Analysis of xx-top500-102-base.sdk
Contents
Original Sudoku
level: medium
position: ..6.83....1....2...........8.3....5....1..4..........674.2........4..1.........8. initial
Autosolve
position: 426.83.17.18...263.376..84.863....512..1364.81.48..3267412.863.38.46.1.26.23...84 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D2: 5,9 => SOL * DIS # D2: 7 => CTR => D2: 5,9 * PRF # D2: 5,9 => SOL * DIS # D2: 7 => CTR => D2: 5,9 * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # B5: 5,9 => SOL * DIS # B5: 7 => CTR => B5: 5,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # E6: 7,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * PRF # F6: 7,9 => SOL * DIS # F6: 5 => CTR => F6: 7,9 * DIS # E6: 7,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * PRF # F6: 7,9 => SOL * DIS # F6: 5 => CTR => F6: 7,9 * DIS # D2: 7,9 => CTR => D2: 5 * PRF # D2: 5 => SOL * PRF # G9: 7,9 => SOL * DIS # G9: 5 => CTR => G9: 7,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # F8: 5,9 => CTR => F8: 7 * PRF # F8: 7 => SOL * DIS # E9: 5,9 => CTR => E9: 1,7 * PRF # F9: 5,9 => SOL * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # B5: 5,9 => SOL * DIS # B5: 7 => CTR => B5: 5,9 * DIS # F8: 5,9 => CTR => F8: 7 * PRF # F8: 7 => SOL * DIS # E9: 5,9 => CTR => E9: 1,7 * PRF # F9: 5,9 => SOL * DIS # E6: 7 => CTR => E6: 5,9 * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # G9: 7,9 => SOL * DIS # G9: 5 => CTR => G9: 7,9 * PRF # F8: 7,9 => SOL * DIS # F8: 5 => CTR => F8: 7,9 * CNT 43 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:
* PRF # D2: 5,9 => SOL * STA D2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6.83....1....2...........8.3....5....1..4..........674.2........4..1.........8. | initial |
| 426.83.17.18...263.376..84.863....512..1364.81.48..3267412.863.38.46.1.26.23...84 | autosolve |
| 426983517918574263537621849863742951259136478174859326741298635385467192692315784 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 5,9 A3: 5,9 D1: 5,9 E3: 1,2 F3: 1,2 G1: 5,9 I3: 5,9 C5: 5,9 B6: 7,9 D4: 7,9 E4: 2,4 F4: 2,4 G4: 7,9 H5: 7,9 C8: 5,9 B9: 5,9 E7: 5,9 I7: 5,9 H8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 16 pairs (_) / F3 = 1 => 17 pairs (_) E9,F9: 1.. / E9 = 1 => 17 pairs (_) / F9 = 1 => 16 pairs (_) E3,E9: 1.. / E3 = 1 => 16 pairs (_) / E9 = 1 => 17 pairs (_) F3,F9: 1.. / F3 = 1 => 17 pairs (_) / F9 = 1 => 16 pairs (_) E3,F3: 2.. / E3 = 2 => 17 pairs (_) / F3 = 2 => 16 pairs (_) E4,F4: 2.. / E4 = 2 => 16 pairs (_) / F4 = 2 => 17 pairs (_) E3,E4: 2.. / E3 = 2 => 17 pairs (_) / E4 = 2 => 16 pairs (_) F3,F4: 2.. / F3 = 2 => 16 pairs (_) / F4 = 2 => 17 pairs (_) E2,F2: 4.. / E2 = 4 => 16 pairs (_) / F2 = 4 => 17 pairs (_) E4,F4: 4.. / E4 = 4 => 17 pairs (_) / F4 = 4 => 16 pairs (_) E2,E4: 4.. / E2 = 4 => 16 pairs (_) / E4 = 4 => 17 pairs (_) F2,F4: 4.. / F2 = 4 => 17 pairs (_) / F4 = 4 => 16 pairs (_) A2,A3: 5.. / A2 = 5 => 0 pairs (X) / A3 = 5 => 0 pairs (_) D1,D2: 5.. / D1 = 5 => 0 pairs (X) / D2 = 5 => 0 pairs (_) G1,I3: 5.. / G1 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) B5,C5: 5.. / B5 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) E6,F6: 5.. / E6 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) C8,B9: 5.. / C8 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) I7,G9: 5.. / I7 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) D1,G1: 5.. / D1 = 5 => 0 pairs (X) / G1 = 5 => 0 pairs (_) A2,D2: 5.. / A2 = 5 => 0 pairs (X) / D2 = 5 => 0 pairs (_) A3,I3: 5.. / A3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) E7,I7: 5.. / E7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) C8,F8: 5.. / C8 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) B5,B9: 5.. / B5 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) C5,C8: 5.. / C5 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) G1,G9: 5.. / G1 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) I3,I7: 5.. / I3 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) B5,B6: 7.. / B5 = 7 => 0 pairs (X) / B6 = 7 => 0 pairs (_) G4,H5: 7.. / G4 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) H8,G9: 7.. / H8 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) D4,G4: 7.. / D4 = 7 => 0 pairs (*) / G4 = 7 => 0 pairs (X) B5,H5: 7.. / B5 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) F8,H8: 7.. / F8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) D2,D4: 7.. / D2 = 7 => 0 pairs (X) / D4 = 7 => 0 pairs (_) G4,G9: 7.. / G4 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) H5,H8: 7.. / H5 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) A2,A3: 9.. / A2 = 9 => 0 pairs (*) / A3 = 9 => 0 pairs (X) G1,I3: 9.. / G1 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) G4,H5: 9.. / G4 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) C8,B9: 9.. / C8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) D1,G1: 9.. / D1 = 9 => 0 pairs (*) / G1 = 9 => 0 pairs (X) A3,I3: 9.. / A3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) D4,G4: 9.. / D4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) E7,I7: 9.. / E7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) C5,C8: 9.. / C5 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) H5,H8: 9.. / H5 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) I3,I7: 9.. / I3 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) * DURATION: 0:01:57.442236 START: 06:14:19.371371 END: 06:16:16.813607 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B6,B9,C5,C8,D1,D4,E3,E4,E7,F3,F4,G1,G4,H5,H8,I3,I7) * 426.83.17.18...263.376..84.863....512..1364.81.48..3267412.863.38.46.1.26.23...84 * PAIR A2: 5,9 ROW 2 D2: 5,9,7 # reduction candidate for 5,9 D2: 5,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 D2: 7 => CTR * 4265839175187..2639376..8458639..7512751364981948..3267412586393894671.26.23...84 * PAIR D1: 5,9 BLK 2 D2: 5,9,7 # reduction candidate for 5,9 D2: 5,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 D2: 7 => CTR * 4265839175187..2639376..8458639..7512751364981948..3267412586393894671.26.23...84 * PAIR G1: 5,9 COL G G9: 5,9,7 # reduction candidate for 5,9 G9: 5,9 => CTR * 426983.17.18...263.376..84.863...7512751364981948..3267412.863.3894651726523..984 G9: 7 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * PAIR C5: 5,9 BLK 4 B5: 5,9,7 # reduction candidate for 5,9 B5: 5,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 B5: 7 => CTR * 4269835179185..2635376..8498637...512751364981948..3267412.863.3894651726523..984 * PAIR B6: 7,9 BLK 4 B5: 7,9,5 # reduction candidate for 7,9 B5: 7,9 => CTR * 4269835179185..2635376..8498637...512.51364.81.48..3267412.863.3894651726523..984 B5: 5 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * PAIR B6: 7,9 ROW 6 E6: 7,9,5 # reduction candidate for 7,9 E6: 7,9 => CTR * 426.83.17.18...263.376..84.863....5125913647817489532674125863.38546.1.26923...84 E6: 5 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 F6: 7,9,5 # reduction candidate for 7,9 F6: 7,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 F6: 5 => CTR * 426.83.17.18...263.376..84.863....5125913647817489532674125863.38546.1.26923...84 * PAIR D4: 7,9 BLK 5 E6: 7,9,5 # reduction candidate for 7,9 E6: 7,9 => CTR * 426.83.17.18...263.376..84.863....5125913647817489532674125863.38546.1.26923...84 E6: 5 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 F6: 7,9,5 # reduction candidate for 7,9 F6: 7,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 F6: 5 => CTR * 426.83.17.18...263.376..84.863....5125913647817489532674125863.38546.1.26923...84 * PAIR D4: 7,9 COL D D2: 7,9,5 # reduction candidate for 7,9 D2: 7,9 => CTR * 426583917518...2639376..8458639..7512751364981948..3267412586393894671.26.23...84 D2: 5 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * PAIR G4: 7,9 COL G G9: 7,9,5 # reduction candidate for 7,9 G9: 7,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 G9: 5 => CTR * 426.83.17.18...263.376..84.863...7512751364981948..3267412.86393894651.26.23...84 * PAIR H5: 7,9 ROW 5 B5: 7,9,5 # reduction candidate for 7,9 B5: 7,9 => CTR * 4269835179185..2635376..8498637...512.51364.81.48..3267412.863.3894651726523..984 B5: 5 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * PAIR C8: 5,9 ROW 8 F8: 5,9,7 # reduction candidate for 5,9 F8: 5,9 => CTR * 426983.17.18...263.376..84.863...7512751364981948..3267412.863.3894651726523..984 F8: 7 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * PAIR B9: 5,9 ROW 9 E9: 5,9,1,7 # reduction candidate for 5,9 E9: 5,9 => CTR * 426.83517.185472635376128498637249512..1364781748..32674129863538.4651.26.23.1784 E9: 1,7 # 20 pairs F9: 5,9,1,7 # reduction candidate for 5,9 F9: 5,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 F9: 1,7 # 20 pairs G9: 5,9,7 # reduction candidate for 5,9 G9: 5,9 => CTR * 426983.17.18...263.376..84.863...7512751364981948..3267412.863.3894651726523..984 G9: 7 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * PAIR B9: 5,9 COL B B5: 5,9,7 # reduction candidate for 5,9 B5: 5,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 B5: 7 => CTR * 4269835179185..2635376..8498637...512751364981948..3267412.863.3894651726523..984 * PAIR E7: 5,9 BLK 8 F8: 5,9,7 # reduction candidate for 5,9 F8: 5,9 => CTR * 426983.17.18...263.376..84.863...7512751364981948..3267412.863.3894651726523..984 F8: 7 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 E9: 5,9,1,7 # reduction candidate for 5,9 E9: 5,9 => CTR * 426.83517.185472635376128498637249512..1364781748..32674129863538.4651.26.23.1784 E9: 1,7 # 20 pairs F9: 5,9,1,7 # reduction candidate for 5,9 F9: 5,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 F9: 1,7 # 20 pairs * PAIR E7: 5,9 COL E E6: 5,9,7 # reduction candidate for 5,9 E6: 7 => CTR * 426.83.17.18...263.376..84.863....512..1364.81.48753267412.863.38546.1.26923...84 E6: 5,9 # 22 pairs * PAIR I7: 5,9 BLK 9 G9: 5,9,7 # reduction candidate for 5,9 G9: 5,9 => CTR * 426983.17.18...263.376..84.863...7512751364981948..3267412.863.3894651726523..984 G9: 7 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * PAIR H8: 7,9 BLK 9 G9: 7,9,5 # reduction candidate for 7,9 G9: 7,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 G9: 5 => CTR * 426.83.17.18...263.376..84.863...7512751364981948..3267412.86393894651.26.23...84 * PAIR H8: 7,9 ROW 8 F8: 7,9,5 # reduction candidate for 7,9 F8: 7,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 F8: 5 => CTR * 4269835179185..2635376..8498637...512..1364.81.48..3267412.863.38.4651726523..984 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-102-base-pr-000.dot * REASONING * PRF # D2: 5,9 => SOL * DIS # D2: 7 => CTR => D2: 5,9 * PRF # D2: 5,9 => SOL * DIS # D2: 7 => CTR => D2: 5,9 * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # B5: 5,9 => SOL * DIS # B5: 7 => CTR => B5: 5,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # E6: 7,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * PRF # F6: 7,9 => SOL * DIS # F6: 5 => CTR => F6: 7,9 * DIS # E6: 7,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * PRF # F6: 7,9 => SOL * DIS # F6: 5 => CTR => F6: 7,9 * DIS # D2: 7,9 => CTR => D2: 5 * PRF # D2: 5 => SOL * PRF # G9: 7,9 => SOL * DIS # G9: 5 => CTR => G9: 7,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # F8: 5,9 => CTR => F8: 7 * PRF # F8: 7 => SOL * DIS # E9: 5,9 => CTR => E9: 1,7 * PRF # F9: 5,9 => SOL * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # B5: 5,9 => SOL * DIS # B5: 7 => CTR => B5: 5,9 * DIS # F8: 5,9 => CTR => F8: 7 * PRF # F8: 7 => SOL * DIS # E9: 5,9 => CTR => E9: 1,7 * PRF # F9: 5,9 => SOL * DIS # E6: 7 => CTR => E6: 5,9 * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # G9: 7,9 => SOL * DIS # G9: 5 => CTR => G9: 7,9 * PRF # F8: 7,9 => SOL * DIS # F8: 5 => CTR => F8: 7,9 * CNT 43 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B6,B9,C5,C8,D1,D4,E3,E4,E7,F3,F4,G1,G4,H5,H8,I3,I7) * 426.83.17.18...263.376..84.863....512..1364.81.48..3267412.863.38.46.1.26.23...84 * PAIR A2: 5,9 ROW 2 D2: 5,9,7 # reduction candidate for 5,9 D2: 5,9 => SOLVED * 426983517918574263537621849863742951259136478174859326741298635385467192692315784 * DURATION: 0:00:02.514649 START: 06:17:31.295147 END: 06:17:33.809796 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-102-base-pr-001.dot * REASONING * PRF # D2: 5,9 => SOL * STA D2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 102 solution: 426983517918574263537621849863742951259136478174859326741298635385467192692315784 info: 1595 FNBTWXY S8.f 14106 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 426983517918574263537621849863742951259136478174859326741298635385467192692315784 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 # D2: 5,9 => SOL * DIS # D2: 7 => CTR => D2: 5,9 * PRF # D2: 5,9 => SOL * DIS # D2: 7 => CTR => D2: 5,9 * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # B5: 5,9 => SOL * DIS # B5: 7 => CTR => B5: 5,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # E6: 7,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * PRF # F6: 7,9 => SOL * DIS # F6: 5 => CTR => F6: 7,9 * DIS # E6: 7,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * PRF # F6: 7,9 => SOL * DIS # F6: 5 => CTR => F6: 7,9 * DIS # D2: 7,9 => CTR => D2: 5 * PRF # D2: 5 => SOL * PRF # G9: 7,9 => SOL * DIS # G9: 5 => CTR => G9: 7,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # F8: 5,9 => CTR => F8: 7 * PRF # F8: 7 => SOL * DIS # E9: 5,9 => CTR => E9: 1,7 * INC # E9: 1,7 => UNS * PRF # F9: 5,9 => SOL * INC # F9: 1,7 => UNS * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # B5: 5,9 => SOL * DIS # B5: 7 => CTR => B5: 5,9 * DIS # F8: 5,9 => CTR => F8: 7 * PRF # F8: 7 => SOL * DIS # E9: 5,9 => CTR => E9: 1,7 * INC # E9: 1,7 => UNS * PRF # F9: 5,9 => SOL * INC # F9: 1,7 => UNS * INC # E6: 5,9 => UNS * DIS # E6: 7 => CTR => E6: 5,9 * DIS # G9: 5,9 => CTR => G9: 7 * PRF # G9: 7 => SOL * PRF # G9: 7,9 => SOL * DIS # G9: 5 => CTR => G9: 7,9 * PRF # F8: 7,9 => SOL * DIS # F8: 5 => CTR => F8: 7,9 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D2: 5,9 => SOL * STA D2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED