Analysis of xx-top500-440-base.sdk
Contents
Original Sudoku
level: medium
position: ..4...53..8..6........1....1..5..7..2.......6.....8....3.4...8.6..1.............. initial
Autosolve
position: .648..531.81.654...2..1486.1965..7.82.8..13.64.36.8.1..3.4.618.64.18...381.2..6.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 7,9 => CTR => A2: 3 * DIS # A3: 7,9 => CTR => A3: 3,5 * DIS # A7: 5 => CTR => A7: 7,9 * DIS # A3: 7,9 => CTR => A3: 3,5 * DIS # D3: 7,9 => CTR => D3: 3 * DIS # D3: 7,9 => CTR => D3: 3 * DIS # I6: 2,9 => CTR => I6: 5 * DIS # E6: 7 => CTR => E6: 2,9 * DIS # E9: 7,9 => CTR => E9: 3,5 * CNT 9 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 7,9 => CTR => A2: 3 * DIS A2: 3 # A3: 7,9 => CTR => A3: 5 * DIS A2: 3 + A3: 5 # I6: 2,9 => CTR => I6: 5 * DIS A2: 3 + A3: 5 + I6: 5 # E7: 7,9 => CTR => E7: 5 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 # E9: 7,9 => CTR => E9: 3 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 # H8: 2,9 => CTR => H8: 5,7 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 # I7: 7 => CTR => I7: 2,9 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 # C8: 5 => CTR => C8: 2,9 * PRF A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 + C8: 2,9 # C7: 7,9 => SOL * STA A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 + C8: 2,9 + C7: 7,9 * CNT 9 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4...53..8..6........1....1..5..7..2.......6.....8....3.4...8.6..1.............. | initial |
| .648..531.81.654...2..1486.1965..7.82.8..13.64.36.8.1..3.4.618.64.18...381.2..6.4 | autosolve |
| 964872531381965427527314869196523748258741396473698215739456182642187953815239674 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 7,9 I3: 7,9 B5: 5,7 B6: 5,7 F4: 2,3 D5: 7,9 H4: 2,4 G6: 2,9 F8: 7,9 G8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 2.. / E1 = 2 => 11 pairs (_) / F1 = 2 => 15 pairs (_) H2,I2: 2.. / H2 = 2 => 15 pairs (_) / I2 = 2 => 12 pairs (_) C7,C8: 2.. / C7 = 2 => 10 pairs (_) / C8 = 2 => 0 pairs (*) C7,I7: 2.. / C7 = 2 => 10 pairs (_) / I7 = 2 => 0 pairs (*) F1,F4: 2.. / F1 = 2 => 15 pairs (_) / F4 = 2 => 11 pairs (_) G6,G8: 2.. / G6 = 2 => 16 pairs (_) / G8 = 2 => 11 pairs (_) A2,A3: 3.. / A2 = 3 => 11 pairs (_) / A3 = 3 => 0 pairs (X) D2,D3: 3.. / D2 = 3 => 0 pairs (X) / D3 = 3 => 11 pairs (_) E4,F4: 3.. / E4 = 3 => 11 pairs (_) / F4 = 3 => 15 pairs (_) E9,F9: 3.. / E9 = 3 => 15 pairs (_) / F9 = 3 => 11 pairs (_) A2,D2: 3.. / A2 = 3 => 11 pairs (_) / D2 = 3 => 0 pairs (X) A3,D3: 3.. / A3 = 3 => 0 pairs (X) / D3 = 3 => 11 pairs (_) E4,E9: 3.. / E4 = 3 => 11 pairs (_) / E9 = 3 => 15 pairs (_) F4,F9: 3.. / F4 = 3 => 15 pairs (_) / F9 = 3 => 11 pairs (_) E4,E5: 4.. / E4 = 4 => 12 pairs (_) / E5 = 4 => 12 pairs (_) H4,H5: 4.. / H4 = 4 => 12 pairs (_) / H5 = 4 => 12 pairs (_) E4,H4: 4.. / E4 = 4 => 12 pairs (_) / H4 = 4 => 12 pairs (_) E5,H5: 4.. / E5 = 4 => 12 pairs (_) / H5 = 4 => 12 pairs (_) A3,C3: 5.. / A3 = 5 => 13 pairs (_) / C3 = 5 => 0 pairs (X) B5,B6: 5.. / B5 = 5 => 10 pairs (_) / B6 = 5 => 0 pairs (X) H5,I6: 5.. / H5 = 5 => 0 pairs (X) / I6 = 5 => 10 pairs (_) E7,E9: 5.. / E7 = 5 => 13 pairs (_) / E9 = 5 => 14 pairs (_) B5,H5: 5.. / B5 = 5 => 10 pairs (_) / H5 = 5 => 0 pairs (X) B6,I6: 5.. / B6 = 5 => 0 pairs (X) / I6 = 5 => 10 pairs (_) C8,H8: 5.. / C8 = 5 => 14 pairs (_) / H8 = 5 => 11 pairs (_) A3,A7: 5.. / A3 = 5 => 13 pairs (_) / A7 = 5 => 0 pairs (X) I6,I7: 5.. / I6 = 5 => 10 pairs (_) / I7 = 5 => 0 pairs (X) B5,B6: 7.. / B5 = 7 => 0 pairs (X) / B6 = 7 => 10 pairs (_) B6,E6: 7.. / B6 = 7 => 10 pairs (_) / E6 = 7 => 0 pairs (X) G6,G8: 9.. / G6 = 9 => 11 pairs (_) / G8 = 9 => 16 pairs (_) * DURATION: 0:00:52.704479 START: 17:48:18.683744 END: 17:49:11.388223 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B5,B6,D5,F4,F8,G6,G8,H4,I3) * .648..531.81.654...2..1486.1965..7.82.8..13.64.36.8.1..3.4.618.64.18...381.2..6.4 * PAIR A1: 7,9 BLK 1 A2: 7,9,3 # reduction candidate for 7,9 A2: 7,9 => CTR * .648..531.813654..325.1486.196532748258.4139647369821553.47618264.18..5381.2536.4 A2: 3 # 11 pairs A3: 7,9,3,5 # reduction candidate for 7,9 A3: 7,9 => CTR * .648..531381.654...2531486.196532748258.4139647369821553.47618264.18..5381.2536.4 A3: 3,5 # 11 pairs C3: 7,9,5 # reduction candidate for 7,9 C3: 7,9 # 13 pairs * PAIR A1: 7,9 ROW 1 E1: 7,9,2 # reduction candidate for 7,9 E1: 7,9 # 15 pairs F1: 7,9,2 # reduction candidate for 7,9 F1: 7,9 # 11 pairs * PAIR A1: 7,9 COL A A7: 7,9,5 # reduction candidate for 7,9 A7: 5 => CTR * .648..531.81.654...25.1486.196532748258.4139647369821553.47618264.18..5381.2536.4 A7: 7,9 # 13 pairs * PAIR I3: 7,9 BLK 3 H2: 7,9,2 # reduction candidate for 7,9 H2: 7,9 # 12 pairs I2: 7,9,2 # reduction candidate for 7,9 I2: 7,9 # 15 pairs * PAIR I3: 7,9 ROW 3 A3: 7,9,3,5 # reduction candidate for 7,9 A3: 7,9 => CTR * .648..531381.654...2531486.196532748258.4139647369821553.47618264.18..5381.2536.4 A3: 3,5 # 11 pairs C3: 7,9,5 # reduction candidate for 7,9 C3: 7,9 # 13 pairs D3: 7,9,3 # reduction candidate for 7,9 D3: 7,9 => CTR * .648..531.813654..325.1486.196532748258.4139647369821553.47618264.18..5381.2536.4 D3: 3 # 11 pairs * PAIR I3: 7,9 COL I I7: 7,9,2,5 # reduction candidate for 7,9 I7: 7,9 # 12 pairs I7: 2,5 # 12 pairs * PAIR F4: 2,3 BLK 5 E4: 2,3,4 # reduction candidate for 2,3 E4: 4 # 12 pairs E4: 2,3 # 12 pairs * PAIR D5: 7,9 BLK 5 E5: 7,9,4 # reduction candidate for 7,9 E5: 7,9 # 12 pairs E6: 7,9,2 # reduction candidate for 7,9 E6: 7,9 # 12 pairs * PAIR D5: 7,9 COL D D2: 7,9,3 # reduction candidate for 7,9 D2: 7,9 # 11 pairs D3: 7,9,3 # reduction candidate for 7,9 D3: 7,9 => CTR * .648..531.813654..325.1486.196532748258.4139647369821553.47618264.18..5381.2536.4 D3: 3 # 11 pairs * PAIR H4: 2,4 ROW 4 E4: 2,4,3 # reduction candidate for 2,4 E4: 2,4 # 15 pairs E4: 3 # 11 pairs * PAIR G6: 2,9 BLK 6 I6: 2,9,5 # reduction candidate for 2,9 I6: 2,9 => CTR * 7648..531.81.654..52.31486.196532748278941356453678.1..32496185645187..3819253674 I6: 5 # 10 pairs * PAIR G6: 2,9 ROW 6 E6: 2,9,7 # reduction candidate for 2,9 E6: 7 => CTR * 7648..531.81.654..52.31486.196532748278941356453678.1..32496185645187..3819253674 E6: 2,9 # 10 pairs * PAIR F8: 7,9 BLK 8 E7: 7,9,5 # reduction candidate for 7,9 E7: 7,9 # 14 pairs E9: 7,9,3,5 # reduction candidate for 7,9 E9: 7,9 => CTR * .6482.531381.654..52.31486.196532748258741396473698215.3.45618.64.189..381.2.36.4 E9: 3,5 # 11 pairs F9: 7,9,3 # reduction candidate for 7,9 F9: 7,9 # 15 pairs * PAIR F8: 7,9 ROW 8 C8: 7,9,2,5 # reduction candidate for 7,9 C8: 7,9 # 14 pairs H8: 7,9,2,5 # reduction candidate for 7,9 H8: 7,9 # 16 pairs * PAIR F8: 7,9 COL F F1: 7,9,2 # reduction candidate for 7,9 F1: 2 # 15 pairs F1: 7,9 # 11 pairs * PAIR G8: 2,9 BLK 9 I7: 2,9,5,7 # reduction candidate for 2,9 I7: 2,9 # 14 pairs H8: 2,9,5,7 # reduction candidate for 2,9 H8: 2,9 # 19 pairs * PAIR G8: 2,9 ROW 8 C8: 2,9,5,7 # reduction candidate for 2,9 C8: 2,9 # 14 pairs C8: 5,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-440-base-pr-000.dot * REASONING * DIS # A2: 7,9 => CTR => A2: 3 * DIS # A3: 7,9 => CTR => A3: 3,5 * DIS # A7: 5 => CTR => A7: 7,9 * DIS # A3: 7,9 => CTR => A3: 3,5 * DIS # D3: 7,9 => CTR => D3: 3 * DIS # D3: 7,9 => CTR => D3: 3 * DIS # I6: 2,9 => CTR => I6: 5 * DIS # E6: 7 => CTR => E6: 2,9 * DIS # E9: 7,9 => CTR => E9: 3,5 * CNT 9 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B5,B6,D5,F4,F8,G6,G8,H4,I3) * .648..531.81.654...2..1486.1965..7.82.8..13.64.36.8.1..3.4.618.64.18...381.2..6.4 * PAIR A1: 7,9 BLK 1 A2: 7,9,3 # reduction candidate for 7,9 A2: 7,9 => CTR * .648..531.813654..325.1486.196532748258.4139647369821553.47618264.18..5381.2536.4 A3: 7,9,5 # reduction candidate for 7,9 A3: 7,9 => CTR * .648..531381.654...2531486.196532748258.4139647369821553.47618264.18..5381.2536.4 * RESTART * PAIR A1: 7,9 ROW 1 E1: 7,9,2 # reduction candidate for 7,9 E1: 7,9 # 15 pairs F1: 7,9,2 # reduction candidate for 7,9 F1: 7,9 # 14 pairs * PAIR I3: 7,9 BLK 3 H2: 7,9,2 # reduction candidate for 7,9 H2: 7,9 # 15 pairs I2: 7,9,2 # reduction candidate for 7,9 I2: 7,9 # 18 pairs * PAIR I3: 7,9 COL I I7: 7,9,2,5 # reduction candidate for 7,9 I7: 7,9 # 15 pairs I7: 2,5 # 15 pairs * PAIR F4: 2,3 BLK 5 E4: 2,3,4 # reduction candidate for 2,3 E4: 2,3 # 15 pairs E4: 4 # 12 pairs * PAIR D5: 7,9 BLK 5 E5: 7,9,4 # reduction candidate for 7,9 E5: 7,9 # 12 pairs E6: 7,9,2 # reduction candidate for 7,9 E6: 7,9 # 15 pairs * PAIR H4: 2,4 ROW 4 E4: 2,4,3 # reduction candidate for 2,4 E4: 2,4 # 15 pairs E4: 3 # 14 pairs * PAIR G6: 2,9 BLK 6 I6: 2,9,5 # reduction candidate for 2,9 I6: 2,9 => CTR * .648..5313817654..52.314867196532748278941356453678.1..32496185645187..381.2536.4 * PAIR F8: 7,9 BLK 8 E7: 7,9,5 # reduction candidate for 7,9 E7: 7,9 => CTR * .648.953138176542952.31486.1965..7.8258..13.64736.8.15.354.618264218.95381.253674 E9: 7,9,3 # reduction candidate for 7,9 E9: 7,9 => CTR * .648..531381.654..52.31486.196532748258.41396473698215.3.45618.64.18.9.381.27.6.4 * RESTART * PAIR F8: 7,9 ROW 8 C8: 7,9,2,5 # reduction candidate for 7,9 C8: 7,9 # 14 pairs H8: 7,9,2,5 # reduction candidate for 7,9 H8: 7,9 # 14 pairs * PAIR G8: 2,9 BLK 9 I7: 2,9,7 # reduction candidate for 2,9 I7: 2,9 # 20 pairs H8: 2,9,5,7 # reduction candidate for 2,9 H8: 2,9 => CTR * .648.2531381.6547252731486.1965.37.8258..13.64736.8.15.3.45618.645187..381.239654 * RESTART * PAIR G8: 2,9 BLK 9 I7: 2,9,7 # reduction candidate for 2,9 I7: 7 => CTR * .648.2531381.654.252.3148691965.3728258..1346473628915.3245618764.18.253815237694 * PAIR G8: 2,9 ROW 8 C8: 2,9,5 # reduction candidate for 2,9 C8: 5 => CTR * .648.2531381.654..52.31486.1965.37.8258..13.64736.8.15.3245618964518...381.23.6.4 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A7,C3,C8,D2,D5,E1,E4,E6,G6,G8,H2,H4,H5,I3,I7) * .648.2531381.654..52.31486.1965.37.8258..13.64736.8.15.3.45618.64.187.53815239674 * PAIR C3: 7,9 COL C C7: 7,9,2 # reduction candidate for 7,9 C7: 7,9 => SOLVED * 964872531381965427527314869196523748258741396473698215739456182642187953815239674 * DURATION: 0:00:31.295480 START: 17:49:51.860538 END: 17:50:23.156018 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-440-base-pr-001.dot * REASONING * DIS # A2: 7,9 => CTR => A2: 3 * DIS A2: 3 # A3: 7,9 => CTR => A3: 5 * DIS A2: 3 + A3: 5 # I6: 2,9 => CTR => I6: 5 * DIS A2: 3 + A3: 5 + I6: 5 # E7: 7,9 => CTR => E7: 5 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 # E9: 7,9 => CTR => E9: 3 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 # H8: 2,9 => CTR => H8: 5,7 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 # I7: 7 => CTR => I7: 2,9 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 # C8: 5 => CTR => C8: 2,9 * PRF A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 + C8: 2,9 # C7: 7,9 => SOL * STA A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 + C8: 2,9 + C7: 7,9 * CNT 9 HDP CHAINS / 26 HYP OPENED
Header Info
Top 500 Minimum 17 440 solution: 964872531381965427527314869196523748258741396473698215739456182642187953815239674 info: 95271 FNBXK S8.f 47137 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 964872531381965427527314869196523748258741396473698215739456182642187953815239674 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: 7,9 => CTR => A2: 3 * INC # A2: 3 => UNS * DIS # A3: 7,9 => CTR => A3: 3,5 * INC # A3: 3,5 => UNS * INC # C3: 7,9 => UNS * INC # E1: 7,9 => UNS * INC # F1: 7,9 => UNS * INC # A7: 7,9 => UNS * DIS # A7: 5 => CTR => A7: 7,9 * INC # H2: 7,9 => UNS * INC # I2: 7,9 => UNS * DIS # A3: 7,9 => CTR => A3: 3,5 * INC # A3: 3,5 => UNS * INC # C3: 7,9 => UNS * DIS # D3: 7,9 => CTR => D3: 3 * INC # D3: 3 => UNS * INC # I7: 7,9 => UNS * INC # I7: 2,5 => UNS * INC # E4: 2,3 => UNS * INC # E4: 4 => UNS * INC # E5: 7,9 => UNS * INC # E6: 7,9 => UNS * INC # D2: 7,9 => UNS * DIS # D3: 7,9 => CTR => D3: 3 * INC # D3: 3 => UNS * INC # E4: 2,4 => UNS * INC # E4: 3 => UNS * DIS # I6: 2,9 => CTR => I6: 5 * INC # I6: 5 => UNS * INC # E6: 2,9 => UNS * DIS # E6: 7 => CTR => E6: 2,9 * INC # E7: 7,9 => UNS * DIS # E9: 7,9 => CTR => E9: 3,5 * INC # E9: 3,5 => UNS * INC # F9: 7,9 => UNS * INC # C8: 7,9 => UNS * INC # H8: 7,9 => UNS * INC # F1: 7,9 => UNS * INC # F1: 2 => UNS * INC # I7: 2,9 => UNS * INC # H8: 2,9 => UNS * INC # C8: 2,9 => UNS * INC # C8: 5,7 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 7,9 => CTR => A2: 3 * DIS A2: 3 # A3: 7,9 => CTR => A3: 5 * INC A2: 3 + A3: 5 # E1: 7,9 => UNS * INC A2: 3 + A3: 5 # F1: 7,9 => UNS * INC A2: 3 + A3: 5 # H2: 7,9 => UNS * INC A2: 3 + A3: 5 # I2: 7,9 => UNS * INC A2: 3 + A3: 5 # I7: 7,9 => UNS * INC A2: 3 + A3: 5 # I7: 2,5 => UNS * INC A2: 3 + A3: 5 # E4: 2,3 => UNS * INC A2: 3 + A3: 5 # E4: 4 => UNS * INC A2: 3 + A3: 5 # E5: 7,9 => UNS * INC A2: 3 + A3: 5 # E6: 7,9 => UNS * INC A2: 3 + A3: 5 # E4: 2,4 => UNS * INC A2: 3 + A3: 5 # E4: 3 => UNS * DIS A2: 3 + A3: 5 # I6: 2,9 => CTR => I6: 5 * DIS A2: 3 + A3: 5 + I6: 5 # E7: 7,9 => CTR => E7: 5 * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 # E9: 7,9 => CTR => E9: 3 * INC A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 # C8: 7,9 => UNS * INC A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 # H8: 7,9 => UNS * INC A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 # I7: 2,9 => UNS * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 # H8: 2,9 => CTR => H8: 5,7 * INC A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 # I7: 2,9 => UNS * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 # I7: 7 => CTR => I7: 2,9 * INC A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 # C8: 2,9 => UNS * DIS A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 # C8: 5 => CTR => C8: 2,9 * PRF A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 + C8: 2,9 # C7: 7,9 => SOL * STA A2: 3 + A3: 5 + I6: 5 + E7: 5 + E9: 3 + H8: 5,7 + I7: 2,9 + C8: 2,9 + C7: 7,9 * CNT 26 HDP CHAINS / 26 HYP OPENED