897..164463915782712486... E5: 2,6 # 15 pairs H5: 5,9,2 # reduction candidate for 5,9 H5: 5,9 # 18 pairs I5: 5,9,1,6 # reduction candidate for 5,9 I5: 5,9 => SOLVED * 375642819148579236926138547651294378897361425234857691589723164463915782712486953 I5: 1,6 # 12 pairs * PAIR D7: 2,7 BLK 8 F7: 2,7,3 # reduction candidate for 2,7 F7: 2,7 => CTR * 97.24381.1485.9...32.1.8.4.6.18.4...8.73.14.62.46.....589732164463915782712486... F7: 3 # 11 pairs * PAIR D7: 2,7 COL D D4: 2,7,8 # reduction candidate for 2,7 D4: 2,7 => SOLVED * 375642819148579236926138547651294378897361425234857691589723164463915782712486953 D4: 8 => CTR * .7.6..81.1485.9..6.261.8.4.6.18.....8.73624.12.47.16.8589237164463915782712486... * PAIR E7: 2,3 BLK 8 F7: 2,3,7 # reduction candidate for 2,3 F7: 7 => CTR * .7...381.1485.9...32.....4.6.1..4...8.73.24.12.4......589.37164463915782712486... F7: 2,3 # 12 pairs * PAIR E7: 2,3 COL E E1: 2,3,4,6 # reduction candidate for 2,3 E1: 2,3 => CTR * .7.23481.1485.9...32.....4.6.184....8.73..4..2.46....8589723164463915782712486... E1: 4,6 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-459-base-pr-000.dot * REASONING * DIS # I1: 5,6 => CTR => I1: 3,9 * DIS # I1: 5,6 => CTR => I1: 3,9 * DIS # E1: 2,6 => CTR => E1: 3,4 * PRF # D6: 1,8 => SOL * DIS # D6: 6,7 => CTR => D6: 1,8 * DIS # F6: 1,8 => CTR => F6: 7 * PRF # F6: 7 => SOL * DIS # E5: 5,9 => CTR => E5: 2,6 * PRF # I5: 5,9 => SOL * DIS # F7: 2,7 => CTR => F7: 3 * PRF # D4: 2,7 => SOL * DIS # D4: 8 => CTR => D4: 2,7 * DIS # F7: 7 => CTR => F7: 2,3 * DIS # E1: 2,3 => CTR => E1: 4,6 * CNT 14 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,C1,C3,D1,D3,D7,E7,F3,F5) * .7....81.1485.9....2.....4.6.1......8.73..4..2.4......589...164463915782712486... * PAIR A1: 3,9 ROW 1 I1: 3,9,5,6 # reduction candidate for 3,9 I1: 5,6 => CTR * 9762..8151485.9...3251.8.4.6.18.....8.73.14.62.46.7..15897..164463915782712486... * PAIR RESTART * PAIR A3: 3,9 ROW 3 G3: 3,9,5 # reduction candidate for 3,9 G3: 3,9 # 18 pairs I3: 3,9,5,7 # reduction candidate for 3,9 I3: 3,9 # 19 pairs * PAIR D3: 1,8 COL D D6: 1,8,6 # reduction candidate for 1,8 D6: 1,8 => SOLVED * 375642819148579236926138547651294378897361425234857691589723164463915782712486953 * DURATION: 0:00:06.519180 START: 18:26:53.885697 END: 18:27:00.404877 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-459-base-pr-001.dot * REASONING * DIS # I1: 5,6 => CTR => I1: 3,9 * PRF I1: 3,9 # D6: 1,8 => SOL * STA I1: 3,9 + D6: 1,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 459 solution: 375642819148579236926138547651294378897361425234857691589723164463915782712486953 info: 95523 FNBTHXYK S8.f 44938 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 375642819148579236926138547651294378897361425234857691589723164463915782712486953 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 # I1: 3,9 => UNS * DIS # I1: 5,6 => CTR => I1: 3,9 * DIS # I1: 5,6 => CTR => I1: 3,9 * INC # I1: 3,9 => UNS * INC # G3: 3,9 => UNS * INC # I3: 3,9 => UNS * INC # G3: 5,6 => UNS * INC # I3: 5,6 => UNS * DIS # E1: 2,6 => CTR => E1: 3,4 * INC # E1: 3,4 => UNS * PRF # D6: 1,8 => SOL * DIS # D6: 6,7 => CTR => D6: 1,8 * DIS # F6: 1,8 => CTR => F6: 7 * PRF # F6: 7 => SOL * INC # B4: 5,9 => UNS * INC # B6: 5,9 => UNS * DIS # E5: 5,9 => CTR => E5: 2,6 * INC # E5: 2,6 => UNS * INC # H5: 5,9 => UNS * PRF # I5: 5,9 => SOL * INC # I5: 1,6 => UNS * DIS # F7: 2,7 => CTR => F7: 3 * INC # F7: 3 => UNS * PRF # D4: 2,7 => SOL * DIS # D4: 8 => CTR => D4: 2,7 * INC # F7: 2,3 => UNS * DIS # F7: 7 => CTR => F7: 2,3 * DIS # E1: 2,3 => CTR => E1: 4,6 * INC # E1: 4,6 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I1: 3,9 => UNS * DIS # I1: 5,6 => CTR => I1: 3,9 * INC I1: 3,9 # G3: 3,9 => UNS * INC I1: 3,9 # I3: 3,9 => UNS * PRF I1: 3,9 # D6: 1,8 => SOL * STA I1: 3,9 + D6: 1,8 * CNT 5 HDP CHAINS / 5 HYP OPENED