Analysis of xx-top95-041-base.sdk
Contents
Original Sudoku
level: medium
position: ...5.1....9....8...6.......4.1..........7..9........3.8.....1.5...2..4.....36.... initial
Autosolve
position: .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,7 => CTR => A2: 1,3,5 * DIS # C2: 2,7 => CTR => C2: 3,5 * PRF # A3: 2,7 => SOL * DIS # A6: 2,7 => CTR => A6: 6,9 * PRF # F2: 2,3 => SOL * DIS # A2: 2,3 => CTR => A2: 1,5,7 * DIS # C2: 2,3 => CTR => C2: 5,7 * PRF # H9: 2,7 => SOL * DIS # A2: 2,7 => CTR => A2: 1,3,5 * DIS # C2: 2,7 => CTR => C2: 3,5 * DIS # A5: 2,6 => CTR => A5: 3,5 * DIS # C7: 6 => CTR => C7: 2,3 * DIS # A8: 5,7 => CTR => A8: 6,9 * DIS # C8: 5,7 => CTR => C8: 6,9 * DIS # C7: 3 => CTR => C7: 2,6 * PRF # H9: 2,7 => SOL * PRF # A9: 5 => SOL * CNT 17 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,7 => CTR => A2: 1,3,5 * DIS A2: 1,3,5 # C2: 2,7 => CTR => C2: 3,5 * PRF A2: 1,3,5 + C2: 3,5 # A3: 2,7 => SOL * STA A2: 1,3,5 + C2: 3,5 + A3: 2,7 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5.1....9....8...6.......4.1..........7..9........3.8.....1.5...2..4.....36.... | initial |
| .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9.. | autosolve |
| 748591326195623847263487519421936758356874291987152634832749165679215483514368972 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) A1: 2,7 E2: 2,3 D3: 4,7 H1: 2,7 H2: 1,4 I2: 2,7 H3: 1,4 D4: 6,9 E4: 2,3 D5: 1,8 D6: 1,8 G5: 2,6 I5: 1,4 I6: 1,4 B7: 2,3 B8: 5,7 D7: 7,9 F7: 7,9 F8: 5,8 F9: 5,8 H7: 2,6 I9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 21 pairs (_) / A3 = 1 => 20 pairs (_) H2,H3: 1.. / H2 = 1 => 20 pairs (_) / H3 = 1 => 21 pairs (_) D5,D6: 1.. / D5 = 1 => 22 pairs (_) / D6 = 1 => 20 pairs (_) I5,I6: 1.. / I5 = 1 => 20 pairs (_) / I6 = 1 => 22 pairs (_) A2,H2: 1.. / A2 = 1 => 21 pairs (_) / H2 = 1 => 20 pairs (_) A3,H3: 1.. / A3 = 1 => 20 pairs (_) / H3 = 1 => 21 pairs (_) D5,I5: 1.. / D5 = 1 => 22 pairs (_) / I5 = 1 => 20 pairs (_) D6,I6: 1.. / D6 = 1 => 20 pairs (_) / I6 = 1 => 22 pairs (_) H1,I2: 2.. / H1 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) A1,H1: 2.. / A1 = 2 => 0 pairs (X) / H1 = 2 => 0 pairs (_) E2,E4: 2.. / E2 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) I2,I9: 2.. / I2 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) B7,C7: 3.. / B7 = 3 => 23 pairs (_) / C7 = 3 => 0 pairs (X) E2,E4: 3.. / E2 = 3 => 24 pairs (_) / E4 = 3 => 0 pairs (*) D2,D3: 4.. / D2 = 4 => 20 pairs (_) / D3 = 4 => 21 pairs (_) H2,H3: 4.. / H2 = 4 => 21 pairs (_) / H3 = 4 => 20 pairs (_) F5,F6: 4.. / F5 = 4 => 20 pairs (_) / F6 = 4 => 22 pairs (_) I5,I6: 4.. / I5 = 4 => 22 pairs (_) / I6 = 4 => 20 pairs (_) D2,H2: 4.. / D2 = 4 => 20 pairs (_) / H2 = 4 => 21 pairs (_) D3,H3: 4.. / D3 = 4 => 21 pairs (_) / H3 = 4 => 20 pairs (_) F5,I5: 4.. / F5 = 4 => 20 pairs (_) / I5 = 4 => 22 pairs (_) F6,I6: 4.. / F6 = 4 => 22 pairs (_) / I6 = 4 => 20 pairs (_) A2,C2: 5.. / A2 = 5 => 0 pairs (X) / C2 = 5 => 22 pairs (_) F8,F9: 5.. / F8 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) A9,F9: 5.. / A9 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) B5,B8: 5.. / B5 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) D2,F2: 6.. / D2 = 6 => 17 pairs (_) / F2 = 6 => 23 pairs (_) H7,H8: 6.. / H7 = 6 => 26 pairs (_) / H8 = 6 => 0 pairs (X) C7,H7: 6.. / C7 = 6 => 0 pairs (X) / H7 = 6 => 26 pairs (_) D2,D4: 6.. / D2 = 6 => 17 pairs (_) / D4 = 6 => 23 pairs (_) H1,I2: 7.. / H1 = 7 => 0 pairs (X) / I2 = 7 => 0 pairs (_) G4,G6: 7.. / G4 = 7 => 28 pairs (_) / G6 = 7 => 27 pairs (_) D7,F7: 7.. / D7 = 7 => 17 pairs (_) / F7 = 7 => 23 pairs (_) A1,H1: 7.. / A1 = 7 => 0 pairs (*) / H1 = 7 => 0 pairs (X) B4,G4: 7.. / B4 = 7 => 27 pairs (_) / G4 = 7 => 28 pairs (_) I2,I9: 7.. / I2 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) B5,B6: 8.. / B5 = 8 => 22 pairs (_) / B6 = 8 => 20 pairs (_) D5,D6: 8.. / D5 = 8 => 20 pairs (_) / D6 = 8 => 22 pairs (_) F8,F9: 8.. / F8 = 8 => 24 pairs (_) / F9 = 8 => 0 pairs (*) H8,H9: 8.. / H8 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) B5,D5: 8.. / B5 = 8 => 22 pairs (_) / D5 = 8 => 20 pairs (_) B6,D6: 8.. / B6 = 8 => 20 pairs (_) / D6 = 8 => 22 pairs (_) F8,H8: 8.. / F8 = 8 => 24 pairs (_) / H8 = 8 => 0 pairs (*) F9,H9: 8.. / F9 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) A6,C6: 9.. / A6 = 9 => 22 pairs (_) / C6 = 9 => 22 pairs (_) D4,F4: 9.. / D4 = 9 => 17 pairs (_) / F4 = 9 => 23 pairs (_) A8,C8: 9.. / A8 = 9 => 22 pairs (_) / C8 = 9 => 22 pairs (_) D7,F7: 9.. / D7 = 9 => 23 pairs (_) / F7 = 9 => 17 pairs (_) A6,A8: 9.. / A6 = 9 => 22 pairs (_) / A8 = 9 => 22 pairs (_) C6,C8: 9.. / C6 = 9 => 22 pairs (_) / C8 = 9 => 22 pairs (_) D4,D7: 9.. / D4 = 9 => 17 pairs (_) / D7 = 9 => 23 pairs (_) F4,F7: 9.. / F4 = 9 => 23 pairs (_) / F7 = 9 => 17 pairs (_) * DURATION: 0:02:11.724745 START: 23:38:18.248230 END: 23:40:29.972975 2017-05-03 * CP COUNT: (52) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D3,D4,D5,D6,D7,E2,E4,F7,F8,F9,G5,H1,H2,H3,H7,I2,I5,I6,I9) * .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9.. * PAIR A1: 2,7 BLK 1 A2: 2,7,1,3,5 # reduction candidate for 2,7 A2: 2,7 => CTR * .485913.6.95...81.163.825494.1.2..5835.87..91.8.15..348...4.1.5...21.4.3.1436.9.. A2: 1,3,5 # 22 pairs C2: 2,7,3,5 # reduction candidate for 2,7 C2: 2,7 => CTR * .485913.659.43681.16378254947162..583...7..9.....5..3.83..4.1.5...21.4.3.1436598. C2: 3,5 # 23 pairs A3: 2,7,1,3 # reduction candidate for 2,7 A3: 2,7 => SOLVED * 748591326195623847263487519421936758356874291987152634832749165679215483514368972 A3: 1,3 # 23 pairs C3: 2,7,3 # reduction candidate for 2,7 C3: 2,7 # 25 pairs * PAIR A1: 2,7 COL A A6: 2,7,6,9 # reduction candidate for 2,7 A6: 2,7 => CTR * 248591376.95...8.2.67482519421.3..58653874291.8915..34832.4.1659762154835143689.. A6: 6,9 # 23 pairs A9: 2,7,5 # reduction candidate for 2,7 A9: 2,7 # 24 pairs * PAIR E2: 2,3 BLK 2 F2: 2,3,6,7 # reduction candidate for 2,3 F2: 2,3 => SOLVED * 748591326195623847263487519421936758356874291987152634832749165679215483514368972 F2: 6,7 # 24 pairs F3: 2,3,7 # reduction candidate for 2,3 F3: 2,3 # 24 pairs * PAIR E2: 2,3 ROW 2 A2: 2,3,1,5,7 # reduction candidate for 2,3 A2: 2,3 => CTR * 748591326.95426817162783549421639758.5687429198715263483.947165.79215483514368972 A2: 1,5,7 # 22 pairs C2: 2,3,5,7 # reduction candidate for 2,3 C2: 2,3 => CTR * .485913.659.4.681716.78.5494.16.9.583...7..9.....5..3.83.9471.5...218473714365982 C2: 5,7 # 23 pairs * PAIR D3: 4,7 BLK 2 D2: 4,7,6 # reduction candidate for 4,7 D2: 4,7 # 23 pairs D2: 6 # 17 pairs * PAIR H1: 2,7 COL H H9: 2,7,8 # reduction candidate for 2,7 H9: 2,7 => SOLVED * 748591326195623847263487519421936758356874291987152634832749165679215483514368972 H9: 8 # 24 pairs * PAIR I2: 2,7 ROW 2 A2: 2,7,1,3,5 # reduction candidate for 2,7 A2: 2,7 => CTR * .485913.6.95...81.163.825494.1.2..5835.87..91.8.15..348...4.1.5...21.4.3.1436.9.. A2: 1,3,5 # 22 pairs C2: 2,7,3,5 # reduction candidate for 2,7 C2: 2,7 => CTR * .485913.659.43681.16378254947162..583...7..9.....5..3.83..4.1.5...21.4.3.1436598. C2: 3,5 # 23 pairs F2: 2,7,3,6 # reduction candidate for 2,7 F2: 2,7 # 20 pairs * PAIR D4: 6,9 BLK 5 F4: 6,9,2,3 # reduction candidate for 6,9 F4: 6,9 # 25 pairs F4: 2,3 # 24 pairs * PAIR E4: 2,3 BLK 5 F4: 2,3,6,9 # reduction candidate for 2,3 F4: 2,3 # 24 pairs F5: 2,3,4,6 # reduction candidate for 2,3 F5: 2,3 # 25 pairs * PAIR E4: 2,3 ROW 4 B4: 2,3,7 # reduction candidate for 2,3 B4: 2,3 # 28 pairs B4: 7 # 27 pairs * PAIR G5: 2,6 BLK 6 G4: 2,6,7 # reduction candidate for 2,6 G4: 2,6 # 27 pairs G6: 2,6,7 # reduction candidate for 2,6 G6: 2,6 # 28 pairs * PAIR G5: 2,6 ROW 5 A5: 2,6,3,5 # reduction candidate for 2,6 A5: 2,6 => CTR * .485913.6.95.2.8.7.62.8.5.9421.3.758653874291.87152634836.4.125.7.21.4.3.1436.9.. A5: 3,5 # 25 pairs C5: 2,6,3,5 # reduction candidate for 2,6 C5: 2,6 # 27 pairs F5: 2,6,3,4 # reduction candidate for 2,6 F5: 2,6 # 27 pairs * PAIR B7: 2,3 BLK 7 C7: 2,3,6 # reduction candidate for 2,3 C7: 6 => CTR * .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.836.4.125...21.463214365987 C7: 2,3 # 26 pairs * PAIR B7: 2,3 COL B B4: 2,3,7 # reduction candidate for 2,3 B4: 2,3 # 28 pairs B5: 2,3,5,8 # reduction candidate for 2,3 B5: 2,3 # 24 pairs * PAIR B8: 5,7 BLK 7 A8: 5,7,6,9 # reduction candidate for 5,7 A8: 5,7 => CTR * .48591376.9....8.2.6..825.94.1.2..586...7.29.9...5..3.8.6.4.125..921846321436.987 A8: 6,9 # 23 pairs C8: 5,7,6,9 # reduction candidate for 5,7 C8: 5,7 => CTR * .48591376.9....8.2.6..825.94.1.2..58....7..9...9.5..3.8.6.4.1259..21846321436.987 C8: 6,9 # 23 pairs A9: 5,7,2 # reduction candidate for 5,7 A9: 5,7 # 26 pairs * PAIR H7: 2,6 ROW 7 C7: 2,6,3 # reduction candidate for 2,6 C7: 3 => CTR * 248591376.95...8.2.674825194.1.2..585...7..9.....5..3.823.4.165...21.4.3.1436.9.. C7: 2,6 # 23 pairs * PAIR I9: 2,7 BLK 9 H9: 2,7,8 # reduction candidate for 2,7 H9: 2,7 => SOLVED * 748591326195623847263487519421936758356874291987152634832749165679215483514368972 H9: 8 # 24 pairs * PAIR I9: 2,7 ROW 9 A9: 2,7,5 # reduction candidate for 2,7 A9: 5 => SOLVED * 748591326195623847263487519421936758356874291987152634832749165679215483514368972 A9: 2,7 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-041-base-pr-000.dot * REASONING * DIS # A2: 2,7 => CTR => A2: 1,3,5 * DIS # C2: 2,7 => CTR => C2: 3,5 * PRF # A3: 2,7 => SOL * DIS # A6: 2,7 => CTR => A6: 6,9 * PRF # F2: 2,3 => SOL * DIS # A2: 2,3 => CTR => A2: 1,5,7 * DIS # C2: 2,3 => CTR => C2: 5,7 * PRF # H9: 2,7 => SOL * DIS # A2: 2,7 => CTR => A2: 1,3,5 * DIS # C2: 2,7 => CTR => C2: 3,5 * DIS # A5: 2,6 => CTR => A5: 3,5 * DIS # C7: 6 => CTR => C7: 2,3 * DIS # A8: 5,7 => CTR => A8: 6,9 * DIS # C8: 5,7 => CTR => C8: 6,9 * DIS # C7: 3 => CTR => C7: 2,6 * PRF # H9: 2,7 => SOL * PRF # A9: 5 => SOL * CNT 17 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D3,D4,D5,D6,D7,E2,E4,F7,F8,F9,G5,H1,H2,H3,H7,I2,I5,I6,I9) * .485913.6.9....8...6..8.5.94.1....58....7..9.....5..3.8...4.1.5...21.4.3.1436.9.. * PAIR A1: 2,7 BLK 1 A2: 2,7,1,3,5 # reduction candidate for 2,7 A2: 2,7 => CTR * .485913.6.95...81.163.825494.1.2..5835.87..91.8.15..348...4.1.5...21.4.3.1436.9.. C2: 2,7,3,5 # reduction candidate for 2,7 C2: 2,7 => CTR * .485913.659.43681.16378254947162..583...7..9.....5..3.83..4.1.5...21.4.3.1436598. A3: 2,7,1,3 # reduction candidate for 2,7 A3: 2,7 => SOLVED * 748591326195623847263487519421936758356874291987152634832749165679215483514368972 * DURATION: 0:00:05.797417 START: 23:41:44.442739 END: 23:41:50.240156 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-041-base-pr-001.dot * REASONING * DIS # A2: 2,7 => CTR => A2: 1,3,5 * DIS A2: 1,3,5 # C2: 2,7 => CTR => C2: 3,5 * PRF A2: 1,3,5 + C2: 3,5 # A3: 2,7 => SOL * STA A2: 1,3,5 + C2: 3,5 + A3: 2,7 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 95 Sudokus 041 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 748591326195623847263487519421936758356874291987152634832749165679215483514368972 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: 2,7 => CTR => A2: 1,3,5 * INC # A2: 1,3,5 => UNS * DIS # C2: 2,7 => CTR => C2: 3,5 * INC # C2: 3,5 => UNS * PRF # A3: 2,7 => SOL * INC # A3: 1,3 => UNS * INC # C3: 2,7 => UNS * DIS # A6: 2,7 => CTR => A6: 6,9 * INC # A6: 6,9 => UNS * INC # A9: 2,7 => UNS * PRF # F2: 2,3 => SOL * INC # F2: 6,7 => UNS * INC # F3: 2,3 => UNS * DIS # A2: 2,3 => CTR => A2: 1,5,7 * INC # A2: 1,5,7 => UNS * DIS # C2: 2,3 => CTR => C2: 5,7 * INC # C2: 5,7 => UNS * INC # D2: 4,7 => UNS * INC # D2: 6 => UNS * PRF # H9: 2,7 => SOL * INC # H9: 8 => UNS * DIS # A2: 2,7 => CTR => A2: 1,3,5 * INC # A2: 1,3,5 => UNS * DIS # C2: 2,7 => CTR => C2: 3,5 * INC # C2: 3,5 => UNS * INC # F2: 2,7 => UNS * INC # F4: 6,9 => UNS * INC # F4: 2,3 => UNS * INC # F4: 2,3 => UNS * INC # F5: 2,3 => UNS * INC # B4: 2,3 => UNS * INC # B4: 7 => UNS * INC # G4: 2,6 => UNS * INC # G6: 2,6 => UNS * DIS # A5: 2,6 => CTR => A5: 3,5 * INC # A5: 3,5 => UNS * INC # C5: 2,6 => UNS * INC # F5: 2,6 => UNS * INC # C7: 2,3 => UNS * DIS # C7: 6 => CTR => C7: 2,3 * INC # B4: 2,3 => UNS * INC # B5: 2,3 => UNS * DIS # A8: 5,7 => CTR => A8: 6,9 * INC # A8: 6,9 => UNS * DIS # C8: 5,7 => CTR => C8: 6,9 * INC # C8: 6,9 => UNS * INC # A9: 5,7 => UNS * INC # C7: 2,6 => UNS * DIS # C7: 3 => CTR => C7: 2,6 * PRF # H9: 2,7 => SOL * INC # H9: 8 => UNS * INC # A9: 2,7 => UNS * PRF # A9: 5 => SOL * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 2,7 => CTR => A2: 1,3,5 * DIS A2: 1,3,5 # C2: 2,7 => CTR => C2: 3,5 * PRF A2: 1,3,5 + C2: 3,5 # A3: 2,7 => SOL * STA A2: 1,3,5 + C2: 3,5 + A3: 2,7 * CNT 3 HDP CHAINS / 3 HYP OPENED