Analysis of xx-top500-457-base.sdk
Contents
Original Sudoku
level: medium
position: .6...1..........2.......4.....47.8...9......1...8.....4..73....1.....59.........6 initial
Autosolve
position: .6..41....4.....2.....2.4.....47.8..894.....1...81...4459736...1.628459....195.46 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 5,6 => CTR => D2: 3,9 * DIS # C2: 7,8 => CTR => C2: 1,3,5 * DIS # D2: 5,6 => CTR => D2: 3,9 * DIS # F4: 2,3 => CTR => F4: 9 * DIS # G5: 7 => CTR => G5: 2,3 * DIS # G5: 3,7 => CTR => G5: 2 * DIS # G5: 3,7 => CTR => G5: 2 * CNT 7 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 5,6 => CTR => D2: 3,9 * DIS D2: 3,9 # D3: 3,9 => CTR => D3: 5,6 * DIS D2: 3,9 + D3: 5,6 # C2: 7,8 => CTR => C2: 1,3,5 * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I3: 7,8 => CTR => I3: 3,5,9 * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 # F4: 2,3 => CTR => F4: 9 * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 # I2: 9 => CTR => I2: 3,7 * PRF D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 + I2: 3,7 # A1: 2,7 => SOL * STA D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 + I2: 3,7 + A1: 2,7 * CNT 7 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6...1..........2.......4.....47.8...9......1...8.....4..73....1.....59.........6 | initial |
| .6..41....4.....2.....2.4.....47.8..894.....1...81...4459736...1.628459....195.46 | autosolve |
| 267941358941358627583627419612479835894563271735812964459736182176284593328195746 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) E2: 5,6 F2: 7,8 F3: 7,8 G2: 1,6 H3: 1,6 D5: 5,6 E5: 5,6 F5: 2,3 H5: 3,7 B8: 3,7 G7: 1,2 H7: 1,8 I7: 2,8 I8: 3,7 G9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H3: 1.. / G2 = 1 => 0 pairs (X) / H3 = 1 => 9 pairs (_) B4,C4: 1.. / B4 = 1 => 15 pairs (_) / C4 = 1 => 0 pairs (X) G7,H7: 1.. / G7 = 1 => 9 pairs (_) / H7 = 1 => 0 pairs (X) C2,G2: 1.. / C2 = 1 => 9 pairs (_) / G2 = 1 => 0 pairs (X) B3,B4: 1.. / B3 = 1 => 0 pairs (X) / B4 = 1 => 15 pairs (_) G2,G7: 1.. / G2 = 1 => 0 pairs (X) / G7 = 1 => 9 pairs (_) H3,H7: 1.. / H3 = 1 => 9 pairs (_) / H7 = 1 => 0 pairs (X) A1,C1: 2.. / A1 = 2 => 18 pairs (_) / C1 = 2 => 15 pairs (_) G7,I7: 2.. / G7 = 2 => 0 pairs (X) / I7 = 2 => 9 pairs (_) F5,G5: 2.. / F5 = 2 => 0 pairs (X) / G5 = 2 => 11 pairs (_) I4,I7: 2.. / I4 = 2 => 0 pairs (X) / I7 = 2 => 9 pairs (_) I8,G9: 3.. / I8 = 3 => 16 pairs (_) / G9 = 3 => 17 pairs (_) B8,I8: 3.. / B8 = 3 => 17 pairs (_) / I8 = 3 => 16 pairs (_) D5,E5: 5.. / D5 = 5 => 13 pairs (_) / E5 = 5 => 0 pairs (X) E2,E5: 5.. / E2 = 5 => 13 pairs (_) / E5 = 5 => 0 pairs (X) G2,H3: 6.. / G2 = 6 => 9 pairs (_) / H3 = 6 => 0 pairs (X) A4,A6: 6.. / A4 = 6 => 16 pairs (_) / A6 = 6 => 10 pairs (_) D5,E5: 6.. / D5 = 6 => 0 pairs (X) / E5 = 6 => 13 pairs (_) D3,H3: 6.. / D3 = 6 => 9 pairs (_) / H3 = 6 => 0 pairs (X) A4,H4: 6.. / A4 = 6 => 16 pairs (_) / H4 = 6 => 10 pairs (_) E2,E5: 6.. / E2 = 6 => 0 pairs (X) / E5 = 6 => 13 pairs (_) G2,G6: 6.. / G2 = 6 => 9 pairs (_) / G6 = 6 => 0 pairs (X) F2,F3: 7.. / F2 = 7 => 13 pairs (_) / F3 = 7 => 13 pairs (_) G5,H5: 7.. / G5 = 7 => 0 pairs (X) / H5 = 7 => 15 pairs (_) I8,G9: 7.. / I8 = 7 => 17 pairs (_) / G9 = 7 => 16 pairs (_) B8,I8: 7.. / B8 = 7 => 16 pairs (_) / I8 = 7 => 17 pairs (_) H1,H5: 7.. / H1 = 7 => 0 pairs (X) / H5 = 7 => 15 pairs (_) F2,F3: 8.. / F2 = 8 => 13 pairs (_) / F3 = 8 => 13 pairs (_) B9,C9: 8.. / B9 = 8 => 15 pairs (_) / C9 = 8 => 13 pairs (_) H7,I7: 8.. / H7 = 8 => 9 pairs (_) / I7 = 8 => 0 pairs (X) B3,B9: 8.. / B3 = 8 => 13 pairs (_) / B9 = 8 => 15 pairs (_) H1,H7: 8.. / H1 = 8 => 0 pairs (X) / H7 = 8 => 9 pairs (_) F4,F6: 9.. / F4 = 9 => 11 pairs (_) / F6 = 9 => 0 pairs (X) I4,G6: 9.. / I4 = 9 => 0 pairs (X) / G6 = 9 => 11 pairs (_) F4,I4: 9.. / F4 = 9 => 11 pairs (_) / I4 = 9 => 0 pairs (X) F6,G6: 9.. / F6 = 9 => 0 pairs (X) / G6 = 9 => 11 pairs (_) G1,G6: 9.. / G1 = 9 => 0 pairs (X) / G6 = 9 => 11 pairs (_) * DURATION: 0:01:11.514804 START: 18:21:55.827437 END: 18:23:07.342241 2017-05-04 * CP COUNT: (37) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D5,E2,E5,F2,F3,F5,G2,G7,G9,H3,H5,H7,I7,I8) * .6..41....4.....2.....2.4.....47.8..894.....1...81...4459736...1.628459....195.46 * PAIR E2: 5,6 BLK 2 D2: 5,6,3,9 # reduction candidate for 5,6 D2: 5,6 => CTR * .6..41....4....12.....2.46.6..47.8..894.....1...81.6.44597362181.628459....195.46 D2: 3,9 # 16 pairs D3: 5,6,3,9 # reduction candidate for 5,6 D3: 5,6 # 18 pairs * PAIR F2: 7,8 ROW 2 C2: 7,8,1,3,5 # reduction candidate for 7,8 C2: 7,8 => CTR * .6..41....4....12.....2.46.6..47.8..894.....1...81.6.44597362181.628459....195.46 C2: 1,3,5 # 15 pairs I2: 7,8,3,5,9 # reduction candidate for 7,8 I2: 7,8 # 16 pairs * PAIR F3: 7,8 ROW 3 B3: 7,8,1,3 # reduction candidate for 7,8 B3: 7,8 # 16 pairs C3: 7,8,1,3,5 # reduction candidate for 7,8 C3: 7,8 # 17 pairs I3: 7,8,3,5,9 # reduction candidate for 7,8 I3: 7,8 # 17 pairs * PAIR D5: 5,6 COL D D2: 5,6,3,9 # reduction candidate for 5,6 D2: 5,6 => CTR * .6..41....4....12.....2.46.6..47.8..894.....1...81.6.44597362181.628459....195.46 D2: 3,9 # 16 pairs D3: 5,6,3,9 # reduction candidate for 5,6 D3: 5,6 # 18 pairs * PAIR F5: 2,3 BLK 5 F4: 2,3,9 # reduction candidate for 2,3 F4: 2,3 => CTR * .6.341978.41958623983627415.1.4738.9894562731375819264459736182136284597728195346 F4: 9 # 11 pairs F6: 2,3,9 # reduction candidate for 2,3 F6: 2,3 # 11 pairs * PAIR F5: 2,3 ROW 5 G5: 2,3,7 # reduction candidate for 2,3 G5: 7 => CTR * .6.341978.4195862398.62.41..1.4738.9894562731.7.8192.4459736182136284597.28195346 G5: 2,3 # 15 pairs * PAIR H5: 3,7 BLK 6 G5: 3,7,2 # reduction candidate for 3,7 G5: 3,7 => CTR * .6.341978.41958623983627415.1.4738.9894562731..78192.44597361821.628459..28195.46 G5: 2 # 11 pairs * PAIR H5: 3,7 COL H H1: 3,7,5,8 # reduction candidate for 3,7 H1: 3,7 # 19 pairs H1: 5,8 # 13 pairs * PAIR B8: 3,7 BLK 7 A9: 3,7,2 # reduction candidate for 3,7 A9: 3,7 # 18 pairs B9: 3,7,2,8 # reduction candidate for 3,7 B9: 3,7 # 18 pairs C9: 3,7,2,8 # reduction candidate for 3,7 C9: 3,7 # 16 pairs * PAIR B8: 3,7 COL B B3: 3,7,1,8 # reduction candidate for 3,7 B3: 3,7 # 20 pairs B6: 3,7,2 # reduction candidate for 3,7 B6: 3,7 # 19 pairs * PAIR I8: 3,7 COL I I1: 3,7,5,8,9 # reduction candidate for 3,7 I1: 3,7 # 17 pairs I2: 3,7,5,8,9 # reduction candidate for 3,7 I2: 3,7 # 16 pairs I3: 3,7,5,8,9 # reduction candidate for 3,7 I3: 3,7 # 16 pairs * PAIR G9: 3,7 ROW 9 A9: 3,7,2 # reduction candidate for 3,7 A9: 3,7 # 18 pairs B9: 3,7,2,8 # reduction candidate for 3,7 B9: 3,7 # 18 pairs C9: 3,7,2,8 # reduction candidate for 3,7 C9: 3,7 # 16 pairs * PAIR G9: 3,7 COL G G1: 3,7,9 # reduction candidate for 3,7 G1: 3,7 # 11 pairs G5: 3,7,2 # reduction candidate for 3,7 G5: 3,7 => CTR * .6.341978.41958623983627415.1.4738.9894562731..78192.44597361821.628459..28195.46 G5: 2 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-457-base-pr-000.dot * REASONING * DIS # D2: 5,6 => CTR => D2: 3,9 * DIS # C2: 7,8 => CTR => C2: 1,3,5 * DIS # D2: 5,6 => CTR => D2: 3,9 * DIS # F4: 2,3 => CTR => F4: 9 * DIS # G5: 7 => CTR => G5: 2,3 * DIS # G5: 3,7 => CTR => G5: 2 * DIS # G5: 3,7 => CTR => G5: 2 * CNT 7 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D5,E2,E5,F2,F3,F5,G2,G7,G9,H3,H5,H7,I7,I8) * .6..41....4.....2.....2.4.....47.8..894.....1...81...4459736...1.628459....195.46 * PAIR E2: 5,6 BLK 2 D2: 5,6,3,9 # reduction candidate for 5,6 D2: 5,6 => CTR * .6..41....4....12.....2.46.6..47.8..894.....1...81.6.44597362181.628459....195.46 D3: 5,6,3,9 # reduction candidate for 5,6 D3: 5,6 # 18 pairs * RESTART * PAIR E2: 5,6 BLK 2 D3: 5,6,3,9 # reduction candidate for 5,6 D3: 3,9 => CTR * .6..41....4..6.12.....2.46.6..47.8..89465...1...81.6.44597362181.628459....195.46 * PAIR F2: 7,8 ROW 2 C2: 7,8,1,3,5 # reduction candidate for 7,8 C2: 7,8 => CTR * .6..41....4....12.....2.46.6..47.8..89465...1...81.6.44597362181.628459....195.46 I2: 7,8,3,5,9 # reduction candidate for 7,8 I2: 7,8 # 19 pairs * RESTART * PAIR F2: 7,8 ROW 2 I2: 7,8,3,5,9 # reduction candidate for 7,8 I2: 7,8 # 19 pairs I2: 3,5,9 # 17 pairs * PAIR RESTART * PAIR F2: 7,8 ROW 2 I2: 7,8,3,5,9 # reduction candidate for 7,8 I2: 7,8 # 19 pairs I2: 3,5,9 # 17 pairs * PAIR F3: 7,8 ROW 3 B3: 7,8,1,3 # reduction candidate for 7,8 B3: 7,8 # 19 pairs C3: 7,8,1,3,5 # reduction candidate for 7,8 C3: 7,8 # 20 pairs I3: 7,8,3,5,9 # reduction candidate for 7,8 I3: 7,8 => CTR * 268.41..7741358629935627418.1347.8..894.....1.2781...4459736182176284593382195746 * PAIR RESTART * PAIR F3: 7,8 ROW 3 B3: 7,8,1,3 # reduction candidate for 7,8 B3: 7,8 # 19 pairs C3: 7,8,1,3,5 # reduction candidate for 7,8 C3: 7,8 # 20 pairs * PAIR F5: 2,3 BLK 5 F4: 2,3,9 # reduction candidate for 2,3 F4: 2,3 => CTR * .6.341978.41958623983627415.1.4738.9894562731375819264459736182136284597728195346 * PAIR I8: 3,7 COL I I2: 3,7,9 # reduction candidate for 3,7 I2: 9 => CTR * .6..417.874135862998.62741..1.4798..894563271..78129.4459736182176284593.28195.46 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A3,A9,B6,B8,C1,C3,C4,D1,D2,G1,G9,H4,H6,I2,I8) * .6..41.58.41.5862..8.627419.1.4798.5894563271...8129.44597361821.628459..28195.46 * PAIR C1: 2,7 BLK 1 A1: 2,7,9 # reduction candidate for 2,7 A1: 2,7 => SOLVED * 267941358941358627583627419612479835894563271735812964459736182176284593328195746 * DURATION: 0:00:23.859380 START: 18:23:44.624386 END: 18:24:08.483766 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-457-base-pr-001.dot * REASONING * DIS # D2: 5,6 => CTR => D2: 3,9 * DIS D2: 3,9 # D3: 3,9 => CTR => D3: 5,6 * DIS D2: 3,9 + D3: 5,6 # C2: 7,8 => CTR => C2: 1,3,5 * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I3: 7,8 => CTR => I3: 3,5,9 * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 # F4: 2,3 => CTR => F4: 9 * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 # I2: 9 => CTR => I2: 3,7 * PRF D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 + I2: 3,7 # A1: 2,7 => SOL * STA D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 + I2: 3,7 + A1: 2,7 * CNT 7 HDP CHAINS / 19 HYP OPENED
Header Info
Top 500 Minimum 17 457 solution: 267941358941358627583627419612479835894563271735812964459736182176284593328195746 info: 95500 FNBHXYK S8.f 21056 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 267941358941358627583627419612479835894563271735812964459736182176284593328195746 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 # D2: 5,6 => CTR => D2: 3,9 * INC # D2: 3,9 => UNS * INC # D3: 5,6 => UNS * DIS # C2: 7,8 => CTR => C2: 1,3,5 * INC # C2: 1,3,5 => UNS * INC # I2: 7,8 => UNS * INC # B3: 7,8 => UNS * INC # C3: 7,8 => UNS * INC # I3: 7,8 => UNS * DIS # D2: 5,6 => CTR => D2: 3,9 * INC # D2: 3,9 => UNS * INC # D3: 5,6 => UNS * DIS # F4: 2,3 => CTR => F4: 9 * INC # F4: 9 => UNS * INC # F6: 2,3 => UNS * INC # G5: 2,3 => UNS * DIS # G5: 7 => CTR => G5: 2,3 * DIS # G5: 3,7 => CTR => G5: 2 * INC # G5: 2 => UNS * INC # H1: 3,7 => UNS * INC # H1: 5,8 => UNS * INC # A9: 3,7 => UNS * INC # B9: 3,7 => UNS * INC # C9: 3,7 => UNS * INC # B3: 3,7 => UNS * INC # B6: 3,7 => UNS * INC # I1: 3,7 => UNS * INC # I2: 3,7 => UNS * INC # I3: 3,7 => UNS * INC # A9: 3,7 => UNS * INC # B9: 3,7 => UNS * INC # C9: 3,7 => UNS * INC # G1: 3,7 => UNS * DIS # G5: 3,7 => CTR => G5: 2 * INC # G5: 2 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 5,6 => CTR => D2: 3,9 * INC D2: 3,9 # D3: 5,6 => UNS * INC D2: 3,9 # D3: 5,6 => UNS * DIS D2: 3,9 # D3: 3,9 => CTR => D3: 5,6 * DIS D2: 3,9 + D3: 5,6 # C2: 7,8 => CTR => C2: 1,3,5 * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I2: 7,8 => UNS * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I2: 7,8 => UNS * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I2: 3,5,9 => UNS * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I2: 7,8 => UNS * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I2: 3,5,9 => UNS * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 # B3: 7,8 => UNS * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 # C3: 7,8 => UNS * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 # I3: 7,8 => CTR => I3: 3,5,9 * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 # B3: 7,8 => UNS * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 # C3: 7,8 => UNS * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 # F4: 2,3 => CTR => F4: 9 * INC D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 # I2: 3,7 => UNS * DIS D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 # I2: 9 => CTR => I2: 3,7 * PRF D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 + I2: 3,7 # A1: 2,7 => SOL * STA D2: 3,9 + D3: 5,6 + C2: 1,3,5 + I3: 3,5,9 + F4: 9 + I2: 3,7 + A1: 2,7 * CNT 19 HDP CHAINS / 19 HYP OPENED