Analysis of xx-top500-169-base.sdk
Contents
Original Sudoku
level: medium
position: 5.....7.2.4....5......1.....2.5.........3..8........1.1.86........7..4..3........ initial
Autosolve
position: 51.8.473284.3..591.37.15846.215.837...513..8..834...15158643927...781453374.5.168 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 7 => CTR => F2: 2,6 * PRF # A8: 2,9 => SOL * DIS # A8: 6 => CTR => A8: 2,9 * DIS # F2: 2,7 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # A4: 6,9 => CTR => A4: 4 * PRF # A4: 4 => SOL * PRF # A5: 6,9 => SOL * DIS # A6: 6,9 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # F5: 6,9 => CTR => F5: 2,7 * DIS # F5: 6,9 => CTR => F5: 2,7 * DIS # A4: 6,9 => CTR => A4: 4 * PRF # A4: 4 => SOL * DIS # F6: 2,7 => CTR => F6: 6,9 * PRF # A4: 4,9 => SOL * DIS # A4: 6 => CTR => A4: 4,9 * DIS # F5: 2,6 => CTR => F5: 7,9 * PRF # F5: 7,9 => SOL * DIS # A5: 4,9 => CTR => A5: 6,7 * PRF # A5: 6,7 => SOL * DIS # F6: 2,6 => CTR => F6: 7,9 * DIS # A8: 6,9 => CTR => A8: 2 * PRF # A8: 2 => SOL * PRF # A8: 2,9 => SOL * DIS # A8: 6 => CTR => A8: 2,9 * DIS # F5: 2,9 => CTR => F5: 6,7 * CNT 27 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 7 => CTR => F2: 2,6 * PRF F2: 2,6 # A8: 2,9 => SOL * STA F2: 2,6 + A8: 2,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.....7.2.4....5......1.....2.5.........3..8........1.1.86........7..4..3........ | initial |
| 51.8.473284.3..591.37.15846.215.837...513..8..834...15158643927...781453374.5.168 | autosolve |
| 516894732842376591937215846421568379695137284783429615158643927269781453374952168 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 6,9 C2: 2,6 A3: 2,9 E1: 6,9 E2: 2,7 D3: 2,9 B5: 6,9 E4: 6,9 E6: 2,7 I4: 4,9 G5: 2,6 I5: 4,9 G6: 2,6 B8: 6,9 C8: 2,9 D9: 2,9 F9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,A3: 2.. / C2 = 2 => 0 pairs (*) / A3 = 2 => 0 pairs (X) G5,G6: 2.. / G5 = 2 => 16 pairs (_) / G6 = 2 => 0 pairs (X) A8,C8: 2.. / A8 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) D9,F9: 2.. / D9 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) A3,D3: 2.. / A3 = 2 => 0 pairs (X) / D3 = 2 => 0 pairs (_) F5,G5: 2.. / F5 = 2 => 0 pairs (X) / G5 = 2 => 16 pairs (_) A3,A8: 2.. / A3 = 2 => 0 pairs (X) / A8 = 2 => 0 pairs (_) C2,C8: 2.. / C2 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) D3,D9: 2.. / D3 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E2,E6: 2.. / E2 = 2 => 0 pairs (X) / E6 = 2 => 16 pairs (_) A4,A5: 4.. / A4 = 4 => 0 pairs (*) / A5 = 4 => 0 pairs (X) I4,I5: 4.. / I4 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) A4,I4: 4.. / A4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) A5,I5: 4.. / A5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) C1,C2: 6.. / C1 = 6 => 0 pairs (*) / C2 = 6 => 0 pairs (X) E1,F2: 6.. / E1 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 16 pairs (_) A8,B8: 6.. / A8 = 6 => 0 pairs (X) / B8 = 6 => 0 pairs (_) C1,E1: 6.. / C1 = 6 => 0 pairs (*) / E1 = 6 => 0 pairs (X) C2,F2: 6.. / C2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) A4,E4: 6.. / A4 = 6 => 0 pairs (X) / E4 = 6 => 0 pairs (_) B5,B8: 6.. / B5 = 6 => 0 pairs (X) / B8 = 6 => 0 pairs (_) E1,E4: 6.. / E1 = 6 => 0 pairs (X) / E4 = 6 => 0 pairs (_) E2,F2: 7.. / E2 = 7 => 16 pairs (_) / F2 = 7 => 0 pairs (X) A5,A6: 7.. / A5 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) A5,F5: 7.. / A5 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) E2,E6: 7.. / E2 = 7 => 16 pairs (_) / E6 = 7 => 0 pairs (X) C1,A3: 9.. / C1 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) E1,D3: 9.. / E1 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) I4,I5: 9.. / I4 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) D9,F9: 9.. / D9 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) C1,E1: 9.. / C1 = 9 => 0 pairs (X) / E1 = 9 => 0 pairs (_) A3,D3: 9.. / A3 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) A6,F6: 9.. / A6 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) B5,B8: 9.. / B5 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) C1,C8: 9.. / C1 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) D3,D9: 9.. / D3 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) E1,E4: 9.. / E1 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) * DURATION: 0:01:14.958834 START: 08:30:35.764236 END: 08:31:50.723070 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B5,B8,C1,C2,C8,D3,D9,E1,E2,E4,E6,F9,G5,G6,I4,I5) * 51.8.473284.3..591.37.15846.215.837...513..8..834...15158643927...781453374.5.168 * PAIR C2: 2,6 ROW 2 F2: 2,6,7 # reduction candidate for 2,6 F2: 7 => CTR * 51.864732846327591237915846621598374..513..8..834...15158643927...781453374.5.168 F2: 2,6 # 16 pairs * PAIR A3: 2,9 COL A A8: 2,9,6 # reduction candidate for 2,9 A8: 2,9 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 A8: 6 => CTR * 51.8.473284.3..591237915846.215983744.5137289.834...15158643927...781453374.5.168 * PAIR E2: 2,7 BLK 2 F2: 2,7,6 # reduction candidate for 2,7 F2: 2,7 => CTR * 51.8647328463..59123791584662159837449513..8..834...15158643927...781453374.5.168 F2: 6 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 * PAIR B5: 6,9 BLK 4 A4: 6,9,4 # reduction candidate for 6,9 A4: 6,9 => CTR * 51.8.473284.3..591.37.15846.215.83744.5137289783429615158643927.92781453374952168 A4: 4 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 A5: 6,9,4,7 # reduction candidate for 6,9 A5: 6,9 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 A5: 4,7 # 18 pairs A6: 6,9,7 # reduction candidate for 6,9 A6: 6,9 => CTR * 516894732842376591937215846421568379795132.84.834...15158643927...781453374.5.168 A6: 7 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 * PAIR B5: 6,9 ROW 5 F5: 6,9,2,7 # reduction candidate for 6,9 F5: 6,9 => CTR * 51.8.473284.3..591.37.158464215683797651392849834..615158643927692781453374.5.168 F5: 2,7 # 19 pairs * PAIR E4: 6,9 BLK 5 F5: 6,9,2,7 # reduction candidate for 6,9 F5: 6,9 => CTR * 51.8.473284.3..591.37.158464215683797651392849834..615158643927692781453374.5.168 F5: 2,7 # 19 pairs F6: 6,9,2,7 # reduction candidate for 6,9 F6: 6,9 # 19 pairs * PAIR E4: 6,9 ROW 4 A4: 6,9,4 # reduction candidate for 6,9 A4: 6,9 => CTR * 51.8.473284.3..591.37.15846.215.83744.5137289783429615158643927.92781453374952168 A4: 4 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 * PAIR E6: 2,7 BLK 5 F5: 2,7,6,9 # reduction candidate for 2,7 F5: 2,7 # 19 pairs F6: 2,7,6,9 # reduction candidate for 2,7 F6: 2,7 => CTR * 5198647328463..5912379158466215.837...513..8.9834..615158643927.92781453374.5.168 F6: 6,9 # 19 pairs * PAIR I4: 4,9 ROW 4 A4: 4,9,6 # reduction candidate for 4,9 A4: 4,9 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 A4: 6 => CTR * 51.8.473284.3..591.37.1584662159837449513..8..834...15158643927...781453374.5.168 * PAIR G5: 2,6 ROW 5 F5: 2,6,7,9 # reduction candidate for 2,6 F5: 2,6 => CTR * 51.8.473284.3..591.37.15846421568379795132684683479.15158643927...781453374.5.168 F5: 7,9 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 * PAIR I5: 4,9 ROW 5 A5: 4,9,6,7 # reduction candidate for 4,9 A5: 4,9 => CTR * 51.894732842376591937215846.215683794.513728.783429615158643927...781453374952168 A5: 6,7 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 * PAIR G6: 2,6 ROW 6 F6: 2,6,7,9 # reduction candidate for 2,6 F6: 2,6 => CTR * 5198647328463275912379158466215.837...513..8.98347..15158643927.92781453374.5.168 F6: 7,9 # 18 pairs * PAIR B8: 6,9 BLK 7 A8: 6,9,2 # reduction candidate for 6,9 A8: 6,9 => CTR * 51.8.473284.3..591237915846.215983744.5137289.834...15158643927...781453374.5.168 A8: 2 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 * PAIR C8: 2,9 BLK 7 A8: 2,9,6 # reduction candidate for 2,9 A8: 2,9 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 A8: 6 => CTR * 51.8.473284.3..591237915846.215983744.5137289.834...15158643927...781453374.5.168 * PAIR F9: 2,9 COL F F5: 2,9,6,7 # reduction candidate for 2,9 F5: 2,9 => CTR * 516894732842376591937215846421568379795132.84.834...15158643927...781453374.5.168 F5: 6,7 # 17 pairs F6: 2,9,6,7 # reduction candidate for 2,9 F6: 2,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-169-base-pr-000.dot * REASONING * DIS # F2: 7 => CTR => F2: 2,6 * PRF # A8: 2,9 => SOL * DIS # A8: 6 => CTR => A8: 2,9 * DIS # F2: 2,7 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # A4: 6,9 => CTR => A4: 4 * PRF # A4: 4 => SOL * PRF # A5: 6,9 => SOL * DIS # A6: 6,9 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # F5: 6,9 => CTR => F5: 2,7 * DIS # F5: 6,9 => CTR => F5: 2,7 * DIS # A4: 6,9 => CTR => A4: 4 * PRF # A4: 4 => SOL * DIS # F6: 2,7 => CTR => F6: 6,9 * PRF # A4: 4,9 => SOL * DIS # A4: 6 => CTR => A4: 4,9 * DIS # F5: 2,6 => CTR => F5: 7,9 * PRF # F5: 7,9 => SOL * DIS # A5: 4,9 => CTR => A5: 6,7 * PRF # A5: 6,7 => SOL * DIS # F6: 2,6 => CTR => F6: 7,9 * DIS # A8: 6,9 => CTR => A8: 2 * PRF # A8: 2 => SOL * PRF # A8: 2,9 => SOL * DIS # A8: 6 => CTR => A8: 2,9 * DIS # F5: 2,9 => CTR => F5: 6,7 * CNT 27 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B5,B8,C1,C2,C8,D3,D9,E1,E2,E4,E6,F9,G5,G6,I4,I5) * 51.8.473284.3..591.37.15846.215.837...513..8..834...15158643927...781453374.5.168 * PAIR C2: 2,6 ROW 2 F2: 2,6,7 # reduction candidate for 2,6 F2: 7 => CTR * 51.864732846327591237915846621598374..513..8..834...15158643927...781453374.5.168 * PAIR RESTART * PAIR A3: 2,9 COL A A8: 2,9,6 # reduction candidate for 2,9 A8: 2,9 => SOLVED * 516894732842376591937215846421568379695137284783429615158643927269781453374952168 * DURATION: 0:00:04.626999 START: 08:32:37.661330 END: 08:32:42.288329 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-169-base-pr-001.dot * REASONING * DIS # F2: 7 => CTR => F2: 2,6 * PRF F2: 2,6 # A8: 2,9 => SOL * STA F2: 2,6 + A8: 2,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 169 solution: 516894732842376591937215846421568379695137284783429615158643927269781453374952168 info: 1824 FNBTWY S8.f 32155 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 516894732842376591937215846421568379695137284783429615158643927269781453374952168 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 # F2: 2,6 => UNS * DIS # F2: 7 => CTR => F2: 2,6 * PRF # A8: 2,9 => SOL * DIS # A8: 6 => CTR => A8: 2,9 * DIS # F2: 2,7 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # A4: 6,9 => CTR => A4: 4 * PRF # A4: 4 => SOL * PRF # A5: 6,9 => SOL * INC # A5: 4,7 => UNS * DIS # A6: 6,9 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # F5: 6,9 => CTR => F5: 2,7 * INC # F5: 2,7 => UNS * DIS # F5: 6,9 => CTR => F5: 2,7 * INC # F5: 2,7 => UNS * INC # F6: 6,9 => UNS * DIS # A4: 6,9 => CTR => A4: 4 * PRF # A4: 4 => SOL * INC # F5: 2,7 => UNS * DIS # F6: 2,7 => CTR => F6: 6,9 * INC # F6: 6,9 => UNS * PRF # A4: 4,9 => SOL * DIS # A4: 6 => CTR => A4: 4,9 * DIS # F5: 2,6 => CTR => F5: 7,9 * PRF # F5: 7,9 => SOL * DIS # A5: 4,9 => CTR => A5: 6,7 * PRF # A5: 6,7 => SOL * DIS # F6: 2,6 => CTR => F6: 7,9 * INC # F6: 7,9 => UNS * DIS # A8: 6,9 => CTR => A8: 2 * PRF # A8: 2 => SOL * PRF # A8: 2,9 => SOL * DIS # A8: 6 => CTR => A8: 2,9 * DIS # F5: 2,9 => CTR => F5: 6,7 * INC # F5: 6,7 => UNS * INC # F6: 2,9 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 2,6 => UNS * DIS # F2: 7 => CTR => F2: 2,6 * PRF F2: 2,6 # A8: 2,9 => SOL * STA F2: 2,6 + A8: 2,9 * CNT 3 HDP CHAINS / 3 HYP OPENED