Analysis of xx-top500-099-base.sdk
Contents
Original Sudoku
level: medium
position: .7.24..3.2...5..........8...3.8.6...........1......5.....3...8.1.4......5........ initial
Autosolve
position: .71248.35248.53.1.35.1..842.3581642.8..5.43.141..3.5.8...3.51841.4....535.34.1... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A7: 7 => CTR => A7: 6,9 * PRF # E3: 7 => SOL * DIS # C7: 6,9 => CTR => C7: 2,7 * PRF # E3: 7 => SOL * DIS # D8: 7 => CTR => D8: 6,9 * PRF # E3: 7,9 => SOL * PRF # A7: 6 => SOL * DIS # H6: 7,9 => CTR => H6: 6 * PRF # D8: 7,9 => SOL * DIS # H6: 7,9 => CTR => H6: 6 * DIS # I9: 7,9 => CTR => I9: 6 * DIS # I9: 7,9 => CTR => I9: 6 * DIS # H6: 7,9 => CTR => H6: 6 * CNT 13 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A7: 7 => CTR => A7: 6,9 * PRF A7: 6,9 # E3: 7 => SOL * STA A7: 6,9 + E3: 7 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.24..3.2...5..........8...3.8.6...........1......5.....3...8.1.4......5........ | initial |
| .71248.35248.53.1.35.1..842.3581642.8..5.43.141..3.5.8...3.51841.4....535.34.1... | autosolve |
| 971248635248653917356179842735816429862594371419732568697325184184967253523481796 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 6,9 C3: 6,9 D2: 6,9 F3: 7,9 G1: 6,9 A4: 7,9 D6: 7,9 I4: 7,9 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,F6: 2.. / E5 = 2 => 13 pairs (_) / F6 = 2 => 11 pairs (_) G8,G9: 2.. / G8 = 2 => 13 pairs (_) / G9 = 2 => 9 pairs (_) C6,F6: 2.. / C6 = 2 => 13 pairs (_) / F6 = 2 => 11 pairs (_) F6,F8: 2.. / F6 = 2 => 11 pairs (_) / F8 = 2 => 13 pairs (_) A1,C3: 6.. / A1 = 6 => 16 pairs (_) / C3 = 6 => 0 pairs (*) D2,E3: 6.. / D2 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) H5,H6: 6.. / H5 = 6 => 0 pairs (X) / H6 = 6 => 10 pairs (_) A1,G1: 6.. / A1 = 6 => 16 pairs (_) / G1 = 6 => 0 pairs (*) C3,E3: 6.. / C3 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) C6,H6: 6.. / C6 = 6 => 0 pairs (X) / H6 = 6 => 10 pairs (_) A1,A7: 6.. / A1 = 6 => 16 pairs (_) / A7 = 6 => 0 pairs (*) D2,D8: 6.. / D2 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) I2,I9: 6.. / I2 = 6 => 0 pairs (X) / I9 = 6 => 10 pairs (_) E3,F3: 7.. / E3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) G2,I2: 7.. / G2 = 7 => 10 pairs (_) / I2 = 7 => 14 pairs (_) A7,C7: 7.. / A7 = 7 => 0 pairs (X) / C7 = 7 => 12 pairs (_) A4,I4: 7.. / A4 = 7 => 12 pairs (_) / I4 = 7 => 0 pairs (X) A4,A7: 7.. / A4 = 7 => 12 pairs (_) / A7 = 7 => 0 pairs (X) D6,D8: 7.. / D6 = 7 => 12 pairs (_) / D8 = 7 => 0 pairs (X) B8,B9: 8.. / B8 = 8 => 9 pairs (_) / B9 = 8 => 9 pairs (_) E8,E9: 8.. / E8 = 8 => 9 pairs (_) / E9 = 8 => 9 pairs (_) B8,E8: 8.. / B8 = 8 => 9 pairs (_) / E8 = 8 => 9 pairs (_) B9,E9: 8.. / B9 = 8 => 9 pairs (_) / E9 = 8 => 9 pairs (_) A1,C3: 9.. / A1 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) A1,G1: 9.. / A1 = 9 => 0 pairs (*) / G1 = 9 => 0 pairs (X) A4,I4: 9.. / A4 = 9 => 0 pairs (X) / I4 = 9 => 12 pairs (_) * DURATION: 0:00:41.886385 START: 06:09:13.923936 END: 06:09:55.810321 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,C3,D2,D6,F3,G1,H9,I4) * .71248.35248.53.1.35.1..842.3581642.8..5.43.141..3.5.8...3.51841.4....535.34.1... * PAIR A1: 6,9 COL A A7: 6,9,7 # reduction candidate for 6,9 A7: 7 => CTR * 6712489352489537163591678429358164278.75.43.141.7325987.23.51841.467.2535.3481679 A7: 6,9 # 12 pairs * PAIR C3: 6,9 ROW 3 E3: 6,9,7 # reduction candidate for 6,9 E3: 7 => SOLVED * 971248635248653917356179842735816429862594371419732568697325184184967253523481796 E3: 6,9 # 11 pairs * PAIR C3: 6,9 COL C C5: 6,9,2,7 # reduction candidate for 6,9 C5: 6,9 # 14 pairs C6: 6,9,2,7 # reduction candidate for 6,9 C6: 6,9 # 14 pairs C7: 6,9,2,7 # reduction candidate for 6,9 C7: 6,9 => CTR * 6712489352489537163591678429358164278675243914127395687263951841946...535.34.1.79 C7: 2,7 # 10 pairs * PAIR D2: 6,9 BLK 2 E3: 6,9,7 # reduction candidate for 6,9 E3: 7 => SOLVED * 971248635248653917356179842735816429862594371419732568697325184184967253523481796 E3: 6,9 # 11 pairs * PAIR D2: 6,9 ROW 2 G2: 6,9,7 # reduction candidate for 6,9 G2: 6,9 # 14 pairs I2: 6,9,7 # reduction candidate for 6,9 I2: 6,9 # 10 pairs * PAIR D2: 6,9 COL D D8: 6,9,7 # reduction candidate for 6,9 D8: 7 => CTR * 971248635248653.1.3561..8427358164298695243714129375686273951841.47629535.34.1..6 D8: 6,9 # 12 pairs * PAIR F3: 7,9 BLK 2 E3: 7,9,6 # reduction candidate for 7,9 E3: 7,9 => SOLVED * 971248635248653917356179842735816429862594371419732568697325184184967253523481796 E3: 6 # 16 pairs * PAIR F3: 7,9 COL F F6: 7,9,2 # reduction candidate for 7,9 F6: 7,9 # 13 pairs F8: 7,9,2 # reduction candidate for 7,9 F8: 7,9 # 11 pairs * PAIR G1: 6,9 BLK 3 G2: 6,9,7 # reduction candidate for 6,9 G2: 6,9 # 14 pairs I2: 6,9,7 # reduction candidate for 6,9 I2: 6,9 # 10 pairs * PAIR G1: 6,9 COL G G8: 6,9,2,7 # reduction candidate for 6,9 G8: 6,9 # 11 pairs G9: 6,9,2,7 # reduction candidate for 6,9 G9: 6,9 # 15 pairs * PAIR A4: 7,9 BLK 4 C5: 7,9,2,6 # reduction candidate for 7,9 C5: 7,9 # 13 pairs C6: 7,9,2,6 # reduction candidate for 7,9 C6: 7,9 # 16 pairs * PAIR A4: 7,9 COL A A7: 7,9,6 # reduction candidate for 7,9 A7: 6 => SOLVED * 971248635248653917356179842735816429862594371419732568697325184184967253523481796 A7: 7,9 # 16 pairs * PAIR D6: 7,9 BLK 5 E5: 7,9,2 # reduction candidate for 7,9 E5: 7,9 # 11 pairs F6: 7,9,2 # reduction candidate for 7,9 F6: 7,9 # 13 pairs * PAIR D6: 7,9 ROW 6 C6: 7,9,2,6 # reduction candidate for 7,9 C6: 7,9 # 16 pairs H6: 7,9,6 # reduction candidate for 7,9 H6: 7,9 => CTR * 671248935248953.1.359167842.3581642.8..594361416732598.6.3251841.46.9.5359348127. H6: 6 # 10 pairs * PAIR D6: 7,9 COL D D8: 7,9,6 # reduction candidate for 7,9 D8: 7,9 => SOLVED * 971248635248653917356179842735816429862594371419732568697325184184967253523481796 D8: 6 # 16 pairs * PAIR I4: 7,9 BLK 6 H5: 7,9,6 # reduction candidate for 7,9 H5: 7,9 # 10 pairs H6: 7,9,6 # reduction candidate for 7,9 H6: 7,9 => CTR * 671248935248953.1.359167842.3581642.8..594361416732598.6.3251841.46.9.5359348127. H6: 6 # 10 pairs * PAIR I4: 7,9 COL I I2: 7,9,6 # reduction candidate for 7,9 I2: 7,9 # 10 pairs I9: 7,9,6 # reduction candidate for 7,9 I9: 7,9 => CTR * 671248935248953716359167842.3581642.8..5.43.141.732598...325184184679253523481679 I9: 6 # 10 pairs * PAIR H9: 7,9 BLK 9 G8: 7,9,2,6 # reduction candidate for 7,9 G8: 7,9 # 12 pairs G9: 7,9,2,6 # reduction candidate for 7,9 G9: 7,9 # 15 pairs I9: 7,9,6 # reduction candidate for 7,9 I9: 7,9 => CTR * 671248935248953716359167842.3581642.8..5.43.141.732598...325184184679253523481679 I9: 6 # 10 pairs * PAIR H9: 7,9 ROW 9 E9: 7,9,2,6,8 # reduction candidate for 7,9 E9: 7,9 # 12 pairs E9: 2,6,8 # 9 pairs * PAIR H9: 7,9 COL H H5: 7,9,6 # reduction candidate for 7,9 H5: 7,9 # 10 pairs H6: 7,9,6 # reduction candidate for 7,9 H6: 7,9 => CTR * 671248935248953.1.359167842.3581642.8..594361416732598.6.3251841.46.9.5359348127. H6: 6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-099-base-pr-000.dot * REASONING * DIS # A7: 7 => CTR => A7: 6,9 * PRF # E3: 7 => SOL * DIS # C7: 6,9 => CTR => C7: 2,7 * PRF # E3: 7 => SOL * DIS # D8: 7 => CTR => D8: 6,9 * PRF # E3: 7,9 => SOL * PRF # A7: 6 => SOL * DIS # H6: 7,9 => CTR => H6: 6 * PRF # D8: 7,9 => SOL * DIS # H6: 7,9 => CTR => H6: 6 * DIS # I9: 7,9 => CTR => I9: 6 * DIS # I9: 7,9 => CTR => I9: 6 * DIS # H6: 7,9 => CTR => H6: 6 * CNT 13 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,C3,D2,D6,F3,G1,H9,I4) * .71248.35248.53.1.35.1..842.3581642.8..5.43.141..3.5.8...3.51841.4....535.34.1... * PAIR A1: 6,9 COL A A7: 6,9,7 # reduction candidate for 6,9 A7: 7 => CTR * 6712489352489537163591678429358164278.75.43.141.7325987.23.51841.467.2535.3481679 * PAIR RESTART * PAIR C3: 6,9 ROW 3 E3: 6,9,7 # reduction candidate for 6,9 E3: 7 => SOLVED * 971248635248653917356179842735816429862594371419732568697325184184967253523481796 * DURATION: 0:00:04.973179 START: 06:10:40.096914 END: 06:10:45.070093 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-099-base-pr-001.dot * REASONING * DIS # A7: 7 => CTR => A7: 6,9 * PRF A7: 6,9 # E3: 7 => SOL * STA A7: 6,9 + E3: 7 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 099 solution: 971248635248653917356179842735816429862594371419732568697325184184967253523481796 info: 1577 FNBTWXY S8.f 22592 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 971248635248653917356179842735816429862594371419732568697325184184967253523481796 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 # A7: 6,9 => UNS * DIS # A7: 7 => CTR => A7: 6,9 * INC # E3: 6,9 => UNS * PRF # E3: 7 => SOL * INC # C5: 6,9 => UNS * INC # C6: 6,9 => UNS * DIS # C7: 6,9 => CTR => C7: 2,7 * INC # C7: 2,7 => UNS * INC # E3: 6,9 => UNS * PRF # E3: 7 => SOL * INC # G2: 6,9 => UNS * INC # I2: 6,9 => UNS * INC # D8: 6,9 => UNS * DIS # D8: 7 => CTR => D8: 6,9 * PRF # E3: 7,9 => SOL * INC # E3: 6 => UNS * INC # F6: 7,9 => UNS * INC # F8: 7,9 => UNS * INC # G2: 6,9 => UNS * INC # I2: 6,9 => UNS * INC # G8: 6,9 => UNS * INC # G9: 6,9 => UNS * INC # C5: 7,9 => UNS * INC # C6: 7,9 => UNS * INC # A7: 7,9 => UNS * PRF # A7: 6 => SOL * INC # E5: 7,9 => UNS * INC # F6: 7,9 => UNS * INC # C6: 7,9 => UNS * DIS # H6: 7,9 => CTR => H6: 6 * INC # H6: 6 => UNS * PRF # D8: 7,9 => SOL * INC # D8: 6 => UNS * INC # H5: 7,9 => UNS * DIS # H6: 7,9 => CTR => H6: 6 * INC # H6: 6 => UNS * INC # I2: 7,9 => UNS * DIS # I9: 7,9 => CTR => I9: 6 * INC # I9: 6 => UNS * INC # G8: 7,9 => UNS * INC # G9: 7,9 => UNS * DIS # I9: 7,9 => CTR => I9: 6 * INC # I9: 6 => UNS * INC # E9: 7,9 => UNS * INC # E9: 2,6,8 => UNS * INC # H5: 7,9 => UNS * DIS # H6: 7,9 => CTR => H6: 6 * INC # H6: 6 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A7: 6,9 => UNS * DIS # A7: 7 => CTR => A7: 6,9 * INC A7: 6,9 # E3: 6,9 => UNS * PRF A7: 6,9 # E3: 7 => SOL * STA A7: 6,9 + E3: 7 * CNT 4 HDP CHAINS / 4 HYP OPENED