Analysis of xx-top500-223-base.sdk
Contents
Original Sudoku
level: medium
position: ....2..5.3.....1.......6....6..5..2.1..4..3..............1.8....2.....7....3..4.. initial
Autosolve
position: ....2.65.3765841922.5..6....6.85..2.15246.38....2..5.6...1.82...2.6.5.7....3.24.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F6: 1,3 => SOL * DIS # I1: 7,8 => CTR => I1: 3,4 * DIS # I3: 3,4 => CTR => I3: 7,8 * PRF # F4: 7,9 => SOL * PRF # F6: 1,3 => SOL * PRF # F4: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 4,9 * DIS # I9: 8 => CTR => I9: 5,9 * DIS # I9: 8,9 => CTR => I9: 5 * PRF # I9: 5 => SOL * CNT 10 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:
* PRF # F6: 1,3 => SOL * STA F6: 1,3 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2..5.3.....1.......6....6..5..2.1..4..3..............1.8....2.....7....3..4.. | initial |
| ....2.65.3765841922.5..6....6.85..2.15246.38....2..5.6...1.82...2.6.5.7....3.24.. | autosolve |
| 819723654376584192245916738463857921152469387798231546534178269921645873687392415 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) D1: 7,9 F1: 1,3 D3: 7,9 E3: 1,3 G3: 7,8 H3: 3,4 F5: 7,9 E6: 1,3 G4: 7,9 I4: 1,4 I5: 7,9 H6: 1,4 A7: 5,6 C8: 1,3 A9: 5,6 E8: 4,9 E9: 7,9 H7: 3,6 I7: 5,9 G8: 8,9 I8: 1,3 H9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,E3: 1.. / F1 = 1 => 0 pairs (X) / E3 = 1 => 0 pairs (_) I4,H6: 1.. / I4 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) I8,H9: 1.. / I8 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) B3,E3: 1.. / B3 = 1 => 0 pairs (X) / E3 = 1 => 0 pairs (_) F4,I4: 1.. / F4 = 1 => 0 pairs (X) / I4 = 1 => 0 pairs (_) C8,I8: 1.. / C8 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) E3,E6: 1.. / E3 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) H6,H9: 1.. / H6 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) I4,I8: 1.. / I4 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) F1,E3: 3.. / F1 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) H7,I8: 3.. / H7 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) F1,I1: 3.. / F1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) C4,F4: 3.. / C4 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) C8,I8: 3.. / C8 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) B6,B7: 3.. / B6 = 3 => 0 pairs (X) / B7 = 3 => 0 pairs (_) E3,E6: 3.. / E3 = 3 => 0 pairs (X) / E6 = 3 => 0 pairs (_) H3,H7: 3.. / H3 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) I4,H6: 4.. / I4 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) E7,E8: 4.. / E7 = 4 => 19 pairs (_) / E8 = 4 => 23 pairs (_) A8,E8: 4.. / A8 = 4 => 19 pairs (_) / E8 = 4 => 23 pairs (_) H3,H6: 4.. / H3 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) A7,A9: 5.. / A7 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) I7,I9: 5.. / I7 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) A7,I7: 5.. / A7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) A9,I9: 5.. / A9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) A7,A9: 6.. / A7 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) H7,H9: 6.. / H7 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) A7,H7: 6.. / A7 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) A9,H9: 6.. / A9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) D1,D3: 7.. / D1 = 7 => 20 pairs (_) / D3 = 7 => 0 pairs (X) A4,A6: 7.. / A4 = 7 => 19 pairs (_) / A6 = 7 => 23 pairs (_) G4,I5: 7.. / G4 = 7 => 0 pairs (X) / I5 = 7 => 19 pairs (_) C7,C9: 7.. / C7 = 7 => 22 pairs (_) / C9 = 7 => 23 pairs (_) E7,E9: 7.. / E7 = 7 => 23 pairs (_) / E9 = 7 => 22 pairs (_) D1,I1: 7.. / D1 = 7 => 20 pairs (_) / I1 = 7 => 0 pairs (X) F5,I5: 7.. / F5 = 7 => 0 pairs (X) / I5 = 7 => 19 pairs (_) A6,F6: 7.. / A6 = 7 => 23 pairs (_) / F6 = 7 => 19 pairs (_) C7,E7: 7.. / C7 = 7 => 22 pairs (_) / E7 = 7 => 23 pairs (_) C9,E9: 7.. / C9 = 7 => 23 pairs (_) / E9 = 7 => 22 pairs (_) G3,G4: 7.. / G3 = 7 => 19 pairs (_) / G4 = 7 => 0 pairs (X) G8,I9: 8.. / G8 = 8 => 19 pairs (_) / I9 = 8 => 0 pairs (X) A8,G8: 8.. / A8 = 8 => 0 pairs (X) / G8 = 8 => 19 pairs (_) G3,G8: 8.. / G3 = 8 => 0 pairs (X) / G8 = 8 => 19 pairs (_) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 20 pairs (_) G4,I5: 9.. / G4 = 9 => 19 pairs (_) / I5 = 9 => 0 pairs (X) B3,D3: 9.. / B3 = 9 => 0 pairs (X) / D3 = 9 => 20 pairs (_) F5,I5: 9.. / F5 = 9 => 19 pairs (_) / I5 = 9 => 0 pairs (X) G4,G8: 9.. / G4 = 9 => 19 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:01:37.941830 START: 10:25:48.421634 END: 10:27:26.363464 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,C8,D1,D3,E3,E6,E8,E9,F1,F5,G3,G4,G8,H3,H6,H7,H9,I4,I5,I7,I8) * ....2.65.3765841922.5..6....6.85..2.15246.38....2..5.6...1.82...2.6.5.7....3.24.. * PAIR F1: 1,3 COL F F4: 1,3,7,9 # reduction candidate for 1,3 F4: 1,3 # 24 pairs F6: 1,3,7,9 # reduction candidate for 1,3 F6: 1,3 => SOLVED * 819723654376584192245916738463857921152469387798231546534178269921645873687392415 F6: 7,9 # 24 pairs * PAIR G3: 7,8 BLK 3 I1: 7,8,3,4 # reduction candidate for 7,8 I1: 7,8 => CTR * .1..2365.3765841922.5.16.3446385..2115246.38.7..231546534178269.216458736.7392415 I1: 3,4 # 23 pairs I3: 7,8,3,4 # reduction candidate for 7,8 I3: 7,8 # 23 pairs * PAIR H3: 3,4 BLK 3 I1: 3,4,7,8 # reduction candidate for 3,4 I1: 3,4 # 23 pairs I3: 3,4,7,8 # reduction candidate for 3,4 I3: 3,4 => CTR * .1..2365837658419228591673446385792115246938779.23.5.6.3.1.826..216.5.736..3.2415 I3: 7,8 # 23 pairs * PAIR F5: 7,9 BLK 5 F4: 7,9,1,3 # reduction candidate for 7,9 F4: 7,9 => SOLVED * 819723654376584192245916738463857921152469387798231546534178269921645873687392415 F4: 1,3 # 24 pairs F6: 7,9,1,3 # reduction candidate for 7,9 F6: 7,9 # 24 pairs * PAIR E6: 1,3 BLK 5 F4: 1,3,7,9 # reduction candidate for 1,3 F4: 1,3 # 24 pairs F6: 1,3,7,9 # reduction candidate for 1,3 F6: 1,3 => SOLVED * 819723654376584192245916738463857921152469387798231546534178269921645873687392415 F6: 7,9 # 24 pairs * PAIR G4: 7,9 ROW 4 A4: 7,9,4 # reduction candidate for 7,9 A4: 7,9 # 26 pairs F4: 7,9,1,3 # reduction candidate for 7,9 F4: 7,9 => SOLVED * 819723654376584192245916738463857921152469387798231546534178269921645873687392415 F4: 1,3 # 24 pairs * PAIR E8: 4,9 BLK 8 E7: 4,9,7 # reduction candidate for 4,9 E7: 7 # 23 pairs E7: 4,9 # 22 pairs * PAIR E8: 4,9 ROW 8 A8: 4,9,8 # reduction candidate for 4,9 A8: 8 => CTR * ....2.65.3765841922.5..68...6.85.72.1524673897..2..5166..1.82358236459715..3.2468 A8: 4,9 # 19 pairs * PAIR E9: 7,9 BLK 8 E7: 7,9,4 # reduction candidate for 7,9 E7: 7,9 # 23 pairs E7: 4 # 19 pairs * PAIR E9: 7,9 ROW 9 C9: 7,9,1,8 # reduction candidate for 7,9 C9: 7,9 # 25 pairs C9: 1,8 # 23 pairs * PAIR I7: 5,9 BLK 9 I9: 5,9,8 # reduction candidate for 5,9 I9: 8 => CTR * ....2.65.3765841922.5..68...6.85.72.1524673897..2..5166..1.82358236459715..3.2468 I9: 5,9 # 19 pairs * PAIR G8: 8,9 BLK 9 I9: 8,9,5 # reduction candidate for 8,9 I9: 8,9 => CTR * ....2.65.3765841922.5..6....6.85..2.15246.38....2..5166..1.8235.236.5.715..3.246. I9: 5 => SOLVED * 819723654376584192245916738463857921152469387798231546534178269921645873687392415 * PAIR G8: 8,9 ROW 8 A8: 8,9,4 # reduction candidate for 8,9 A8: 8,9 # 23 pairs A8: 4 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-223-base-pr-000.dot * REASONING * PRF # F6: 1,3 => SOL * DIS # I1: 7,8 => CTR => I1: 3,4 * DIS # I3: 3,4 => CTR => I3: 7,8 * PRF # F4: 7,9 => SOL * PRF # F6: 1,3 => SOL * PRF # F4: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 4,9 * DIS # I9: 8 => CTR => I9: 5,9 * DIS # I9: 8,9 => CTR => I9: 5 * PRF # I9: 5 => SOL * CNT 10 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,C8,D1,D3,E3,E6,E8,E9,F1,F5,G3,G4,G8,H3,H6,H7,H9,I4,I5,I7,I8) * ....2.65.3765841922.5..6....6.85..2.15246.38....2..5.6...1.82...2.6.5.7....3.24.. * PAIR F1: 1,3 COL F F4: 1,3,7,9 # reduction candidate for 1,3 F4: 1,3 # 24 pairs F6: 1,3,7,9 # reduction candidate for 1,3 F6: 1,3 => SOLVED * 819723654376584192245916738463857921152469387798231546534178269921645873687392415 * DURATION: 0:00:03.655340 START: 10:28:04.183071 END: 10:28:07.838411 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-223-base-pr-001.dot * REASONING * PRF # F6: 1,3 => SOL * STA F6: 1,3 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 223 solution: 819723654376584192245916738463857921152469387798231546534178269921645873687392415 info: 1996 FNBTHWY S8.f 3230 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 819723654376584192245916738463857921152469387798231546534178269921645873687392415 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 # F4: 1,3 => UNS * PRF # F6: 1,3 => SOL * INC # F6: 7,9 => UNS * DIS # I1: 7,8 => CTR => I1: 3,4 * INC # I1: 3,4 => UNS * INC # I3: 7,8 => UNS * INC # I1: 3,4 => UNS * DIS # I3: 3,4 => CTR => I3: 7,8 * INC # I3: 7,8 => UNS * PRF # F4: 7,9 => SOL * INC # F4: 1,3 => UNS * INC # F6: 7,9 => UNS * INC # F4: 1,3 => UNS * PRF # F6: 1,3 => SOL * INC # F6: 7,9 => UNS * INC # A4: 7,9 => UNS * PRF # F4: 7,9 => SOL * INC # F4: 1,3 => UNS * INC # E7: 4,9 => UNS * INC # E7: 7 => UNS * INC # A8: 4,9 => UNS * DIS # A8: 8 => CTR => A8: 4,9 * INC # E7: 7,9 => UNS * INC # E7: 4 => UNS * INC # C9: 7,9 => UNS * INC # C9: 1,8 => UNS * INC # I9: 5,9 => UNS * DIS # I9: 8 => CTR => I9: 5,9 * DIS # I9: 8,9 => CTR => I9: 5 * PRF # I9: 5 => SOL * INC # A8: 8,9 => UNS * INC # A8: 4 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F4: 1,3 => UNS * PRF # F6: 1,3 => SOL * STA F6: 1,3 * CNT 2 HDP CHAINS / 2 HYP OPENED