Analysis of xx-top500-278-base.sdk
Contents
Original Sudoku
level: medium
position: ..21..4...83...............5..4..7..6...2.....1............8.631..7............8. initial
Autosolve
position: ..21..4...83........1......5294..7..63..2....81.......2759481631987.....346...987 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 7,9 => CTR => E1: 3,5,6,8 * DIS # H1: 7,9 => CTR => H1: 3,5 * DIS # E1: 5,6 => CTR => E1: 3,7,8,9 * DIS # I1: 5,6 => CTR => I1: 8,9 * DIS # D3: 5,6 => CTR => D3: 2,3,8 * DIS # F3: 5,6 => CTR => F3: 2,3,4,7,9 * DIS # G3: 5,6 => CTR => G3: 2,3,8 * PRF # D3: 5,8 => SOL * DIS # D3: 2,3,6 => CTR => D3: 5,8 * DIS # E4: 1,3 => CTR => E4: 6,8 * DIS # G3: 5,8 => CTR => G3: 2,3,6 * PRF # G3: 2,3,6 => SOL * PRF # E1: 3,6 => SOL * DIS # E4: 3,6 => CTR => E4: 1,8 * DIS # E6: 3,6 => CTR => E6: 5,7,9 * DIS # F1: 3,6 => CTR => F1: 5,7,9 * DIS # F3: 3,6 => CTR => F3: 2,4,5,7,9 * DIS # F6: 3,6 => CTR => F6: 5,7,9 * DIS # F9: 1 => CTR => F9: 2,5 * DIS # D2: 2,5 => CTR => D2: 6 * PRF # D2: 6 => SOL * DIS # D3: 2,5 => CTR => D3: 3,6,8 * DIS # F9: 2 => CTR => F9: 1,5 * PRF # G2: 2,5 => SOL * DIS # G2: 6 => CTR => G2: 2,5 * DIS # G3: 2,5 => CTR => G3: 3,6,8 * DIS # G6: 2,5 => CTR => G6: 3,6 * CNT 27 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 7,9 => CTR => E1: 3,5,6,8 * DIS E1: 3,5,6,8 # H1: 7,9 => CTR => H1: 3,5 * DIS E1: 3,5,6,8 + H1: 3,5 # F1: 3,5,6 => CTR => F1: 7,9 * DIS E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 # E1: 5,6 => CTR => E1: 3,8 * DIS E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 # I1: 5,6 => CTR => I1: 8 * PRF E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 + I1: 8 => SOL * STA E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 + I1: 8 * CNT 6 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..21..4...83...............5..4..7..6...2.....1............8.631..7............8. | initial |
| ..21..4...83........1......5294..7..63..2....81.......2759481631987.....346...987 | autosolve |
| 962137458783654219451892376529486731637521894814379625275948163198763542346215987 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 7,9 B1: 5,6 B3: 5,6 C5: 4,7 C6: 4,7 D5: 5,8 H4: 1,3 G5: 5,8 E8: 3,6 F8: 3,6 D9: 2,5 E9: 1,5 G8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,I2: 1.. / H2 = 1 => 0 pairs (*) / I2 = 1 => 0 pairs (X) E9,F9: 1.. / E9 = 1 => 13 pairs (_) / F9 = 1 => 0 pairs (X) E4,E9: 1.. / E4 = 1 => 0 pairs (X) / E9 = 1 => 13 pairs (_) D9,F9: 2.. / D9 = 2 => 16 pairs (_) / F9 = 2 => 0 pairs (X) E8,F8: 3.. / E8 = 3 => 14 pairs (_) / F8 = 3 => 12 pairs (_) D3,D6: 3.. / D3 = 3 => 0 pairs (X) / D6 = 3 => 0 pairs (_) G3,G6: 3.. / G3 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) A2,A3: 4.. / A2 = 4 => 14 pairs (_) / A3 = 4 => 14 pairs (_) F2,F3: 4.. / F2 = 4 => 14 pairs (_) / F3 = 4 => 14 pairs (_) C5,C6: 4.. / C5 = 4 => 0 pairs (X) / C6 = 4 => 12 pairs (_) H8,I8: 4.. / H8 = 4 => 15 pairs (_) / I8 = 4 => 15 pairs (_) A2,F2: 4.. / A2 = 4 => 14 pairs (_) / F2 = 4 => 14 pairs (_) A3,F3: 4.. / A3 = 4 => 14 pairs (_) / F3 = 4 => 14 pairs (_) B1,B3: 5.. / B1 = 5 => 11 pairs (_) / B3 = 5 => 11 pairs (_) D5,G5: 5.. / D5 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) B1,B3: 6.. / B1 = 6 => 11 pairs (_) / B3 = 6 => 11 pairs (_) E8,F8: 6.. / E8 = 6 => 12 pairs (_) / F8 = 6 => 14 pairs (_) C5,C6: 7.. / C5 = 7 => 12 pairs (_) / C6 = 7 => 0 pairs (X) C5,F5: 7.. / C5 = 7 => 12 pairs (_) / F5 = 7 => 0 pairs (X) E4,D5: 8.. / E4 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) I4,G5: 8.. / I4 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) E1,I1: 8.. / E1 = 8 => 0 pairs (X) / I1 = 8 => 0 pairs (_) E4,I4: 8.. / E4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) D5,G5: 8.. / D5 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) D3,D5: 8.. / D3 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) G3,G5: 8.. / G3 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) * DURATION: 0:00:37.652422 START: 12:26:22.948523 END: 12:27:00.600945 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,B3,C5,C6,D5,D9,E8,E9,F8,G5,G8,H4) * ..21..4...83........1......5294..7..63..2....81.......2759481631987.....346...987 * PAIR A1: 7,9 BLK 1 A2: 7,9,4 # reduction candidate for 7,9 A2: 7,9 # 14 pairs A3: 7,9,4 # reduction candidate for 7,9 A3: 7,9 # 14 pairs * PAIR A1: 7,9 ROW 1 E1: 7,9,3,5,6,8 # reduction candidate for 7,9 E1: 7,9 => CTR * .621..458.8365.2...518.23.652948673163.5218..81.3..6.52759481631987.....346215987 E1: 3,5,6,8 # 13 pairs F1: 7,9,3,5,6 # reduction candidate for 7,9 F1: 7,9 # 15 pairs H1: 7,9,3,5 # reduction candidate for 7,9 H1: 7,9 => CTR * .621..4.8.836.......18..3.652948673163.5218..81.3..6..275948163198763...346215987 H1: 3,5 # 14 pairs * PAIR B1: 5,6 ROW 1 E1: 5,6,3,7,8,9 # reduction candidate for 5,6 E1: 5,6 => CTR * .6215.4.8.836......518..3.652948673163.5218..81.3..6..2759481631987.....346215987 E1: 3,7,8,9 # 13 pairs F1: 5,6,3,7,9 # reduction candidate for 5,6 F1: 5,6 # 15 pairs I1: 5,6,8,9 # reduction candidate for 5,6 I1: 5,6 => CTR * ..218.4...83...6....1...8..5294..7.863.82.5..81....3.62759481631987..2..346...987 I1: 8,9 # 14 pairs * PAIR B3: 5,6 ROW 3 D3: 5,6,2,3,8 # reduction candidate for 5,6 D3: 5,6 => CTR * ..21..4...83........1......5294..7..63.82.5..81.3.....2759481631987..2..346...987 D3: 2,3,8 # 13 pairs E3: 5,6,3,7,8,9 # reduction candidate for 5,6 E3: 5,6 # 14 pairs F3: 5,6,2,3,4,7,9 # reduction candidate for 5,6 F3: 5,6 => CTR * ..21..4...83..46..4.1...8..5294..7.863.82.5..81....3.62759481631987..2..346512987 F3: 2,3,4,7,9 # 13 pairs G3: 5,6,2,3,8 # reduction candidate for 5,6 G3: 5,6 => CTR * ..21..4...83........1......5294..7..63..2.8..81....3..2759481631987.....346...987 G3: 2,3,8 # 13 pairs I3: 5,6,2,8,9 # reduction candidate for 5,6 I3: 5,6 # 14 pairs * PAIR D5: 5,8 COL D D3: 5,8,2,3,6 # reduction candidate for 5,8 D3: 5,8 => SOLVED * 962137458783654219451892376529486731637521894814379625275948163198763542346215987 D3: 2,3,6 => CTR * ..21..4...83...6....1...8..5294..7.863.82.5..81....3.62759481631987..2..346...987 * PAIR H4: 1,3 ROW 4 E4: 1,3,6,8 # reduction candidate for 1,3 E4: 1,3 => CTR * ..218.4...83...6....1...8..5294.67.863.82.5..81....3.62759481631987632..346...987 E4: 6,8 # 14 pairs F4: 1,3,6 # reduction candidate for 1,3 F4: 1,3 # 16 pairs * PAIR G5: 5,8 COL G G3: 5,8,2,3,6 # reduction candidate for 5,8 G3: 5,8 => CTR * ..21..4...83...6....13.....5294..71.63.8215..81.6..3..2759481631987..2..346.1.987 G3: 2,3,6 => SOLVED * 962137458783654219451892376529486731637521894814379625275948163198763542346215987 * PAIR E8: 3,6 COL E E1: 3,6,5,7,8,9 # reduction candidate for 3,6 E1: 3,6 => SOLVED * 962137458783654219451892376529486731637521894814379625275948163198763542346215987 E1: 5,7,8,9 # 13 pairs E3: 3,6,5,7,8,9 # reduction candidate for 3,6 E3: 3,6 # 15 pairs E4: 3,6,1,8 # reduction candidate for 3,6 E4: 3,6 => CTR * ..218.4...83...6....1...8..5294..7.863.82.5..81....3.62759481631987..2..346.1.987 E4: 1,8 # 14 pairs E6: 3,6,5,7,9 # reduction candidate for 3,6 E6: 3,6 => CTR * ..21.34...836.......18..3..52948173663.52.8..81.36....275948163198736...346215987 E6: 5,7,9 # 13 pairs * PAIR F8: 3,6 COL F F1: 3,6,5,7,9 # reduction candidate for 3,6 F1: 3,6 => CTR * .621.34.8.836......518..3..52948173663.52.8..81.36....275948163198736...346215987 F1: 5,7,9 # 13 pairs F3: 3,6,2,4,5,7,9 # reduction candidate for 3,6 F3: 3,6 => CTR * ..21..4...83..46..4.1...8..5294..7.863.82.5..81....3.62759481631987..2..346512987 F3: 2,4,5,7,9 # 13 pairs F4: 3,6,1 # reduction candidate for 3,6 F4: 3,6 # 14 pairs F6: 3,6,5,7,9 # reduction candidate for 3,6 F6: 3,6 => CTR * .6213.458.836.......1...3..52948173663.52.8..81.3.6...275948163198763...346215987 F6: 5,7,9 # 13 pairs * PAIR D9: 2,5 BLK 8 F9: 2,5,1 # reduction candidate for 2,5 F9: 1 => CTR * ..21..4...83........1......52941.73863.82.5..81.......2759481631987.....346251987 F9: 2,5 # 13 pairs * PAIR D9: 2,5 COL D D2: 2,5,6 # reduction candidate for 2,5 D2: 2,5 => CTR * ..21..4...83...6....1...8..5294..7.863.82.5..81....3.62759481631987..2..346...987 D2: 6 => SOLVED * 962137458783654219451892376529486731637521894814379625275948163198763542346215987 D3: 2,5,3,6,8 # reduction candidate for 2,5 D3: 2,5 => CTR * ..21..4...83........1......5294..7..63.82.5..81.3.....2759481631987..2..346...987 D3: 3,6,8 # 13 pairs * PAIR E9: 1,5 BLK 8 F9: 1,5,2 # reduction candidate for 1,5 F9: 2 => CTR * ..21..4...83...6....1...8..5294..7.863.82.5..81....3.62759481631987..2..346512987 F9: 1,5 # 16 pairs * PAIR G8: 2,5 BLK 9 H8: 2,5,4 # reduction candidate for 2,5 H8: 2,5 # 15 pairs I8: 2,5,4 # reduction candidate for 2,5 I8: 2,5 # 15 pairs * PAIR G8: 2,5 COL G G2: 2,5,6 # reduction candidate for 2,5 G2: 2,5 => SOLVED * 962137458783654219451892376529486731637521894814379625275948163198763542346215987 G2: 6 => CTR * ..21..4...83...6....1...8..5294..7.863.82.5..81....3.62759481631987..2..346...987 G3: 2,5,3,6,8 # reduction candidate for 2,5 G3: 2,5 => CTR * ..21..4...83........1......5294..7..63..2.8..81....3..2759481631987.....346...987 G3: 3,6,8 # 13 pairs G6: 2,5,3,6 # reduction candidate for 2,5 G6: 2,5 => CTR * ..21..4...83...6....1...3..5294..7..63..2.8..81.3.....2759481631987.....346...987 G6: 3,6 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-278-base-pr-000.dot * REASONING * DIS # E1: 7,9 => CTR => E1: 3,5,6,8 * DIS # H1: 7,9 => CTR => H1: 3,5 * DIS # E1: 5,6 => CTR => E1: 3,7,8,9 * DIS # I1: 5,6 => CTR => I1: 8,9 * DIS # D3: 5,6 => CTR => D3: 2,3,8 * DIS # F3: 5,6 => CTR => F3: 2,3,4,7,9 * DIS # G3: 5,6 => CTR => G3: 2,3,8 * PRF # D3: 5,8 => SOL * DIS # D3: 2,3,6 => CTR => D3: 5,8 * DIS # E4: 1,3 => CTR => E4: 6,8 * DIS # G3: 5,8 => CTR => G3: 2,3,6 * PRF # G3: 2,3,6 => SOL * PRF # E1: 3,6 => SOL * DIS # E4: 3,6 => CTR => E4: 1,8 * DIS # E6: 3,6 => CTR => E6: 5,7,9 * DIS # F1: 3,6 => CTR => F1: 5,7,9 * DIS # F3: 3,6 => CTR => F3: 2,4,5,7,9 * DIS # F6: 3,6 => CTR => F6: 5,7,9 * DIS # F9: 1 => CTR => F9: 2,5 * DIS # D2: 2,5 => CTR => D2: 6 * PRF # D2: 6 => SOL * DIS # D3: 2,5 => CTR => D3: 3,6,8 * DIS # F9: 2 => CTR => F9: 1,5 * PRF # G2: 2,5 => SOL * DIS # G2: 6 => CTR => G2: 2,5 * DIS # G3: 2,5 => CTR => G3: 3,6,8 * DIS # G6: 2,5 => CTR => G6: 3,6 * CNT 27 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,B3,C5,C6,D5,D9,E8,E9,F8,G5,G8,H4) * ..21..4...83........1......5294..7..63..2....81.......2759481631987.....346...987 * PAIR A1: 7,9 BLK 1 A2: 7,9,4 # reduction candidate for 7,9 A2: 7,9 # 14 pairs A3: 7,9,4 # reduction candidate for 7,9 A3: 7,9 # 14 pairs * PAIR A1: 7,9 ROW 1 E1: 7,9,3,5,6,8 # reduction candidate for 7,9 E1: 7,9 => CTR * .621..458.8365.2...518.23.652948673163.5218..81.3..6.52759481631987.....346215987 F1: 7,9,3,5,6 # reduction candidate for 7,9 F1: 7,9 # 15 pairs H1: 7,9,3,5 # reduction candidate for 7,9 H1: 7,9 => CTR * .621..4.8.836.......18..3.652948673163.5218..81.3..6..275948163198763...346215987 * RESTART * PAIR A1: 7,9 ROW 1 F1: 7,9,3,5,6 # reduction candidate for 7,9 F1: 3,5,6 => CTR * 7.218.4.9.83...6....1...8..5294..7.863.82.5..81....3.62759481631987..2..346...987 * PAIR RESTART * PAIR A1: 7,9 BLK 1 A2: 7,9,4 # reduction candidate for 7,9 A2: 7,9 # 16 pairs A3: 7,9,4 # reduction candidate for 7,9 A3: 7,9 # 16 pairs * PAIR B1: 5,6 ROW 1 E1: 5,6,3,8 # reduction candidate for 5,6 E1: 5,6 => CTR * ..21..438.83........1......52948371663.52....81.......2759481631987.....346...987 I1: 5,6,8 # reduction candidate for 5,6 I1: 5,6 => CTR * .6218.435.83...6.1.51......5294..71863.8215..81....3.62759481631987..2..346.1.987 I1: 8 => SOLVED * 962137458783654219451892376529486731637521894814379625275948163198763542346215987 * DURATION: 0:00:09.910793 START: 12:27:45.384208 END: 12:27:55.295001 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-278-base-pr-001.dot * REASONING * DIS # E1: 7,9 => CTR => E1: 3,5,6,8 * DIS E1: 3,5,6,8 # H1: 7,9 => CTR => H1: 3,5 * DIS E1: 3,5,6,8 + H1: 3,5 # F1: 3,5,6 => CTR => F1: 7,9 * DIS E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 # E1: 5,6 => CTR => E1: 3,8 * DIS E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 # I1: 5,6 => CTR => I1: 8 * PRF E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 + I1: 8 => SOL * STA E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 + I1: 8 * CNT 6 HDP CHAINS / 11 HYP OPENED
Header Info
Top 500 Minimum 17 278 solution: 962137458783654219451892376529486731637521894814379625275948163198763542346215987 info: 2211 FNBTHWY S8.f 13284 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 962137458783654219451892376529486731637521894814379625275948163198763542346215987 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 # A2: 7,9 => UNS * INC # A3: 7,9 => UNS * DIS # E1: 7,9 => CTR => E1: 3,5,6,8 * INC # E1: 3,5,6,8 => UNS * INC # F1: 7,9 => UNS * DIS # H1: 7,9 => CTR => H1: 3,5 * INC # H1: 3,5 => UNS * DIS # E1: 5,6 => CTR => E1: 3,7,8,9 * INC # E1: 3,7,8,9 => UNS * INC # F1: 5,6 => UNS * DIS # I1: 5,6 => CTR => I1: 8,9 * INC # I1: 8,9 => UNS * DIS # D3: 5,6 => CTR => D3: 2,3,8 * INC # D3: 2,3,8 => UNS * INC # E3: 5,6 => UNS * DIS # F3: 5,6 => CTR => F3: 2,3,4,7,9 * INC # F3: 2,3,4,7,9 => UNS * DIS # G3: 5,6 => CTR => G3: 2,3,8 * INC # G3: 2,3,8 => UNS * INC # I3: 5,6 => UNS * PRF # D3: 5,8 => SOL * DIS # D3: 2,3,6 => CTR => D3: 5,8 * DIS # E4: 1,3 => CTR => E4: 6,8 * INC # E4: 6,8 => UNS * INC # F4: 1,3 => UNS * DIS # G3: 5,8 => CTR => G3: 2,3,6 * PRF # G3: 2,3,6 => SOL * PRF # E1: 3,6 => SOL * INC # E1: 5,7,8,9 => UNS * INC # E3: 3,6 => UNS * DIS # E4: 3,6 => CTR => E4: 1,8 * INC # E4: 1,8 => UNS * DIS # E6: 3,6 => CTR => E6: 5,7,9 * INC # E6: 5,7,9 => UNS * DIS # F1: 3,6 => CTR => F1: 5,7,9 * INC # F1: 5,7,9 => UNS * DIS # F3: 3,6 => CTR => F3: 2,4,5,7,9 * INC # F3: 2,4,5,7,9 => UNS * INC # F4: 3,6 => UNS * DIS # F6: 3,6 => CTR => F6: 5,7,9 * INC # F6: 5,7,9 => UNS * INC # F9: 2,5 => UNS * DIS # F9: 1 => CTR => F9: 2,5 * DIS # D2: 2,5 => CTR => D2: 6 * PRF # D2: 6 => SOL * DIS # D3: 2,5 => CTR => D3: 3,6,8 * INC # D3: 3,6,8 => UNS * INC # F9: 1,5 => UNS * DIS # F9: 2 => CTR => F9: 1,5 * INC # H8: 2,5 => UNS * INC # I8: 2,5 => UNS * PRF # G2: 2,5 => SOL * DIS # G2: 6 => CTR => G2: 2,5 * DIS # G3: 2,5 => CTR => G3: 3,6,8 * INC # G3: 3,6,8 => UNS * DIS # G6: 2,5 => CTR => G6: 3,6 * INC # G6: 3,6 => UNS * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 7,9 => UNS * INC # A3: 7,9 => UNS * DIS # E1: 7,9 => CTR => E1: 3,5,6,8 * INC E1: 3,5,6,8 # F1: 7,9 => UNS * DIS E1: 3,5,6,8 # H1: 7,9 => CTR => H1: 3,5 * INC E1: 3,5,6,8 + H1: 3,5 # F1: 7,9 => UNS * DIS E1: 3,5,6,8 + H1: 3,5 # F1: 3,5,6 => CTR => F1: 7,9 * INC E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 # A2: 7,9 => UNS * INC E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 # A3: 7,9 => UNS * DIS E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 # E1: 5,6 => CTR => E1: 3,8 * DIS E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 # I1: 5,6 => CTR => I1: 8 * PRF E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 + I1: 8 => SOL * STA E1: 3,5,6,8 + H1: 3,5 + F1: 7,9 + E1: 3,8 + I1: 8 * CNT 12 HDP CHAINS / 11 HYP OPENED