Analysis of xx-top95-074-base.sdk
Contents
Original Sudoku
level: medium
position: .2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4. initial
Autosolve
position: .26..7..889562..73.74.8....457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E9: 6 => CTR => E9: 3,5 * DIS # D1: 3,9 => CTR => D1: 4 * PRF # D1: 4 => SOL * DIS # H3: 5,9 => CTR => H3: 2 * PRF # H3: 2 => SOL * PRF # G1: 9 => SOL * PRF # G9: 6 => SOL * DIS # E9: 3,6 => CTR => E9: 5 * PRF # E9: 5 => SOL * PRF # G9: 3,6 => SOL * DIS # G9: 9 => CTR => G9: 3,6 * PRF # D1: 3,4 => SOL * DIS # D1: 9 => CTR => D1: 3,4 * DIS # E9: 3,6 => CTR => E9: 5 * PRF # E9: 5 => SOL * DIS # G8: 3,6 => CTR => G8: 1,2 * DIS # I9: 5,6 => CTR => I9: 9 * PRF # I9: 9 => SOL * DIS # G8: 1,6 => CTR => G8: 2,3 * DIS # G8: 1,6 => CTR => G8: 2,3 * PRF # I3: 1,6 => SOL * DIS # I3: 9 => CTR => I3: 1,6 * CNT 22 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E9: 6 => CTR => E9: 3,5 * DIS E9: 3,5 # D1: 3,9 => CTR => D1: 4 * PRF E9: 3,5 + D1: 4 => SOL * STA E9: 3,5 + D1: 4 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4. | initial |
| .26..7..889562..73.74.8....457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. | autosolve |
| 126437958895621473374985126457193862983246517612578394269314785548769231731852649 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 1,3 A3: 1,3 E1: 3,5 F2: 1,4 D3: 3,9 F3: 1,5 H1: 5,9 G2: 1,4 G6: 3,9 H6: 3,9 B7: 3,6 B9: 3,6 D7: 3,4 F7: 4,5 E8: 3,6 I7: 5,6 H8: 2,3 I8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 0 pairs (*) / A3 = 1 => 0 pairs (X) F2,F3: 1.. / F2 = 1 => 0 pairs (*) / F3 = 1 => 0 pairs (X) G8,I8: 1.. / G8 = 1 => 0 pairs (X) / I8 = 1 => 18 pairs (_) A1,G1: 1.. / A1 = 1 => 0 pairs (*) / G1 = 1 => 0 pairs (X) F2,G2: 1.. / F2 = 1 => 0 pairs (*) / G2 = 1 => 0 pairs (X) I3,I8: 1.. / I3 = 1 => 0 pairs (X) / I8 = 1 => 18 pairs (_) G3,H3: 2.. / G3 = 2 => 0 pairs (X) / H3 = 2 => 0 pairs (_) G8,H8: 2.. / G8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) G3,G8: 2.. / G3 = 2 => 0 pairs (X) / G8 = 2 => 0 pairs (_) H3,H8: 2.. / H3 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A1,A3: 3.. / A1 = 3 => 0 pairs (X) / A3 = 3 => 0 pairs (_) G6,H6: 3.. / G6 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) B7,B9: 3.. / B7 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) A3,D3: 3.. / A3 = 3 => 0 pairs (*) / D3 = 3 => 0 pairs (X) B7,D7: 3.. / B7 = 3 => 0 pairs (X) / D7 = 3 => 0 pairs (_) H6,H8: 3.. / H6 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) D1,F2: 4.. / D1 = 4 => 0 pairs (*) / F2 = 4 => 0 pairs (X) G1,G2: 4.. / G1 = 4 => 0 pairs (X) / G2 = 4 => 0 pairs (_) D7,F7: 4.. / D7 = 4 => 0 pairs (X) / F7 = 4 => 0 pairs (_) D1,G1: 4.. / D1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) F2,G2: 4.. / F2 = 4 => 0 pairs (X) / G2 = 4 => 0 pairs (_) D1,D7: 4.. / D1 = 4 => 0 pairs (*) / D7 = 4 => 0 pairs (X) F2,F7: 4.. / F2 = 4 => 0 pairs (X) / F7 = 4 => 0 pairs (_) E1,F3: 5.. / E1 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) H1,H3: 5.. / H1 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) F7,E9: 5.. / F7 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) I7,I9: 5.. / I7 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) E1,H1: 5.. / E1 = 5 => 0 pairs (X) / H1 = 5 => 0 pairs (_) F3,H3: 5.. / F3 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) F7,I7: 5.. / F7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) E9,I9: 5.. / E9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) E1,E9: 5.. / E1 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) F3,F7: 5.. / F3 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) G3,I3: 6.. / G3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) B7,B9: 6.. / B7 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) E8,E9: 6.. / E8 = 6 => 20 pairs (_) / E9 = 6 => 0 pairs (X) B7,I7: 6.. / B7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) G6,H6: 9.. / G6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) G9,I9: 9.. / G9 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) I3,I9: 9.. / I3 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) * DURATION: 0:01:54.283985 START: 00:35:25.841878 END: 00:37:20.125863 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,B9,D3,D7,E1,E8,F2,F3,F7,G2,G6,H1,H6,H8,I7,I8) * .26..7..889562..73.74.8....457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. * PAIR E1: 3,5 COL E E9: 3,5,6 # reduction candidate for 3,5 E9: 6 => CTR * .26.57.9889562..73.74981.56457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. E9: 3,5 # 20 pairs * PAIR D3: 3,9 BLK 2 D1: 3,9,4 # reduction candidate for 3,9 D1: 3,9 => CTR * .26..74.8895624173.74.81.5.457193862983246517612578..42.9415786548769.2176183294. D1: 4 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 * PAIR H1: 5,9 BLK 3 H3: 5,9,2 # reduction candidate for 5,9 H3: 5,9 => CTR * .26437.58895621473.74.8.2.6457193862983246517612578..4269314785548769.21731852649 H3: 2 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 * PAIR G2: 1,4 BLK 3 G1: 1,4,9 # reduction candidate for 1,4 G1: 9 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 G1: 1,4 # 19 pairs * PAIR G6: 3,9 COL G G9: 3,9,6 # reduction candidate for 3,9 G9: 6 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 G9: 3,9 # 22 pairs * PAIR B9: 3,6 ROW 9 E9: 3,6,5 # reduction candidate for 3,6 E9: 3,6 => CTR * .26.57.9889562..73.74981.56457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. E9: 5 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 G9: 3,6,9 # reduction candidate for 3,6 G9: 3,6 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 G9: 9 => CTR * .269.7458895624173.7438...94571938629832465176125783942.9.1.78.5487.9.317.18.294. * PAIR D7: 3,4 COL D D1: 3,4,9 # reduction candidate for 3,4 D1: 3,4 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 D1: 9 => CTR * .269.7458895624173.7438....457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. * PAIR E8: 3,6 BLK 8 E9: 3,6,5 # reduction candidate for 3,6 E9: 3,6 => CTR * .26.57.9889562..73.74981.56457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. E9: 5 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 * PAIR E8: 3,6 ROW 8 G8: 3,6,1,2 # reduction candidate for 3,6 G8: 3,6 => CTR * .26437.58895621473.74.8.2.6457193862983246517612578..4269314785548769321731852649 G8: 1,2 # 19 pairs * PAIR I7: 5,6 BLK 9 I9: 5,6,9 # reduction candidate for 5,6 I9: 5,6 => CTR * .269.7458895624173.7438...9457193862983246517612578.942.9.1.78.5487.9.317.18.294. I9: 9 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 * PAIR H8: 2,3 BLK 9 G8: 2,3,1,6 # reduction candidate for 2,3 G8: 1,6 => CTR * .26..7..889562..73.74.8.2.6457193862983246517612578..42693147855487.9...7.18.2.4. G8: 2,3 # 20 pairs * PAIR I8: 1,6 BLK 9 G8: 1,6,2,3 # reduction candidate for 1,6 G8: 1,6 => CTR * .26..7..889562..73.74.8.2.6457193862983246517612578..42693147855487.9...7.18.2.4. G8: 2,3 # 20 pairs * PAIR I8: 1,6 COL I I3: 1,6,9 # reduction candidate for 1,6 I3: 1,6 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 I3: 9 => CTR * .269.7458895624173.7438.629457193862983246517612578.942.9.1.78.5487.92317.18.294. * INCONCLUSIVE * SAVE PR GRAPH xx-top95-074-base-pr-000.dot * REASONING * DIS # E9: 6 => CTR => E9: 3,5 * DIS # D1: 3,9 => CTR => D1: 4 * PRF # D1: 4 => SOL * DIS # H3: 5,9 => CTR => H3: 2 * PRF # H3: 2 => SOL * PRF # G1: 9 => SOL * PRF # G9: 6 => SOL * DIS # E9: 3,6 => CTR => E9: 5 * PRF # E9: 5 => SOL * PRF # G9: 3,6 => SOL * DIS # G9: 9 => CTR => G9: 3,6 * PRF # D1: 3,4 => SOL * DIS # D1: 9 => CTR => D1: 3,4 * DIS # E9: 3,6 => CTR => E9: 5 * PRF # E9: 5 => SOL * DIS # G8: 3,6 => CTR => G8: 1,2 * DIS # I9: 5,6 => CTR => I9: 9 * PRF # I9: 9 => SOL * DIS # G8: 1,6 => CTR => G8: 2,3 * DIS # G8: 1,6 => CTR => G8: 2,3 * PRF # I3: 1,6 => SOL * DIS # I3: 9 => CTR => I3: 1,6 * CNT 22 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,B9,D3,D7,E1,E8,F2,F3,F7,G2,G6,H1,H6,H8,I7,I8) * .26..7..889562..73.74.8....457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. * PAIR E1: 3,5 COL E E9: 3,5,6 # reduction candidate for 3,5 E9: 6 => CTR * .26.57.9889562..73.74981.56457193862983246517612578..42.9.1.78.5487.9...7.18.2.4. * PAIR RESTART * PAIR D3: 3,9 BLK 2 D1: 3,9,4 # reduction candidate for 3,9 D1: 3,9 => CTR * .26..74.8895624173.74.81.5.457193862983246517612578..42.9415786548769.2176183294. D1: 4 => SOLVED * 126437958895621473374985126457193862983246517612578394269314785548769231731852649 * DURATION: 0:00:07.802410 START: 00:38:10.461632 END: 00:38:18.264042 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-074-base-pr-001.dot * REASONING * DIS # E9: 6 => CTR => E9: 3,5 * DIS E9: 3,5 # D1: 3,9 => CTR => D1: 4 * PRF E9: 3,5 + D1: 4 => SOL * STA E9: 3,5 + D1: 4 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 95 Sudokus 074 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 126437958895621473374985126457193862983246517612578394269314785548769231731852649 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 # E9: 3,5 => UNS * DIS # E9: 6 => CTR => E9: 3,5 * DIS # D1: 3,9 => CTR => D1: 4 * PRF # D1: 4 => SOL * DIS # H3: 5,9 => CTR => H3: 2 * PRF # H3: 2 => SOL * INC # G1: 1,4 => UNS * PRF # G1: 9 => SOL * INC # G9: 3,9 => UNS * PRF # G9: 6 => SOL * DIS # E9: 3,6 => CTR => E9: 5 * PRF # E9: 5 => SOL * PRF # G9: 3,6 => SOL * DIS # G9: 9 => CTR => G9: 3,6 * PRF # D1: 3,4 => SOL * DIS # D1: 9 => CTR => D1: 3,4 * DIS # E9: 3,6 => CTR => E9: 5 * PRF # E9: 5 => SOL * DIS # G8: 3,6 => CTR => G8: 1,2 * INC # G8: 1,2 => UNS * DIS # I9: 5,6 => CTR => I9: 9 * PRF # I9: 9 => SOL * INC # G8: 2,3 => UNS * DIS # G8: 1,6 => CTR => G8: 2,3 * DIS # G8: 1,6 => CTR => G8: 2,3 * INC # G8: 2,3 => UNS * PRF # I3: 1,6 => SOL * DIS # I3: 9 => CTR => I3: 1,6 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E9: 3,5 => UNS * DIS # E9: 6 => CTR => E9: 3,5 * DIS E9: 3,5 # D1: 3,9 => CTR => D1: 4 * PRF E9: 3,5 + D1: 4 => SOL * STA E9: 3,5 + D1: 4 * CNT 4 HDP CHAINS / 3 HYP OPENED