Analysis of xx-top500-184-base.sdk
Contents
Original Sudoku
level: medium
position: 1.35..2......4..7.6.........4..87...3.......1...............84.2..1........3..... initial
Autosolve
position: 1.35..2.4....4..7.6.4.......41.87...3.......1..........1....8432381.4...4..3.8... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 6,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # D2: 6,9 => SOL * DIS # H1: 6,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * PRF # D2: 2,9 => SOL * DIS # D3: 2,9 => CTR => D3: 7,8 * DIS # B3: 2,9 => CTR => B3: 5,7,8 * DIS # A6: 5,9 => CTR => A6: 7,8 * DIS # H4: 5,9 => CTR => H4: 2,3,6 * DIS # A2: 5,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # A7: 5,9 => SOL * DIS # A7: 7 => CTR => A7: 5,9 * CNT 14 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 6,9 => CTR => E1: 7 * PRF E1: 7 => SOL * STA E1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.35..2......4..7.6.........4..87...3.......1...............84.2..1........3..... | initial |
| 1.35..2.4....4..7.6.4.......41.87...3.......1..........1....8432381.4...4..3.8... | autosolve |
| 193576284825943176674812935541687329382459761769231458916725843238164597457398612 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) F1: 6,9 F2: 1,3 E3: 1,3 F3: 2,9 G2: 1,3 A4: 5,9 E6: 1,3 F6: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,E3: 1.. / F2 = 1 => 3 pairs (_) / E3 = 1 => 3 pairs (_) E6,F6: 1.. / E6 = 1 => 3 pairs (_) / F6 = 1 => 3 pairs (_) G9,H9: 1.. / G9 = 1 => 4 pairs (_) / H9 = 1 => 8 pairs (_) F2,G2: 1.. / F2 = 1 => 3 pairs (_) / G2 = 1 => 3 pairs (_) E3,E6: 1.. / E3 = 1 => 3 pairs (_) / E6 = 1 => 3 pairs (_) F2,F6: 1.. / F2 = 1 => 3 pairs (_) / F6 = 1 => 3 pairs (_) H3,H9: 1.. / H3 = 1 => 4 pairs (_) / H9 = 1 => 8 pairs (_) H9,I9: 2.. / H9 = 2 => 4 pairs (_) / I9 = 2 => 8 pairs (_) E5,E7: 2.. / E5 = 2 => 17 pairs (_) / E7 = 2 => 8 pairs (_) F2,E3: 3.. / F2 = 3 => 3 pairs (_) / E3 = 3 => 3 pairs (_) E6,F6: 3.. / E6 = 3 => 3 pairs (_) / F6 = 3 => 3 pairs (_) G4,H4: 3.. / G4 = 3 => 4 pairs (_) / H4 = 3 => 8 pairs (_) F2,G2: 3.. / F2 = 3 => 3 pairs (_) / G2 = 3 => 3 pairs (_) E3,E6: 3.. / E3 = 3 => 3 pairs (_) / E6 = 3 => 3 pairs (_) F2,F6: 3.. / F2 = 3 => 3 pairs (_) / F6 = 3 => 3 pairs (_) H3,H4: 3.. / H3 = 3 => 4 pairs (_) / H4 = 3 => 8 pairs (_) D5,D6: 4.. / D5 = 4 => 8 pairs (_) / D6 = 4 => 0 pairs (X) G5,G6: 4.. / G5 = 4 => 0 pairs (X) / G6 = 4 => 8 pairs (_) D5,G5: 4.. / D5 = 4 => 8 pairs (_) / G5 = 4 => 0 pairs (X) D6,G6: 4.. / D6 = 4 => 0 pairs (X) / G6 = 4 => 8 pairs (_) E5,F5: 5.. / E5 = 5 => 9 pairs (_) / F5 = 5 => 8 pairs (_) F5,F7: 5.. / F5 = 5 => 8 pairs (_) / F7 = 5 => 9 pairs (_) H1,I2: 6.. / H1 = 6 => 0 pairs (X) / I2 = 6 => 9 pairs (_) D2,I2: 6.. / D2 = 6 => 0 pairs (X) / I2 = 6 => 9 pairs (_) B1,B3: 7.. / B1 = 7 => 0 pairs (X) / B3 = 7 => 0 pairs (_) E1,D3: 7.. / E1 = 7 => 0 pairs (*) / D3 = 7 => 0 pairs (X) B1,E1: 7.. / B1 = 7 => 0 pairs (X) / E1 = 7 => 0 pairs (_) B3,D3: 7.. / B3 = 7 => 0 pairs (*) / D3 = 7 => 0 pairs (X) C5,G5: 7.. / C5 = 7 => 0 pairs (X) / G5 = 7 => 8 pairs (_) A6,A7: 7.. / A6 = 7 => 0 pairs (*) / A7 = 7 => 0 pairs (X) D3,D7: 7.. / D3 = 7 => 0 pairs (X) / D7 = 7 => 0 pairs (_) D2,D3: 8.. / D2 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) B1,H1: 8.. / B1 = 8 => 0 pairs (X) / H1 = 8 => 0 pairs (_) B5,H5: 8.. / B5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) A2,A6: 8.. / A2 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) * DURATION: 0:00:55.049054 START: 08:58:58.360237 END: 08:59:53.409291 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,E3,E6,F1,F2,F3,F6,G2) * 1.35..2.4....4..7.6.4.......41.87...3.......1..........1....8432381.4...4..3.8... * PAIR F1: 6,9 BLK 2 E1: 6,9,7 # reduction candidate for 6,9 E1: 6,9 => CTR * 1735..284....4..766.47......41.87...38......1........8.1....8432381.4...4..3.8... E1: 7 => SOLVED * 193576284825943176674812935541687329382459761769231458916725843238164597457398612 D2: 6,9,2,8 # reduction candidate for 6,9 D2: 6,9 => SOLVED * 193576284825943176674812935541687329382459761769231458916725843238164597457398612 D2: 2,8 # 11 pairs * PAIR F1: 6,9 ROW 1 H1: 6,9,8 # reduction candidate for 6,9 H1: 6,9 => CTR * 18357.2.4....4..7.674.......41.87...3......818........71....8432381.4...4..3.8... H1: 8 => SOLVED * 193576284825943176674812935541687329382459761769231458916725843238164597457398612 * PAIR F1: 6,9 COL F F5: 6,9,2,5 # reduction candidate for 6,9 F5: 6,9 # 9 pairs F7: 6,9,2,5 # reduction candidate for 6,9 F7: 6,9 # 8 pairs * PAIR E3: 1,3 ROW 3 G3: 1,3,5,9 # reduction candidate for 1,3 G3: 1,3 # 8 pairs H3: 1,3,5,8,9 # reduction candidate for 1,3 H3: 1,3 # 10 pairs * PAIR F3: 2,9 BLK 2 D2: 2,9,6,8 # reduction candidate for 2,9 D2: 2,9 => SOLVED * 193576284825943176674812935541687329382459761769231458916725843238164597457398612 D2: 6,8 # 9 pairs D3: 2,9,7,8 # reduction candidate for 2,9 D3: 2,9 => CTR * 1.357.2.4...84..76674.......41.87...3.......18........71....8432381.4...4..3.8... D3: 7,8 # 9 pairs * PAIR F3: 2,9 ROW 3 B3: 2,9,5,7,8 # reduction candidate for 2,9 B3: 2,9 => CTR * 1735..284....4..766.4.......41.87...3.......1..........1....8432381.4...4..3.8... B3: 5,7,8 # 8 pairs * PAIR F3: 2,9 COL F F5: 2,9,5,6 # reduction candidate for 2,9 F5: 2,9 # 13 pairs F7: 2,9,5,6 # reduction candidate for 2,9 F7: 2,9 # 10 pairs * PAIR G2: 1,3 BLK 3 G3: 1,3,5,9 # reduction candidate for 1,3 G3: 1,3 # 8 pairs H3: 1,3,5,8,9 # reduction candidate for 1,3 H3: 1,3 # 10 pairs * PAIR A4: 5,9 BLK 4 A6: 5,9,7,8 # reduction candidate for 5,9 A6: 5,9 => CTR * 1.35..2.48...4..7.6.48......41.87...3.......1........871....8432381.4...4..3.8... A6: 7,8 # 9 pairs B6: 5,9,2,6,8 # reduction candidate for 5,9 B6: 5,9 # 10 pairs C6: 5,9,2,6,7 # reduction candidate for 5,9 C6: 5,9 # 10 pairs * PAIR A4: 5,9 ROW 4 G4: 5,9,3,6 # reduction candidate for 5,9 G4: 5,9 # 11 pairs H4: 5,9,2,3,6 # reduction candidate for 5,9 H4: 5,9 => CTR * 183579264...643178674812.3..412873.63.....781....31....1.72.8432381.4...4.73.8.12 H4: 2,3,6 # 8 pairs I4: 5,9,2,6 # reduction candidate for 5,9 I4: 5,9 # 11 pairs * PAIR A4: 5,9 COL A A2: 5,9,8 # reduction candidate for 5,9 A2: 5,9 => CTR * 1.35..2.4....4..7.6.47......41.87...3......818........71....8432381.4...4..3.8... A2: 8 => SOLVED * 193576284825943176674812935541687329382459761769231458916725843238164597457398612 A7: 5,9,7 # reduction candidate for 5,9 A7: 5,9 => SOLVED * 193576284825943176674812935541687329382459761769231458916725843238164597457398612 A7: 7 => CTR * 1735..284...84..766847.2....41.87...3.......18........71....8432381.4...4..3.8... * INCONCLUSIVE * SAVE PR GRAPH xx-top500-184-base-pr-000.dot * REASONING * DIS # E1: 6,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # D2: 6,9 => SOL * DIS # H1: 6,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * PRF # D2: 2,9 => SOL * DIS # D3: 2,9 => CTR => D3: 7,8 * DIS # B3: 2,9 => CTR => B3: 5,7,8 * DIS # A6: 5,9 => CTR => A6: 7,8 * DIS # H4: 5,9 => CTR => H4: 2,3,6 * DIS # A2: 5,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # A7: 5,9 => SOL * DIS # A7: 7 => CTR => A7: 5,9 * CNT 14 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,E3,E6,F1,F2,F3,F6,G2) * 1.35..2.4....4..7.6.4.......41.87...3.......1..........1....8432381.4...4..3.8... * PAIR F1: 6,9 BLK 2 E1: 6,9,7 # reduction candidate for 6,9 E1: 6,9 => CTR * 1735..284....4..766.47......41.87...38......1........8.1....8432381.4...4..3.8... E1: 7 => SOLVED * 193576284825943176674812935541687329382459761769231458916725843238164597457398612 * DURATION: 0:00:01.778809 START: 09:00:23.451850 END: 09:00:25.230659 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-184-base-pr-001.dot * REASONING * DIS # E1: 6,9 => CTR => E1: 7 * PRF E1: 7 => SOL * STA E1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 184 solution: 193576284825943176674812935541687329382459761769231458916725843238164597457398612 info: 1829 FNBTHWY S8.f 26017 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 193576284825943176674812935541687329382459761769231458916725843238164597457398612 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 # E1: 6,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # D2: 6,9 => SOL * INC # D2: 2,8 => UNS * DIS # H1: 6,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * INC # F5: 6,9 => UNS * INC # F7: 6,9 => UNS * INC # G3: 1,3 => UNS * INC # H3: 1,3 => UNS * PRF # D2: 2,9 => SOL * INC # D2: 6,8 => UNS * DIS # D3: 2,9 => CTR => D3: 7,8 * INC # D3: 7,8 => UNS * DIS # B3: 2,9 => CTR => B3: 5,7,8 * INC # B3: 5,7,8 => UNS * INC # F5: 2,9 => UNS * INC # F7: 2,9 => UNS * INC # G3: 1,3 => UNS * INC # H3: 1,3 => UNS * DIS # A6: 5,9 => CTR => A6: 7,8 * INC # A6: 7,8 => UNS * INC # B6: 5,9 => UNS * INC # C6: 5,9 => UNS * INC # G4: 5,9 => UNS * DIS # H4: 5,9 => CTR => H4: 2,3,6 * INC # H4: 2,3,6 => UNS * INC # I4: 5,9 => UNS * DIS # A2: 5,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # A7: 5,9 => SOL * DIS # A7: 7 => CTR => A7: 5,9 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 6,9 => CTR => E1: 7 * PRF E1: 7 => SOL * STA E1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED