Analysis of xx-top95-029-base.sdk
Contents
Original Sudoku
level: medium
position: .47.8...1............6..7..6....357......5....1..6....28..4.....9.1...4.....2.69. initial
Autosolve
position: .47.8..61.6..........6..7..62..1357......5..6.1..6....28..4.....9.1...4.....2.69. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 3,5 => SOL * DIS # A3: 3,5 => CTR => A3: 1,8,9 * DIS # C3: 3,5 => CTR => C3: 1,2,8,9 * DIS # H3: 3,5 => CTR => H3: 2,8 * DIS # I3: 3,5 => CTR => I3: 2,4,8,9 * PRF # B9: 7 => SOL * DIS # D1: 2,9 => CTR => D1: 3,5 * PRF # B9: 3,7 => SOL * DIS # B9: 5 => CTR => B9: 3,7 * DIS # D5: 7,9 => CTR => D5: 2,4,8 * PRF # A5: 7,9 => SOL * CNT 11 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 3,5 => SOL * STA C2: 3,5 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .47.8...1............6..7..6....357......5....1..6....28..4.....9.1...4.....2.69. | initial |
| .47.8..61.6..........6..7..62..1357......5..6.1..6....28..4.....9.1...4.....2.69. | autosolve |
| 947582361863471952152639784624813579738295416519764823285946137396157248471328695 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B3: 3,5 F1: 2,9 B5: 3,7 E5: 7,9 A9: 1,4 C9: 1,4 F9: 7,8 G7: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 1.. / F2 = 1 => 8 pairs (_) / F3 = 1 => 9 pairs (_) G5,H5: 1.. / G5 = 1 => 13 pairs (_) / H5 = 1 => 8 pairs (_) A9,C9: 1.. / A9 = 1 => 9 pairs (_) / C9 = 1 => 6 pairs (_) G7,H7: 1.. / G7 = 1 => 8 pairs (_) / H7 = 1 => 13 pairs (_) G5,G7: 1.. / G5 = 1 => 13 pairs (_) / G7 = 1 => 8 pairs (_) H5,H7: 1.. / H5 = 1 => 8 pairs (_) / H7 = 1 => 13 pairs (_) C2,C3: 2.. / C2 = 2 => 8 pairs (_) / C3 = 2 => 8 pairs (_) G8,I8: 2.. / G8 = 2 => 10 pairs (_) / I8 = 2 => 9 pairs (_) A9,C9: 4.. / A9 = 4 => 6 pairs (_) / C9 = 4 => 9 pairs (_) F3,I3: 4.. / F3 = 4 => 8 pairs (_) / I3 = 4 => 9 pairs (_) A6,C6: 5.. / A6 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) A1,D1: 5.. / A1 = 5 => 0 pairs (X) / D1 = 5 => 12 pairs (_) B3,B9: 5.. / B3 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) C7,C8: 6.. / C7 = 6 => 12 pairs (_) / C8 = 6 => 13 pairs (_) F7,F8: 6.. / F7 = 6 => 13 pairs (_) / F8 = 6 => 12 pairs (_) C7,F7: 6.. / C7 = 6 => 12 pairs (_) / F7 = 6 => 13 pairs (_) C8,F8: 6.. / C8 = 6 => 13 pairs (_) / F8 = 6 => 12 pairs (_) A8,B9: 7.. / A8 = 7 => 12 pairs (_) / B9 = 7 => 0 pairs (*) B5,B9: 7.. / B5 = 7 => 12 pairs (_) / B9 = 7 => 0 pairs (*) D7,F7: 9.. / D7 = 9 => 12 pairs (_) / F7 = 9 => 12 pairs (_) * DURATION: 0:00:24.108877 START: 23:25:27.935821 END: 23:25:52.044698 2017-05-03 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,B5,C9,E5,F1,F9,G7) * .47.8..61.6..........6..7..62..1357......5..6.1..6....28..4.....9.1...4.....2.69. * PAIR B3: 3,5 BLK 1 A1: 3,5,9 # reduction candidate for 3,5 A1: 3,5 # 9 pairs A2: 3,5,1,8,9 # reduction candidate for 3,5 A2: 3,5 # 13 pairs C2: 3,5,1,2,8,9 # reduction candidate for 3,5 C2: 3,5 => SOLVED * 947582361863471952152639784624813579738295416519764823285946137396157248471328695 C2: 1,2,8,9 # 8 pairs A3: 3,5,1,8,9 # reduction candidate for 3,5 A3: 3,5 => CTR * 947582361.6..3.......69.7..62..1357.....75..6715.6....28..4.1...9.15..4.....2.69. A3: 1,8,9 # 8 pairs C3: 3,5,1,2,8,9 # reduction candidate for 3,5 C3: 3,5 => CTR * .47.8..61.62.........6..7..62..1357......5..6.1..6....28..4.....9.1...4.4.1.2.69. C3: 1,2,8,9 # 8 pairs * PAIR B3: 3,5 ROW 3 E3: 3,5,9 # reduction candidate for 3,5 E3: 3,5 # 10 pairs H3: 3,5,2,8 # reduction candidate for 3,5 H3: 3,5 => CTR * .47.82.61.6........5.69.73.62..1357..3..75..6715.6....28..4....59.13..4..7.528693 H3: 2,8 # 9 pairs I3: 3,5,2,4,8,9 # reduction candidate for 3,5 I3: 3,5 => CTR * .47.82.61.6.7.1....5.6947.362..1357..3..75..6715.69...28.94....59.13..4..7..2869. I3: 2,4,8,9 # 8 pairs * PAIR B3: 3,5 COL B B9: 3,5,7 # reduction candidate for 3,5 B9: 7 => SOLVED * 947582361863471952152639784624813579738295416519764823285946137396157248471328695 B9: 3,5 # 12 pairs * PAIR F1: 2,9 BLK 2 D1: 2,9,3,5 # reduction candidate for 2,9 D1: 2,9 => CTR * 547.8.361.6..7.....3.65.7..62..1357..7..95.16.15.6....28.5491377931...4..5..2.69. D1: 3,5 # 9 pairs D2: 2,9,3,4,5,7 # reduction candidate for 2,9 D2: 2,9 # 15 pairs F2: 2,9,1,4,7 # reduction candidate for 2,9 F2: 2,9 # 19 pairs F3: 2,9,1,4 # reduction candidate for 2,9 F3: 2,9 # 15 pairs * PAIR F1: 2,9 ROW 1 G1: 2,9,3 # reduction candidate for 2,9 G1: 2,9 # 11 pairs G1: 3 # 10 pairs * PAIR F1: 2,9 COL F F6: 2,9,4,7,8 # reduction candidate for 2,9 F6: 2,9 # 15 pairs F6: 4,7,8 # 8 pairs * PAIR B5: 3,7 BLK 4 A5: 3,7,4,8,9 # reduction candidate for 3,7 A5: 3,7 # 13 pairs A6: 3,7,4,5,8,9 # reduction candidate for 3,7 A6: 3,7 # 13 pairs * PAIR B5: 3,7 COL B B9: 3,7,5 # reduction candidate for 3,7 B9: 3,7 => SOLVED * 947582361863471952152639784624813579738295416519764823285946137396157248471328695 B9: 5 => CTR * .47.8..61.6..7.....3.65.7..62..1357..7..95..6.1..6....28.549..779.136.4..5..2.69. * PAIR E5: 7,9 BLK 5 D5: 7,9,2,4,8 # reduction candidate for 7,9 D5: 7,9 => CTR * .4758..61.6........5.6..7..629.1357..3...5..6715.6....28..4....59.1...4..7.328695 D5: 2,4,8 # 8 pairs D6: 7,9,2,4,8 # reduction candidate for 7,9 D6: 7,9 # 10 pairs F6: 7,9,2,4,8 # reduction candidate for 7,9 F6: 7,9 # 12 pairs * PAIR E5: 7,9 ROW 5 A5: 7,9,3,4,8 # reduction candidate for 7,9 A5: 7,9 => SOLVED * 947582361863471952152639784624813579738295416519764823285946137396157248471328695 A5: 3,4,8 # 8 pairs * PAIR E5: 7,9 COL E E2: 7,9,3,5 # reduction candidate for 7,9 E2: 7,9 # 12 pairs E2: 3,5 # 12 pairs * PAIR F9: 7,8 BLK 8 F8: 7,8,6 # reduction candidate for 7,8 F8: 7,8 # 13 pairs D9: 7,8,3,5 # reduction candidate for 7,8 D9: 7,8 # 21 pairs * PAIR F9: 7,8 ROW 9 I9: 7,8,3,5 # reduction candidate for 7,8 I9: 7,8 # 15 pairs I9: 3,5 # 13 pairs * PAIR F9: 7,8 COL F F6: 7,8,2,4,9 # reduction candidate for 7,8 F6: 7,8 # 14 pairs F6: 2,4,9 # 8 pairs * PAIR G7: 1,3 BLK 9 H7: 1,3,5 # reduction candidate for 1,3 H7: 1,3 # 12 pairs H7: 5 # 9 pairs * PAIR G7: 1,3 COL G G5: 1,3,2,4,8,9 # reduction candidate for 1,3 G5: 1,3 # 13 pairs G5: 2,4,8,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-029-base-pr-000.dot * REASONING * PRF # C2: 3,5 => SOL * DIS # A3: 3,5 => CTR => A3: 1,8,9 * DIS # C3: 3,5 => CTR => C3: 1,2,8,9 * DIS # H3: 3,5 => CTR => H3: 2,8 * DIS # I3: 3,5 => CTR => I3: 2,4,8,9 * PRF # B9: 7 => SOL * DIS # D1: 2,9 => CTR => D1: 3,5 * PRF # B9: 3,7 => SOL * DIS # B9: 5 => CTR => B9: 3,7 * DIS # D5: 7,9 => CTR => D5: 2,4,8 * PRF # A5: 7,9 => SOL * CNT 11 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,B5,C9,E5,F1,F9,G7) * .47.8..61.6..........6..7..62..1357......5..6.1..6....28..4.....9.1...4.....2.69. * PAIR B3: 3,5 BLK 1 A1: 3,5,9 # reduction candidate for 3,5 A1: 3,5 # 9 pairs A2: 3,5,1,8,9 # reduction candidate for 3,5 A2: 3,5 # 13 pairs C2: 3,5,1,2,8,9 # reduction candidate for 3,5 C2: 3,5 => SOLVED * 947582361863471952152639784624813579738295416519764823285946137396157248471328695 * DURATION: 0:00:03.942484 START: 23:26:24.374668 END: 23:26:28.317152 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-029-base-pr-001.dot * REASONING * PRF # C2: 3,5 => SOL * STA C2: 3,5 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 95 Sudokus 029 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 947582361863471952152639784624813579738295416519764823285946137396157248471328695 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: 3,5 => UNS * INC # A2: 3,5 => UNS * PRF # C2: 3,5 => SOL * INC # C2: 1,2,8,9 => UNS * DIS # A3: 3,5 => CTR => A3: 1,8,9 * INC # A3: 1,8,9 => UNS * DIS # C3: 3,5 => CTR => C3: 1,2,8,9 * INC # C3: 1,2,8,9 => UNS * INC # E3: 3,5 => UNS * DIS # H3: 3,5 => CTR => H3: 2,8 * INC # H3: 2,8 => UNS * DIS # I3: 3,5 => CTR => I3: 2,4,8,9 * INC # I3: 2,4,8,9 => UNS * INC # B9: 3,5 => UNS * PRF # B9: 7 => SOL * DIS # D1: 2,9 => CTR => D1: 3,5 * INC # D1: 3,5 => UNS * INC # D2: 2,9 => UNS * INC # F2: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # G1: 2,9 => UNS * INC # G1: 3 => UNS * INC # F6: 2,9 => UNS * INC # F6: 4,7,8 => UNS * INC # A5: 3,7 => UNS * INC # A6: 3,7 => UNS * PRF # B9: 3,7 => SOL * DIS # B9: 5 => CTR => B9: 3,7 * DIS # D5: 7,9 => CTR => D5: 2,4,8 * INC # D5: 2,4,8 => UNS * INC # D6: 7,9 => UNS * INC # F6: 7,9 => UNS * PRF # A5: 7,9 => SOL * INC # A5: 3,4,8 => UNS * INC # E2: 7,9 => UNS * INC # E2: 3,5 => UNS * INC # F8: 7,8 => UNS * INC # D9: 7,8 => UNS * INC # I9: 7,8 => UNS * INC # I9: 3,5 => UNS * INC # F6: 7,8 => UNS * INC # F6: 2,4,9 => UNS * INC # H7: 1,3 => UNS * INC # H7: 5 => UNS * INC # G5: 1,3 => UNS * INC # G5: 2,4,8,9 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,5 => UNS * INC # A2: 3,5 => UNS * PRF # C2: 3,5 => SOL * STA C2: 3,5 * CNT 3 HDP CHAINS / 3 HYP OPENED