Analysis of xx-top500-369-base.sdk
Contents
Original Sudoku
level: medium
position: ...6..1..83.......5........2.....43....1..2.....75.....71..........8..5.....3.... initial
Autosolve
position: 7.46.518383..1.5.751.378...2578..431..81432751437528...715..3.83...8175..85.37.1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 2,9 => SOL * DIS # B8: 2,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # D2: 4 => CTR => D2: 2,9 * DIS # E7: 6 => CTR => E7: 2,9 * DIS # D2: 4,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # F7: 4,9 => CTR => F7: 6 * DIS # H3: 6,9 => CTR => H3: 2,4 * DIS # I3: 6,9 => CTR => I3: 2,4 * DIS # C3: 2 => CTR => C3: 6,9 * PRF # A9: 4 => SOL * PRF # B8: 6,9 => SOL * DIS # B8: 2 => CTR => B8: 6,9 * DIS # E7: 6,9 => CTR => E7: 2 * PRF # E7: 2 => SOL * DIS # F7: 4 => CTR => F7: 6,9 * DIS # H3: 6,9 => CTR => H3: 2,4 * DIS # I3: 6,9 => CTR => I3: 2,4 * DIS # I9: 6,9 => CTR => I9: 2,4 * PRF # A9: 4,9 => SOL * DIS # A9: 6 => CTR => A9: 4,9 * DIS # F7: 4,9 => CTR => F7: 6 * PRF # H7: 4,9 => SOL * DIS # H7: 2 => CTR => H7: 4,9 * DIS # B8: 2,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # C2: 2,9 => SOL * DIS # F7: 4,9 => CTR => F7: 6 * PRF # D9: 4,9 => SOL * DIS # D9: 2 => CTR => D9: 4,9 * PRF # I8: 4,9 => SOL * DIS # I8: 6 => CTR => I8: 4,9 * DIS # D2: 4,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # I9: 6,9 => CTR => I9: 2,4 * PRF # A9: 4 => SOL * CNT 37 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 2,9 => SOL * STA C2: 2,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6..1..83.......5........2.....43....1..2.....75.....71..........8..5.....3.... | initial |
| 7.46.518383..1.5.751.378...2578..431..81432751437528...715..3.83...8175..85.37.1. | autosolve |
| 724695183839214567516378924257869431698143275143752896971526348362481759485937612 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 2,9 E1: 2,9 F2: 4,9 G3: 6,9 A5: 6,9 B5: 6,9 E4: 6,9 F4: 6,9 H6: 6,9 I6: 6,9 A7: 4,9 C8: 2,9 D8: 4,9 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,D2: 2.. / E1 = 2 => 0 pairs (X) / D2 = 2 => 0 pairs (_) B8,C8: 2.. / B8 = 2 => 0 pairs (X) / C8 = 2 => 0 pairs (_) E7,D9: 2.. / E7 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) H7,I9: 2.. / H7 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) B1,E1: 2.. / B1 = 2 => 0 pairs (*) / E1 = 2 => 0 pairs (X) E7,H7: 2.. / E7 = 2 => 0 pairs (*) / H7 = 2 => 0 pairs (X) D9,I9: 2.. / D9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) B1,B8: 2.. / B1 = 2 => 0 pairs (*) / B8 = 2 => 0 pairs (X) D2,D9: 2.. / D2 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E1,E7: 2.. / E1 = 2 => 0 pairs (X) / E7 = 2 => 0 pairs (_) I3,I9: 2.. / I3 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) D2,F2: 4.. / D2 = 4 => 0 pairs (X) / F2 = 4 => 15 pairs (_) H3,I3: 4.. / H3 = 4 => 15 pairs (_) / I3 = 4 => 0 pairs (*) A7,A9: 4.. / A7 = 4 => 18 pairs (_) / A9 = 4 => 0 pairs (*) D8,I8: 4.. / D8 = 4 => 19 pairs (_) / I8 = 4 => 0 pairs (X) F2,F7: 4.. / F2 = 4 => 15 pairs (_) / F7 = 4 => 0 pairs (X) H3,H7: 4.. / H3 = 4 => 15 pairs (_) / H7 = 4 => 0 pairs (*) C2,C3: 6.. / C2 = 6 => 16 pairs (_) / C3 = 6 => 0 pairs (*) A5,B5: 6.. / A5 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) E4,F4: 6.. / E4 = 6 => 13 pairs (_) / F4 = 6 => 0 pairs (X) H6,I6: 6.. / H6 = 6 => 15 pairs (_) / I6 = 6 => 0 pairs (*) B8,A9: 6.. / B8 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) E7,F7: 6.. / E7 = 6 => 0 pairs (X) / F7 = 6 => 13 pairs (_) C2,H2: 6.. / C2 = 6 => 16 pairs (_) / H2 = 6 => 0 pairs (*) B8,I8: 6.. / B8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) A5,A9: 6.. / A5 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) B5,B8: 6.. / B5 = 6 => 0 pairs (X) / B8 = 6 => 0 pairs (_) E4,E7: 6.. / E4 = 6 => 13 pairs (_) / E7 = 6 => 0 pairs (X) F4,F7: 6.. / F4 = 6 => 0 pairs (X) / F7 = 6 => 13 pairs (_) G3,G9: 6.. / G3 = 6 => 17 pairs (_) / G9 = 6 => 0 pairs (*) A5,B5: 9.. / A5 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) E4,F4: 9.. / E4 = 9 => 0 pairs (X) / F4 = 9 => 13 pairs (_) H6,I6: 9.. / H6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) B1,E1: 9.. / B1 = 9 => 0 pairs (X) / E1 = 9 => 0 pairs (_) G3,G9: 9.. / G3 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) * DURATION: 0:01:04.093153 START: 15:27:07.052129 END: 15:28:11.145282 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B1,B5,C8,D8,E1,E4,F2,F4,G3,G9,H6,I6) * 7.46.518383..1.5.751.378...2578..431..81432751437528...715..3.83...8175..85.37.1. * PAIR B1: 2,9 BLK 1 C2: 2,9,6 # reduction candidate for 2,9 C2: 2,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 C2: 6 # 16 pairs C3: 2,9,6 # reduction candidate for 2,9 C3: 2,9 # 16 pairs * PAIR B1: 2,9 COL B B8: 2,9,6 # reduction candidate for 2,9 B8: 2,9 => CTR * 7.46.518383..1.5.751.3786..2578..4319681432751437528694715..3283..481756685237914 B8: 6 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 * PAIR E1: 2,9 BLK 2 D2: 2,9,4 # reduction candidate for 2,9 D2: 4 => CTR * 7.462518383.4195.751.378...257896431..81432751437528...71564328329.8175..85.37.1. D2: 2,9 # 15 pairs * PAIR E1: 2,9 COL E E7: 2,9,6 # reduction candidate for 2,9 E7: 6 => CTR * 79462518383291456751.378...257896431..81432751437528...7156.328329481756685237914 E7: 2,9 # 13 pairs * PAIR F2: 4,9 BLK 2 D2: 4,9,2 # reduction candidate for 4,9 D2: 4,9 => CTR * 79462518383291456751.378...2578..431..81432751437528...715..328329481756685237914 D2: 2 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 * PAIR F2: 4,9 COL F F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 => CTR * 7.4625183832.1.567516378942257896431..8143275143752896.7156.3283...8175..85237.1. F7: 6 # 13 pairs * PAIR G3: 6,9 BLK 3 H2: 6,9,2 # reduction candidate for 6,9 H2: 6,9 # 19 pairs H3: 6,9,2,4 # reduction candidate for 6,9 H3: 6,9 => CTR * 7.46.518383.2145.7512378..42578..4316981432751437528...715..3483..48175.485.37.12 H3: 2,4 # 15 pairs I3: 6,9,2,4 # reduction candidate for 6,9 I3: 6,9 => CTR * 7.46.518383.2145.7512378.4.2578..431..81432751437528..471526398329.8175..85.37.12 I3: 2,4 # 15 pairs * PAIR G3: 6,9 ROW 3 C3: 6,9,2 # reduction candidate for 6,9 C3: 2 => CTR * 7.46.5183836.1.5.7512378...2578..431..81432751437528...715..3.8329481756685.3791. C3: 6,9 # 19 pairs * PAIR A5: 6,9 COL A A9: 6,9,4 # reduction candidate for 6,9 A9: 4 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 A9: 6,9 # 18 pairs * PAIR B5: 6,9 COL B B8: 6,9,2 # reduction candidate for 6,9 B8: 6,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 B8: 2 => CTR * 79462518383.9145.751.37864.2578..431.681432751437528...715..3.8329481756685.37914 * PAIR E4: 6,9 COL E E7: 6,9,2 # reduction candidate for 6,9 E7: 6,9 => CTR * 79462518383291456751.378...2578..431..81432751437528...715..328329481756685237914 E7: 2 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 * PAIR F4: 6,9 COL F F7: 6,9,4 # reduction candidate for 6,9 F7: 4 => CTR * 7.4625183832.1.5.751.378...2578.6431..81432751437528...715643283..981754485237.1. F7: 6,9 # 15 pairs * PAIR H6: 6,9 COL H H2: 6,9,2 # reduction candidate for 6,9 H2: 6,9 # 19 pairs H3: 6,9,2,4 # reduction candidate for 6,9 H3: 6,9 => CTR * 7.46.518383.2145.7512378..42578..4316981432751437528...715..3483..48175.485.37.12 H3: 2,4 # 15 pairs * PAIR I6: 6,9 COL I I3: 6,9,2,4 # reduction candidate for 6,9 I3: 6,9 => CTR * 7.46.518383.2145.7512378.4.2578..431..81432751437528..471526398329.8175..85.37.12 I3: 2,4 # 15 pairs I8: 6,9,4 # reduction candidate for 6,9 I8: 6,9 # 19 pairs I9: 6,9,2,4 # reduction candidate for 6,9 I9: 6,9 => CTR * 7.4625183832419567516378942257896431..81432751437528969715..3283...81754.85237.1. I9: 2,4 # 15 pairs * PAIR A7: 4,9 BLK 7 A9: 4,9,6 # reduction candidate for 4,9 A9: 4,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 A9: 6 => CTR * 7.46.518383..145.751.37864.2578..4319681432751437528694715..3283...81756685237914 * PAIR A7: 4,9 ROW 7 F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 => CTR * 7.4625183832.1.567516378942257896431..8143275143752896.7156.3283...8175..85237.1. F7: 6 # 13 pairs H7: 4,9,2 # reduction candidate for 4,9 H7: 4,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 H7: 2 => CTR * 7.4625183832.1.5675163789422578..431..8143275143752896.715..3283...8175..85237.1. * PAIR C8: 2,9 BLK 7 B8: 2,9,6 # reduction candidate for 2,9 B8: 2,9 => CTR * 7.46.518383..1.5.751.3786..2578..4319681432751437528694715..3283..481756685237914 B8: 6 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 * PAIR C8: 2,9 COL C C2: 2,9,6 # reduction candidate for 2,9 C2: 2,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 C2: 6 # 16 pairs C3: 2,9,6 # reduction candidate for 2,9 C3: 2,9 # 16 pairs * PAIR D8: 4,9 BLK 8 F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 => CTR * 7.4625183832.1.567516378942257896431..8143275143752896.7156.3283...8175..85237.1. F7: 6 # 13 pairs D9: 4,9,2 # reduction candidate for 4,9 D9: 4,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 D9: 2 => CTR * 7.462518383..1.5.751.378..22578..431..81432751437528...715..328329481756685237914 * PAIR D8: 4,9 ROW 8 I8: 4,9,6 # reduction candidate for 4,9 I8: 4,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 I8: 6 => CTR * 7.46.518383.9145.751.37864.2578..431..81432751437528...715..3.83..481756685.37914 * PAIR D8: 4,9 COL D D2: 4,9,2 # reduction candidate for 4,9 D2: 4,9 => CTR * 79462518383291456751.378...2578..431..81432751437528...715..328329481756685237914 D2: 2 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 * PAIR G9: 6,9 BLK 9 I8: 6,9,4 # reduction candidate for 6,9 I8: 6,9 # 19 pairs I9: 6,9,2,4 # reduction candidate for 6,9 I9: 6,9 => CTR * 7.4625183832419567516378942257896431..81432751437528969715..3283...81754.85237.1. I9: 2,4 # 15 pairs * PAIR G9: 6,9 ROW 9 A9: 6,9,4 # reduction candidate for 6,9 A9: 4 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 A9: 6,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-369-base-pr-000.dot * REASONING * PRF # C2: 2,9 => SOL * DIS # B8: 2,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # D2: 4 => CTR => D2: 2,9 * DIS # E7: 6 => CTR => E7: 2,9 * DIS # D2: 4,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # F7: 4,9 => CTR => F7: 6 * DIS # H3: 6,9 => CTR => H3: 2,4 * DIS # I3: 6,9 => CTR => I3: 2,4 * DIS # C3: 2 => CTR => C3: 6,9 * PRF # A9: 4 => SOL * PRF # B8: 6,9 => SOL * DIS # B8: 2 => CTR => B8: 6,9 * DIS # E7: 6,9 => CTR => E7: 2 * PRF # E7: 2 => SOL * DIS # F7: 4 => CTR => F7: 6,9 * DIS # H3: 6,9 => CTR => H3: 2,4 * DIS # I3: 6,9 => CTR => I3: 2,4 * DIS # I9: 6,9 => CTR => I9: 2,4 * PRF # A9: 4,9 => SOL * DIS # A9: 6 => CTR => A9: 4,9 * DIS # F7: 4,9 => CTR => F7: 6 * PRF # H7: 4,9 => SOL * DIS # H7: 2 => CTR => H7: 4,9 * DIS # B8: 2,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # C2: 2,9 => SOL * DIS # F7: 4,9 => CTR => F7: 6 * PRF # D9: 4,9 => SOL * DIS # D9: 2 => CTR => D9: 4,9 * PRF # I8: 4,9 => SOL * DIS # I8: 6 => CTR => I8: 4,9 * DIS # D2: 4,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # I9: 6,9 => CTR => I9: 2,4 * PRF # A9: 4 => SOL * CNT 37 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B1,B5,C8,D8,E1,E4,F2,F4,G3,G9,H6,I6) * 7.46.518383..1.5.751.378...2578..431..81432751437528...715..3.83...8175..85.37.1. * PAIR B1: 2,9 BLK 1 C2: 2,9,6 # reduction candidate for 2,9 C2: 2,9 => SOLVED * 724695183839214567516378924257869431698143275143752896971526348362481759485937612 * DURATION: 0:00:02.029309 START: 15:29:14.299371 END: 15:29:16.328680 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-369-base-pr-001.dot * REASONING * PRF # C2: 2,9 => SOL * STA C2: 2,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 369 solution: 724695183839214567516378924257869431698143275143752896971526348362481759485937612 info: 5149 FNBTWXY S8.f 10517 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 724695183839214567516378924257869431698143275143752896971526348362481759485937612 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:
* PRF # C2: 2,9 => SOL * INC # C2: 6 => UNS * INC # C3: 2,9 => UNS * DIS # B8: 2,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * INC # D2: 2,9 => UNS * DIS # D2: 4 => CTR => D2: 2,9 * INC # E7: 2,9 => UNS * DIS # E7: 6 => CTR => E7: 2,9 * DIS # D2: 4,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # F7: 4,9 => CTR => F7: 6 * INC # F7: 6 => UNS * INC # H2: 6,9 => UNS * DIS # H3: 6,9 => CTR => H3: 2,4 * INC # H3: 2,4 => UNS * DIS # I3: 6,9 => CTR => I3: 2,4 * INC # I3: 2,4 => UNS * INC # C3: 6,9 => UNS * DIS # C3: 2 => CTR => C3: 6,9 * INC # A9: 6,9 => UNS * PRF # A9: 4 => SOL * PRF # B8: 6,9 => SOL * DIS # B8: 2 => CTR => B8: 6,9 * DIS # E7: 6,9 => CTR => E7: 2 * PRF # E7: 2 => SOL * INC # F7: 6,9 => UNS * DIS # F7: 4 => CTR => F7: 6,9 * INC # H2: 6,9 => UNS * DIS # H3: 6,9 => CTR => H3: 2,4 * INC # H3: 2,4 => UNS * DIS # I3: 6,9 => CTR => I3: 2,4 * INC # I3: 2,4 => UNS * INC # I8: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 2,4 * INC # I9: 2,4 => UNS * PRF # A9: 4,9 => SOL * DIS # A9: 6 => CTR => A9: 4,9 * DIS # F7: 4,9 => CTR => F7: 6 * INC # F7: 6 => UNS * PRF # H7: 4,9 => SOL * DIS # H7: 2 => CTR => H7: 4,9 * DIS # B8: 2,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # C2: 2,9 => SOL * INC # C2: 6 => UNS * INC # C3: 2,9 => UNS * DIS # F7: 4,9 => CTR => F7: 6 * INC # F7: 6 => UNS * PRF # D9: 4,9 => SOL * DIS # D9: 2 => CTR => D9: 4,9 * PRF # I8: 4,9 => SOL * DIS # I8: 6 => CTR => I8: 4,9 * DIS # D2: 4,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * INC # I8: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 2,4 * INC # I9: 2,4 => UNS * INC # A9: 6,9 => UNS * PRF # A9: 4 => SOL * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 2,9 => SOL * STA C2: 2,9 * CNT 1 HDP CHAINS / 1 HYP OPENED