Analysis of xx-top500-295-base.sdk
Contents
Original Sudoku
level: medium
position: ...32....7..6.....1.....8......81....6.....3........2...4...1.7.3.4...........5.. initial
Autosolve
position: ...32..1.7..61.3..1.3...8..3...816...6.....31.1.....28..48..1.7.314..28....1..543 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 5,9 => CTR => I2: 2,4 * DIS # H3: 5,9 => CTR => H3: 6,7 * DIS # I3: 5,9 => CTR => I3: 2,4,6 * DIS # F2: 5,9 => CTR => F2: 4,8 * PRF # H4: 5,9 => SOL * DIS # H4: 7 => CTR => H4: 5,9 * DIS # H4: 7,9 => CTR => H4: 5 * PRF # H4: 5 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 4 => CTR => G6: 7,9 * DIS # G1: 7,9 => CTR => G1: 4 * PRF # G1: 4 => SOL * DIS # F7: 6,9 => CTR => F7: 2,3,5 * DIS # E8: 6,9 => CTR => E8: 5,7 * DIS # F7: 6,9 => CTR => F7: 2,3,5 * DIS # H3: 6,9 => CTR => H3: 5,7 * PRF # H3: 5,7 => SOL * DIS # E8: 6,9 => CTR => E8: 5,7 * PRF # I3: 6,9 => SOL * DIS # I3: 2,4,5 => CTR => I3: 6,9 * CNT 20 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 5,9 => CTR => I2: 2,4 * DIS I2: 2,4 # H3: 5,9 => CTR => H3: 6,7 * DIS I2: 2,4 + H3: 6,7 # I3: 5,9 => CTR => I3: 2,4,6 * DIS I2: 2,4 + H3: 6,7 + I3: 2,4,6 # I1: 4 => CTR => I1: 5,9 * DIS I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 # F2: 5,9 => CTR => F2: 4,8 * PRF I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # G6: 7,9 => SOL * STA I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 + G6: 7,9 * CNT 6 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...32....7..6.....1.....8......81....6.....3........2...4...1.7.3.4...........5.. | initial |
| ...32..1.7..61.3..1.3...8..3...816...6.....31.1.....28..48..1.7.314..28....1..543 | autosolve |
| 986327415745618392123954876392781654568249731417536928254893167631475289879162543 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) H2: 5,9 E6: 3,6 F6: 3,6 G5: 7,9 E9: 6,9 H7: 6,9 I8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 2.. / I2 = 2 => 8 pairs (_) / I3 = 2 => 0 pairs (X) D4,D5: 2.. / D4 = 2 => 11 pairs (_) / D5 = 2 => 9 pairs (_) F7,F9: 2.. / F7 = 2 => 9 pairs (_) / F9 = 2 => 7 pairs (_) B3,I3: 2.. / B3 = 2 => 8 pairs (_) / I3 = 2 => 0 pairs (X) E6,F6: 3.. / E6 = 3 => 5 pairs (_) / F6 = 3 => 6 pairs (_) E7,F7: 3.. / E7 = 3 => 6 pairs (_) / F7 = 3 => 5 pairs (_) E6,E7: 3.. / E6 = 3 => 5 pairs (_) / E7 = 3 => 6 pairs (_) F6,F7: 3.. / F6 = 3 => 6 pairs (_) / F7 = 3 => 5 pairs (_) B4,A6: 4.. / B4 = 4 => 0 pairs (X) / A6 = 4 => 0 pairs (_) E5,F5: 4.. / E5 = 4 => 7 pairs (_) / F5 = 4 => 7 pairs (_) I4,G6: 4.. / I4 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) B4,I4: 4.. / B4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) A6,G6: 4.. / A6 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) A1,A6: 4.. / A1 = 4 => 0 pairs (X) / A6 = 4 => 0 pairs (_) E3,E5: 4.. / E3 = 4 => 7 pairs (_) / E5 = 4 => 7 pairs (_) G1,G6: 4.. / G1 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) H4,I4: 5.. / H4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) A1,C1: 6.. / A1 = 6 => 0 pairs (X) / C1 = 6 => 7 pairs (_) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) E6,F6: 6.. / E6 = 6 => 6 pairs (_) / F6 = 6 => 5 pairs (_) H7,I8: 6.. / H7 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) C1,C9: 6.. / C1 = 6 => 7 pairs (_) / C9 = 6 => 0 pairs (X) H3,H7: 6.. / H3 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) I3,I8: 6.. / I3 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) G1,H3: 7.. / G1 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) B9,C9: 7.. / B9 = 7 => 7 pairs (_) / C9 = 7 => 0 pairs (X) E8,F8: 7.. / E8 = 7 => 7 pairs (_) / F8 = 7 => 0 pairs (X) F1,G1: 7.. / F1 = 7 => 0 pairs (*) / G1 = 7 => 0 pairs (X) B4,B9: 7.. / B4 = 7 => 0 pairs (X) / B9 = 7 => 7 pairs (_) H3,H4: 7.. / H3 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) F1,F2: 8.. / F1 = 8 => 0 pairs (X) / F2 = 8 => 7 pairs (_) A5,C5: 8.. / A5 = 8 => 10 pairs (_) / C5 = 8 => 7 pairs (_) H7,I8: 9.. / H7 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:00:57.133364 START: 13:03:09.524978 END: 13:04:06.658342 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E6,E9,F6,G5,H2,H7,I8) * ...32..1.7..61.3..1.3...8..3...816...6.....31.1.....28..48..1.7.314..28....1..543 * PAIR H2: 5,9 BLK 3 I1: 5,9,4 # reduction candidate for 5,9 I1: 5,9 # 13 pairs I2: 5,9,2,4 # reduction candidate for 5,9 I2: 5,9 => CTR * 4.632.7197..61.3..1.3...8623...81675.6....931.1....428..48..197.314..286.7.1..543 I2: 2,4 # 8 pairs H3: 5,9,6,7 # reduction candidate for 5,9 H3: 5,9 => CTR * 4..32.71.7..61.3..1.3...8.63...81675.6....931.1....428..48..167.314..289.7.1..543 H3: 6,7 # 8 pairs I3: 5,9,2,4,6 # reduction candidate for 5,9 I3: 5,9 => CTR * 4.632.7197..61.3.2123...86.3...81675.6....931.1....428..48..197.314..286.7.1..543 I3: 2,4,6 # 7 pairs * PAIR H2: 5,9 ROW 2 B2: 5,9,2,4,8 # reduction candidate for 5,9 B2: 5,9 # 11 pairs C2: 5,9,2,8 # reduction candidate for 5,9 C2: 5,9 # 11 pairs F2: 5,9,4,8 # reduction candidate for 5,9 F2: 5,9 => CTR * 456328719782619354193...862349281675268...931.1....428.248..197.314..286.7.1.2543 F2: 4,8 # 8 pairs * PAIR H2: 5,9 COL H H4: 5,9,7 # reduction candidate for 5,9 H4: 5,9 => SOLVED * 986327415745618392123954876392781654568249731417536928254893167631475289879162543 H4: 7 => CTR * 4.632.7197.261.3541.3...862349281675268...931.1....428..48..197.314..286.7.1..543 * PAIR E6: 3,6 COL E E7: 3,6,5,9 # reduction candidate for 3,6 E7: 3,6 # 9 pairs E7: 5,9 # 6 pairs * PAIR F6: 3,6 COL F F7: 3,6,2,5,9 # reduction candidate for 3,6 F7: 3,6 # 8 pairs F7: 2,5,9 # 7 pairs * PAIR G5: 7,9 BLK 6 H4: 7,9,5 # reduction candidate for 7,9 H4: 7,9 => CTR * 4.632.7197.261.3541.3...862349281675268...931.1....428..48..197.314..286.7.1..543 H4: 5 => SOLVED * 986327415745618392123954876392781654568249731417536928254893167631475289879162543 G6: 7,9,4 # reduction candidate for 7,9 G6: 7,9 => SOLVED * 986327415745618392123954876392781654568249731417536928254893167631475289879162543 G6: 4 => CTR * 4.632.7197.261.3541.3...862349281675268...931.1....428..48..197.314..286.7.1..543 * PAIR G5: 7,9 ROW 5 C5: 7,9,2,5,8 # reduction candidate for 7,9 C5: 7,9 # 15 pairs D5: 7,9,2,5 # reduction candidate for 7,9 D5: 7,9 # 14 pairs E5: 7,9,4,5 # reduction candidate for 7,9 E5: 7,9 # 10 pairs F5: 7,9,4,5 # reduction candidate for 7,9 F5: 7,9 # 10 pairs * PAIR G5: 7,9 COL G G1: 7,9,4 # reduction candidate for 7,9 G1: 7,9 => CTR * 4.632.7197.261.3541.3...862349281675268...931.1....428..48..197.314..286.7.1..543 G1: 4 => SOLVED * 986327415745618392123954876392781654568249731417536928254893167631475289879162543 * PAIR E9: 6,9 BLK 8 E7: 6,9,3,5 # reduction candidate for 6,9 E7: 6,9 # 11 pairs F7: 6,9,2,3,5 # reduction candidate for 6,9 F7: 6,9 => CTR * 4.632.7197..61.35.1.3...86.34..81675.6....93151..634282548361979314..286678192543 F7: 2,3,5 # 7 pairs E8: 6,9,5,7 # reduction candidate for 6,9 E8: 6,9 => CTR * 4.632.7197..61.35.1.3...86.34298167586....93191....428..48..197531497286.79162543 E8: 5,7 # 8 pairs F8: 6,9,5,7 # reduction candidate for 6,9 F8: 6,9 # 12 pairs F9: 6,9,2 # reduction candidate for 6,9 F9: 6,9 # 9 pairs * PAIR E9: 6,9 ROW 9 A9: 6,9,2,8 # reduction candidate for 6,9 A9: 6,9 # 10 pairs C9: 6,9,2,7,8 # reduction candidate for 6,9 C9: 6,9 # 8 pairs * PAIR H7: 6,9 ROW 7 A7: 6,9,2,5 # reduction candidate for 6,9 A7: 6,9 # 10 pairs E7: 6,9,3,5 # reduction candidate for 6,9 E7: 6,9 # 11 pairs F7: 6,9,2,3,5 # reduction candidate for 6,9 F7: 6,9 => CTR * 4.632.7197..61.35.1.3...86.34..81675.6....93151..634282548361979314..286678192543 F7: 2,3,5 # 7 pairs * PAIR H7: 6,9 COL H H3: 6,9,5,7 # reduction candidate for 6,9 H3: 6,9 => CTR * 4.632.7197.261.3541.3...862349281675268...931.1....428..48..197.314..286.7.1..543 H3: 5,7 => SOLVED * 986327415745618392123954876392781654568249731417536928254893167631475289879162543 * PAIR I8: 6,9 ROW 8 A8: 6,9,5 # reduction candidate for 6,9 A8: 6,9 # 11 pairs E8: 6,9,5,7 # reduction candidate for 6,9 E8: 6,9 => CTR * 4.632.7197..61.35.1.3...86.34298167586....93191....428..48..197531497286.79162543 E8: 5,7 # 8 pairs F8: 6,9,5,7 # reduction candidate for 6,9 F8: 6,9 # 12 pairs * PAIR I8: 6,9 COL I I3: 6,9,2,4,5 # reduction candidate for 6,9 I3: 6,9 => SOLVED * 986327415745618392123954876392781654568249731417536928254893167631475289879162543 I3: 2,4,5 => CTR * 4.632.7197.261.3541.3...862349281675268...931.1....428..48..197.314..286.7.1..543 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-295-base-pr-000.dot * REASONING * DIS # I2: 5,9 => CTR => I2: 2,4 * DIS # H3: 5,9 => CTR => H3: 6,7 * DIS # I3: 5,9 => CTR => I3: 2,4,6 * DIS # F2: 5,9 => CTR => F2: 4,8 * PRF # H4: 5,9 => SOL * DIS # H4: 7 => CTR => H4: 5,9 * DIS # H4: 7,9 => CTR => H4: 5 * PRF # H4: 5 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 4 => CTR => G6: 7,9 * DIS # G1: 7,9 => CTR => G1: 4 * PRF # G1: 4 => SOL * DIS # F7: 6,9 => CTR => F7: 2,3,5 * DIS # E8: 6,9 => CTR => E8: 5,7 * DIS # F7: 6,9 => CTR => F7: 2,3,5 * DIS # H3: 6,9 => CTR => H3: 5,7 * PRF # H3: 5,7 => SOL * DIS # E8: 6,9 => CTR => E8: 5,7 * PRF # I3: 6,9 => SOL * DIS # I3: 2,4,5 => CTR => I3: 6,9 * CNT 20 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E6,E9,F6,G5,H2,H7,I8) * ...32..1.7..61.3..1.3...8..3...816...6.....31.1.....28..48..1.7.314..28....1..543 * PAIR H2: 5,9 BLK 3 I1: 5,9,4 # reduction candidate for 5,9 I1: 5,9 # 13 pairs I2: 5,9,2,4 # reduction candidate for 5,9 I2: 5,9 => CTR * 4.632.7197..61.3..1.3...8623...81675.6....931.1....428..48..197.314..286.7.1..543 H3: 5,9,6,7 # reduction candidate for 5,9 H3: 5,9 => CTR * 4..32.71.7..61.3..1.3...8.63...81675.6....931.1....428..48..167.314..289.7.1..543 I3: 5,9,2,4,6 # reduction candidate for 5,9 I3: 5,9 => CTR * 4.632.7197..61.3.2123...86.3...81675.6....931.1....428..48..197.314..286.7.1..543 * RESTART * PAIR H2: 5,9 BLK 3 I1: 5,9,4 # reduction candidate for 5,9 I1: 4 => CTR * ...32..147..61.352123...8.634..816.5.6.....31.1....428..48..167.314..289.7.1..543 * PAIR H2: 5,9 ROW 2 B2: 5,9,2,4,8 # reduction candidate for 5,9 B2: 5,9 # 16 pairs C2: 5,9,2,8 # reduction candidate for 5,9 C2: 5,9 # 16 pairs F2: 5,9,4,8 # reduction candidate for 5,9 F2: 5,9 => CTR * 456328719782619354193...862349281675268...931.1....428.248..197.314..286.7.1.2543 * PAIR RESTART * PAIR H2: 5,9 ROW 2 B2: 5,9,2,4,8 # reduction candidate for 5,9 B2: 5,9 # 16 pairs C2: 5,9,2,8 # reduction candidate for 5,9 C2: 5,9 # 16 pairs * PAIR E6: 3,6 COL E E7: 3,6,5,9 # reduction candidate for 3,6 E7: 3,6 # 16 pairs E7: 5,9 # 13 pairs * PAIR F6: 3,6 COL F F7: 3,6,2,5,9 # reduction candidate for 3,6 F7: 3,6 # 15 pairs F7: 2,5,9 # 14 pairs * PAIR G5: 7,9 BLK 6 G6: 7,9,4 # reduction candidate for 7,9 G6: 7,9 => SOLVED * 986327415745618392123954876392781654568249731417536928254893167631475289879162543 * DURATION: 0:00:16.838036 START: 13:04:53.193375 END: 13:05:10.031411 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-295-base-pr-001.dot * REASONING * DIS # I2: 5,9 => CTR => I2: 2,4 * DIS I2: 2,4 # H3: 5,9 => CTR => H3: 6,7 * DIS I2: 2,4 + H3: 6,7 # I3: 5,9 => CTR => I3: 2,4,6 * DIS I2: 2,4 + H3: 6,7 + I3: 2,4,6 # I1: 4 => CTR => I1: 5,9 * DIS I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 # F2: 5,9 => CTR => F2: 4,8 * PRF I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # G6: 7,9 => SOL * STA I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 + G6: 7,9 * CNT 6 HDP CHAINS / 16 HYP OPENED
Header Info
Top 500 Minimum 17 295 solution: 986327415745618392123954876392781654568249731417536928254893167631475289879162543 info: 2417 FNBTHWY S8.f 8699 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 986327415745618392123954876392781654568249731417536928254893167631475289879162543 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: 5,9 => UNS * DIS # I2: 5,9 => CTR => I2: 2,4 * INC # I2: 2,4 => UNS * DIS # H3: 5,9 => CTR => H3: 6,7 * INC # H3: 6,7 => UNS * DIS # I3: 5,9 => CTR => I3: 2,4,6 * INC # I3: 2,4,6 => UNS * INC # B2: 5,9 => UNS * INC # C2: 5,9 => UNS * DIS # F2: 5,9 => CTR => F2: 4,8 * INC # F2: 4,8 => UNS * PRF # H4: 5,9 => SOL * DIS # H4: 7 => CTR => H4: 5,9 * INC # E7: 3,6 => UNS * INC # E7: 5,9 => UNS * INC # F7: 3,6 => UNS * INC # F7: 2,5,9 => UNS * DIS # H4: 7,9 => CTR => H4: 5 * PRF # H4: 5 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 4 => CTR => G6: 7,9 * INC # C5: 7,9 => UNS * INC # D5: 7,9 => UNS * INC # E5: 7,9 => UNS * INC # F5: 7,9 => UNS * DIS # G1: 7,9 => CTR => G1: 4 * PRF # G1: 4 => SOL * INC # E7: 6,9 => UNS * DIS # F7: 6,9 => CTR => F7: 2,3,5 * INC # F7: 2,3,5 => UNS * DIS # E8: 6,9 => CTR => E8: 5,7 * INC # E8: 5,7 => UNS * INC # F8: 6,9 => UNS * INC # F9: 6,9 => UNS * INC # A9: 6,9 => UNS * INC # C9: 6,9 => UNS * INC # A7: 6,9 => UNS * INC # E7: 6,9 => UNS * DIS # F7: 6,9 => CTR => F7: 2,3,5 * INC # F7: 2,3,5 => UNS * DIS # H3: 6,9 => CTR => H3: 5,7 * PRF # H3: 5,7 => SOL * INC # A8: 6,9 => UNS * DIS # E8: 6,9 => CTR => E8: 5,7 * INC # E8: 5,7 => UNS * INC # F8: 6,9 => UNS * PRF # I3: 6,9 => SOL * DIS # I3: 2,4,5 => CTR => I3: 6,9 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I1: 5,9 => UNS * DIS # I2: 5,9 => CTR => I2: 2,4 * DIS I2: 2,4 # H3: 5,9 => CTR => H3: 6,7 * DIS I2: 2,4 + H3: 6,7 # I3: 5,9 => CTR => I3: 2,4,6 * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 # I1: 5,9 => UNS * DIS I2: 2,4 + H3: 6,7 + I3: 2,4,6 # I1: 4 => CTR => I1: 5,9 * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 # B2: 5,9 => UNS * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 # C2: 5,9 => UNS * DIS I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 # F2: 5,9 => CTR => F2: 4,8 * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # B2: 5,9 => UNS * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # C2: 5,9 => UNS * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # E7: 3,6 => UNS * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # E7: 5,9 => UNS * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # F7: 3,6 => UNS * INC I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # F7: 2,5,9 => UNS * PRF I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 # G6: 7,9 => SOL * STA I2: 2,4 + H3: 6,7 + I3: 2,4,6 + I1: 5,9 + F2: 4,8 + G6: 7,9 * CNT 16 HDP CHAINS / 16 HYP OPENED