Analysis of xx-top95-005-base.sdk
Contents
Original Sudoku
level: medium
position: ....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8... initial
Autosolve
position: .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 5,9 => CTR => A2: 1,4,8 * PRF # A3: 5,9 => SOL * DIS # A6: 5,9 => CTR => A6: 3,4,7 * DIS # A2: 5,8 => CTR => A2: 1,4,9 * DIS # C2: 5,8 => CTR => C2: 4,9 * PRF # H9: 5,9 => SOL * DIS # A2: 5,9 => CTR => A2: 1,4,8 * DIS # C7: 7 => CTR => C7: 5,8 * DIS # A8: 4,9 => CTR => A8: 3,7 * DIS # C8: 4,9 => CTR => C8: 3,7 * DIS # C7: 8 => CTR => C7: 5,7 * PRF # H9: 5,9 => SOL * PRF # A9: 4 => SOL * CNT 13 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 5,9 => CTR => A2: 1,4,8 * PRF A2: 1,4,8 # A3: 5,9 => SOL * STA A2: 1,4,8 + A3: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8... | initial |
| .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83.. | autosolve |
| 962314857134587269578296413847962531651873942329145786285639174793451628416728395 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A1: 5,9 D2: 5,8 H1: 5,9 H2: 1,6 I2: 5,9 H3: 1,6 D5: 5,8 D6: 1,4 G4: 5,7 I4: 1,6 I6: 1,6 B7: 5,8 B8: 4,9 E7: 3,9 F7: 3,9 D8: 1,4 F8: 1,2 E9: 2,4 H7: 5,7 I9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 19 pairs (_) / A3 = 1 => 23 pairs (_) H2,H3: 1.. / H2 = 1 => 23 pairs (_) / H3 = 1 => 19 pairs (_) I4,I6: 1.. / I4 = 1 => 18 pairs (_) / I6 = 1 => 18 pairs (_) D8,F8: 1.. / D8 = 1 => 20 pairs (_) / F8 = 1 => 0 pairs (*) A2,H2: 1.. / A2 = 1 => 19 pairs (_) / H2 = 1 => 23 pairs (_) A3,H3: 1.. / A3 = 1 => 23 pairs (_) / H3 = 1 => 19 pairs (_) F4,I4: 1.. / F4 = 1 => 18 pairs (_) / I4 = 1 => 18 pairs (_) D6,D8: 1.. / D6 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) B4,B6: 2.. / B4 = 2 => 20 pairs (_) / B6 = 2 => 22 pairs (_) F8,E9: 2.. / F8 = 2 => 20 pairs (_) / E9 = 2 => 0 pairs (*) H8,H9: 2.. / H8 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) F8,H8: 2.. / F8 = 2 => 20 pairs (_) / H8 = 2 => 0 pairs (*) E9,H9: 2.. / E9 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) A6,C6: 3.. / A6 = 3 => 20 pairs (_) / C6 = 3 => 20 pairs (_) E5,F5: 3.. / E5 = 3 => 20 pairs (_) / F5 = 3 => 20 pairs (_) A8,C8: 3.. / A8 = 3 => 20 pairs (_) / C8 = 3 => 20 pairs (_) E7,F7: 3.. / E7 = 3 => 20 pairs (_) / F7 = 3 => 20 pairs (_) A6,A8: 3.. / A6 = 3 => 20 pairs (_) / A8 = 3 => 20 pairs (_) C6,C8: 3.. / C6 = 3 => 20 pairs (_) / C8 = 3 => 20 pairs (_) E5,E7: 3.. / E5 = 3 => 20 pairs (_) / E7 = 3 => 20 pairs (_) F5,F7: 3.. / F5 = 3 => 20 pairs (_) / F7 = 3 => 20 pairs (_) A2,C2: 4.. / A2 = 4 => 26 pairs (_) / C2 = 4 => 20 pairs (_) D8,E9: 4.. / D8 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) A9,E9: 4.. / A9 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) D6,D8: 4.. / D6 = 4 => 20 pairs (_) / D8 = 4 => 0 pairs (*) H1,I2: 5.. / H1 = 5 => 0 pairs (*) / I2 = 5 => 0 pairs (X) A1,H1: 5.. / A1 = 5 => 0 pairs (X) / H1 = 5 => 0 pairs (_) D2,D5: 5.. / D2 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) I2,I9: 5.. / I2 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) H2,H3: 6.. / H2 = 6 => 19 pairs (_) / H3 = 6 => 23 pairs (_) I4,I6: 6.. / I4 = 6 => 18 pairs (_) / I6 = 6 => 18 pairs (_) E2,F2: 7.. / E2 = 7 => 21 pairs (_) / F2 = 7 => 21 pairs (_) H7,H8: 7.. / H7 = 7 => 24 pairs (_) / H8 = 7 => 0 pairs (X) C7,H7: 7.. / C7 = 7 => 0 pairs (X) / H7 = 7 => 24 pairs (_) B7,C7: 8.. / B7 = 8 => 21 pairs (_) / C7 = 8 => 0 pairs (X) D2,D5: 8.. / D2 = 8 => 22 pairs (_) / D5 = 8 => 0 pairs (*) H1,I2: 9.. / H1 = 9 => 0 pairs (X) / I2 = 9 => 0 pairs (_) G5,G6: 9.. / G5 = 9 => 25 pairs (_) / G6 = 9 => 23 pairs (_) E7,F7: 9.. / E7 = 9 => 20 pairs (_) / F7 = 9 => 20 pairs (_) A1,H1: 9.. / A1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) B5,G5: 9.. / B5 = 9 => 23 pairs (_) / G5 = 9 => 25 pairs (_) I2,I9: 9.. / I2 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) * DURATION: 0:01:42.163175 START: 22:53:13.397832 END: 22:54:55.561007 2017-05-03 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D2,D5,D6,D8,E7,E9,F7,F8,G4,H1,H2,H3,H7,I2,I4,I6,I9) * .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83.. * PAIR A1: 5,9 BLK 1 A2: 5,9,1,4,8 # reduction candidate for 5,9 A2: 5,9 => CTR * .623148.7.348..21.1782954638..9..53.691583742.53...98.285639174..9.5.6.8.167.83.. A2: 1,4,8 # 20 pairs C2: 5,9,4,8 # reduction candidate for 5,9 C2: 5,9 # 18 pairs A3: 5,9,1,8 # reduction candidate for 5,9 A3: 5,9 => SOLVED * 962314857134587269578296413847962531651873942329145786285639174793451628416728395 A3: 1,8 # 21 pairs C3: 5,9,8 # reduction candidate for 5,9 C3: 5,9 # 23 pairs * PAIR A1: 5,9 COL A A6: 5,9,3,4,7 # reduction candidate for 5,9 A6: 5,9 => CTR * 562314897.34...2.5.792.54.37.89..53.6.15837429.3....8.2856..1743.7.5.6.84167283.. A6: 3,4,7 # 20 pairs A9: 5,9,4 # reduction candidate for 5,9 A9: 5,9 # 20 pairs * PAIR D2: 5,8 ROW 2 A2: 5,8,1,4,9 # reduction candidate for 5,8 A2: 5,8 => CTR * 9623148575348..2191782954638.79..531651...9423.91..7862..6..174793451628416728395 A2: 1,4,9 # 20 pairs C2: 5,8,4,9 # reduction candidate for 5,8 C2: 5,8 => CTR * .6231485743....21917.2..4638..9...3.6.1....42...4...8.2856..1.4...1526.8.1674832. C2: 4,9 # 21 pairs * PAIR H1: 5,9 COL H H9: 5,9,2 # reduction candidate for 5,9 H9: 5,9 => SOLVED * 962314857134587269578296413847962531651873942329145786285639174793451628416728395 H9: 2 # 20 pairs * PAIR I2: 5,9 ROW 2 A2: 5,9,1,4,8 # reduction candidate for 5,9 A2: 5,9 => CTR * .623148.7.348..21.1782954638..9..53.691583742.53...98.285639174..9.5.6.8.167.83.. A2: 1,4,8 # 20 pairs C2: 5,9,4,8 # reduction candidate for 5,9 C2: 5,9 # 18 pairs F2: 5,9,6,7 # reduction candidate for 5,9 F2: 5,9 # 22 pairs * PAIR D5: 5,8 ROW 5 B5: 5,8,9 # reduction candidate for 5,8 B5: 5,8 # 25 pairs B5: 9 # 23 pairs * PAIR G4: 5,7 BLK 6 G5: 5,7,9 # reduction candidate for 5,7 G5: 5,7 # 23 pairs G6: 5,7,9 # reduction candidate for 5,7 G6: 5,7 # 25 pairs * PAIR G4: 5,7 ROW 4 A4: 5,7,4,8 # reduction candidate for 5,7 A4: 5,7 # 27 pairs C4: 5,7,4,8 # reduction candidate for 5,7 C4: 5,7 # 24 pairs F4: 5,7,1,2,6 # reduction candidate for 5,7 F4: 5,7 # 26 pairs * PAIR I4: 1,6 ROW 4 F4: 1,6,2,5,7 # reduction candidate for 1,6 F4: 2,5,7 # 21 pairs F4: 1,6 # 21 pairs * PAIR I6: 1,6 ROW 6 F6: 1,6,2,5,7 # reduction candidate for 1,6 F6: 1,6 # 22 pairs F6: 2,5,7 # 20 pairs * PAIR B7: 5,8 BLK 7 C7: 5,8,7 # reduction candidate for 5,8 C7: 7 => CTR * .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2876..154....5.678516748329 C7: 5,8 # 24 pairs * PAIR B7: 5,8 COL B B4: 5,8,2,4 # reduction candidate for 5,8 B4: 5,8 # 25 pairs B5: 5,8,9 # reduction candidate for 5,8 B5: 5,8 # 25 pairs * PAIR B8: 4,9 BLK 7 A8: 4,9,3,7 # reduction candidate for 4,9 A8: 4,9 => CTR * .62314897.3....2.5.7.2.54.37..9..53.6.15...423......8.2.76..154..3.526785167.8329 A8: 3,7 # 21 pairs C8: 4,9,3,7 # reduction candidate for 4,9 C8: 4,9 => CTR * .62314897.3....2.5.7.2.54.3...9...3.6.15...42..3....8.2.76..1543...526785167.8329 C8: 3,7 # 21 pairs A9: 4,9,5 # reduction candidate for 4,9 A9: 4,9 # 24 pairs * PAIR B8: 4,9 COL B B6: 4,9,2,5 # reduction candidate for 4,9 B6: 4,9 # 25 pairs B6: 2,5 # 21 pairs * PAIR F8: 1,2 COL F F4: 1,2,5,6,7 # reduction candidate for 1,2 F4: 1,2 # 21 pairs F6: 1,2,5,6,7 # reduction candidate for 1,2 F6: 1,2 # 19 pairs * PAIR E9: 2,4 COL E E4: 2,4,6,7,8 # reduction candidate for 2,4 E4: 2,4 # 24 pairs E6: 2,4,6,7 # reduction candidate for 2,4 E6: 2,4 # 21 pairs * PAIR H7: 5,7 ROW 7 C7: 5,7,8 # reduction candidate for 5,7 C7: 8 => CTR * .623148.7.34...2...7.2..4.34..9...3.6.1....42.......8.2586..174.4.152698916748325 C7: 5,7 # 21 pairs * PAIR I9: 5,9 BLK 9 H9: 5,9,2 # reduction candidate for 5,9 H9: 5,9 => SOLVED * 962314857134587269578296413847962531651873942329145786285639174793451628416728395 H9: 2 # 20 pairs * PAIR I9: 5,9 ROW 9 A9: 5,9,4 # reduction candidate for 5,9 A9: 4 => SOLVED * 962314857134587269578296413847962531651873942329145786285639174793451628416728395 A9: 5,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-005-base-pr-000.dot * REASONING * DIS # A2: 5,9 => CTR => A2: 1,4,8 * PRF # A3: 5,9 => SOL * DIS # A6: 5,9 => CTR => A6: 3,4,7 * DIS # A2: 5,8 => CTR => A2: 1,4,9 * DIS # C2: 5,8 => CTR => C2: 4,9 * PRF # H9: 5,9 => SOL * DIS # A2: 5,9 => CTR => A2: 1,4,8 * DIS # C7: 7 => CTR => C7: 5,8 * DIS # A8: 4,9 => CTR => A8: 3,7 * DIS # C8: 4,9 => CTR => C8: 3,7 * DIS # C7: 8 => CTR => C7: 5,7 * PRF # H9: 5,9 => SOL * PRF # A9: 4 => SOL * CNT 13 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D2,D5,D6,D8,E7,E9,F7,F8,G4,H1,H2,H3,H7,I2,I4,I6,I9) * .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83.. * PAIR A1: 5,9 BLK 1 A2: 5,9,1,4,8 # reduction candidate for 5,9 A2: 5,9 => CTR * .623148.7.348..21.1782954638..9..53.691583742.53...98.285639174..9.5.6.8.167.83.. C2: 5,9,4,8 # reduction candidate for 5,9 C2: 5,9 # 18 pairs A3: 5,9,1,8 # reduction candidate for 5,9 A3: 5,9 => SOLVED * 962314857134587269578296413847962531651873942329145786285639174793451628416728395 * DURATION: 0:00:06.221203 START: 22:56:04.435517 END: 22:56:10.656720 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-005-base-pr-001.dot * REASONING * DIS # A2: 5,9 => CTR => A2: 1,4,8 * PRF A2: 1,4,8 # A3: 5,9 => SOL * STA A2: 1,4,8 + A3: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 95 Sudokus 005 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 962314857134587269578296413847962531651873942329145786285639174793451628416728395 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:
* DIS # A2: 5,9 => CTR => A2: 1,4,8 * INC # A2: 1,4,8 => UNS * INC # C2: 5,9 => UNS * PRF # A3: 5,9 => SOL * INC # A3: 1,8 => UNS * INC # C3: 5,9 => UNS * DIS # A6: 5,9 => CTR => A6: 3,4,7 * INC # A6: 3,4,7 => UNS * INC # A9: 5,9 => UNS * DIS # A2: 5,8 => CTR => A2: 1,4,9 * INC # A2: 1,4,9 => UNS * DIS # C2: 5,8 => CTR => C2: 4,9 * INC # C2: 4,9 => UNS * PRF # H9: 5,9 => SOL * INC # H9: 2 => UNS * DIS # A2: 5,9 => CTR => A2: 1,4,8 * INC # A2: 1,4,8 => UNS * INC # C2: 5,9 => UNS * INC # F2: 5,9 => UNS * INC # B5: 5,8 => UNS * INC # B5: 9 => UNS * INC # G5: 5,7 => UNS * INC # G6: 5,7 => UNS * INC # A4: 5,7 => UNS * INC # C4: 5,7 => UNS * INC # F4: 5,7 => UNS * INC # F4: 1,6 => UNS * INC # F4: 2,5,7 => UNS * INC # F6: 1,6 => UNS * INC # F6: 2,5,7 => UNS * INC # C7: 5,8 => UNS * DIS # C7: 7 => CTR => C7: 5,8 * INC # B4: 5,8 => UNS * INC # B5: 5,8 => UNS * DIS # A8: 4,9 => CTR => A8: 3,7 * INC # A8: 3,7 => UNS * DIS # C8: 4,9 => CTR => C8: 3,7 * INC # C8: 3,7 => UNS * INC # A9: 4,9 => UNS * INC # B6: 4,9 => UNS * INC # B6: 2,5 => UNS * INC # F4: 1,2 => UNS * INC # F6: 1,2 => UNS * INC # E4: 2,4 => UNS * INC # E6: 2,4 => UNS * INC # C7: 5,7 => UNS * DIS # C7: 8 => CTR => C7: 5,7 * PRF # H9: 5,9 => SOL * INC # H9: 2 => UNS * INC # A9: 5,9 => UNS * PRF # A9: 4 => SOL * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 5,9 => CTR => A2: 1,4,8 * INC A2: 1,4,8 # C2: 5,9 => UNS * PRF A2: 1,4,8 # A3: 5,9 => SOL * STA A2: 1,4,8 + A3: 5,9 * CNT 3 HDP CHAINS / 3 HYP OPENED