Analysis of xx-top500-416-base.sdk
Contents
Original Sudoku
level: medium
position: ..71..........85..6...............41...2...7.3........58....3.....72....1...4.... initial
Autosolve
position: ..71..4......785..6.....7..7......41...2...733....7...584...3279..725184172843... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I1: 2,8 => SOL * DIS # I1: 6,9 => CTR => I1: 2,8 * DIS # D4: 6,9 => CTR => D4: 3,5 * DIS # E4: 6,9 => CTR => E4: 3,5,8 * DIS # E5: 6,9 => CTR => E5: 1,5,8 * DIS # F5: 6,9 => CTR => F5: 1,4 * PRF # D6: 6,9 => SOL * DIS # D6: 4 => CTR => D6: 6,9 * DIS # E6: 6,9 => CTR => E6: 1,8 * DIS # B4: 6,9 => CTR => B4: 2,5 * DIS # G4: 6,9 => CTR => G4: 2,8 * PRF # F1: 6,9 => SOL * DIS # F1: 2 => CTR => F1: 6,9 * DIS # F7: 6,9 => CTR => F7: 1 * DIS # F7: 6,9 => CTR => F7: 1 * DIS # D2: 6,9 => CTR => D2: 3,4 * DIS # D4: 6,9 => CTR => D4: 3,5 * PRF # D6: 6,9 => SOL * DIS # D6: 4 => CTR => D6: 6,9 * DIS # G4: 6,9 => CTR => G4: 2,8 * DIS # G6: 6,9 => CTR => G6: 2,8 * CNT 21 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I1: 2,8 => SOL * STA I1: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..71..........85..6...............41...2...7.3........58....3.....72....1...4.... | initial |
| ..71..4......785..6.....7..7......41...2...733....7...584...3279..725184172843... | autosolve |
| 257196438419378562638452719726539841895214673341687295584961327963725184172843956 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A1: 2,8 A2: 2,4 A5: 4,8 F4: 6,9 B8: 3,6 C8: 3,6 D7: 6,9 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 1.. / H2 = 1 => 10 pairs (_) / H3 = 1 => 8 pairs (_) E7,F7: 1.. / E7 = 1 => 0 pairs (X) / F7 = 1 => 11 pairs (_) F5,F7: 1.. / F5 = 1 => 0 pairs (X) / F7 = 1 => 11 pairs (_) A1,A2: 2.. / A1 = 2 => 0 pairs (*) / A2 = 2 => 0 pairs (X) F1,F3: 2.. / F1 = 2 => 0 pairs (X) / F3 = 2 => 0 pairs (_) B4,B6: 2.. / B4 = 2 => 8 pairs (_) / B6 = 2 => 0 pairs (X) G4,G6: 2.. / G4 = 2 => 0 pairs (X) / G6 = 2 => 8 pairs (_) A2,I2: 2.. / A2 = 2 => 0 pairs (X) / I2 = 2 => 0 pairs (_) F3,I3: 2.. / F3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) B4,G4: 2.. / B4 = 2 => 8 pairs (_) / G4 = 2 => 0 pairs (X) B6,G6: 2.. / B6 = 2 => 0 pairs (X) / G6 = 2 => 8 pairs (_) D4,E4: 3.. / D4 = 3 => 9 pairs (_) / E4 = 3 => 9 pairs (_) B8,C8: 3.. / B8 = 3 => 7 pairs (_) / C8 = 3 => 7 pairs (_) F5,D6: 4.. / F5 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) B6,D6: 4.. / B6 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) A2,A5: 4.. / A2 = 4 => 0 pairs (*) / A5 = 4 => 0 pairs (X) F3,F5: 4.. / F3 = 4 => 0 pairs (X) / F5 = 4 => 0 pairs (_) H6,I6: 5.. / H6 = 5 => 10 pairs (_) / I6 = 5 => 10 pairs (_) H9,I9: 5.. / H9 = 5 => 10 pairs (_) / I9 = 5 => 10 pairs (_) B1,E1: 5.. / B1 = 5 => 8 pairs (_) / E1 = 5 => 15 pairs (_) D3,D4: 5.. / D3 = 5 => 9 pairs (_) / D4 = 5 => 9 pairs (_) H6,H9: 5.. / H6 = 5 => 10 pairs (_) / H9 = 5 => 10 pairs (_) I6,I9: 5.. / I6 = 5 => 10 pairs (_) / I9 = 5 => 10 pairs (_) B8,C8: 6.. / B8 = 6 => 7 pairs (_) / C8 = 6 => 7 pairs (_) A1,C3: 8.. / A1 = 8 => 0 pairs (X) / C3 = 8 => 0 pairs (_) I1,I3: 8.. / I1 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) A1,I1: 8.. / A1 = 8 => 0 pairs (X) / I1 = 8 => 0 pairs (_) C3,I3: 8.. / C3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) A1,A5: 8.. / A1 = 8 => 0 pairs (X) / A5 = 8 => 0 pairs (_) * DURATION: 0:00:42.815916 START: 17:02:51.773982 END: 17:03:34.589898 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A5,B8,C8,D7,F4,G9) * ..71..4......785..6.....7..7......41...2...733....7...584...3279..725184172843... * PAIR A1: 2,8 ROW 1 I1: 2,8,6,9 # reduction candidate for 2,8 I1: 2,8 => SOLVED * 257196438419378562638452719726539841895214673341687295584961327963725184172843956 I1: 6,9 => CTR * 8.71.24..2...785..6.....7..7......41...2...733....7...584...3279..725184172843... * PAIR F4: 6,9 BLK 5 D4: 6,9,3,5 # reduction candidate for 6,9 D4: 6,9 => CTR * .5716.43....3785..6..5947127.5.3.841...251.733..4872..584.1.3279..725184172843... D4: 3,5 # 9 pairs E4: 6,9,3,5,8 # reduction candidate for 6,9 E4: 6,9 => CTR * .571.24.8....785..6..5.47.27253..841...251.733..4872..584.1.3279..725184172843... E4: 3,5,8 # 8 pairs E5: 6,9,1,5,8 # reduction candidate for 6,9 E5: 6,9 => CTR * ..71.24.8....785..6....47.27......41...2.1.733..487...584.1.3279..725184172843... E5: 1,5,8 # 8 pairs F5: 6,9,1,4 # reduction candidate for 6,9 F5: 6,9 => CTR * ..71.24.8....785..6....47.27......41...2...733..4.7...584..13279..725184172843... F5: 1,4 # 9 pairs D6: 6,9,4 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 257196438419378562638452719726539841895214673341687295584961327963725184172843956 D6: 4 => CTR * ..71.24.8....785..6....47.27......41...2...733..4.7...584...3279..725184172843... E6: 6,9,1,8 # reduction candidate for 6,9 E6: 6,9 => CTR * ..71.24.8....785..6....47.27......41...2.1.733..4.7...584.1.3279..725184172843... E6: 1,8 # 9 pairs * PAIR F4: 6,9 ROW 4 B4: 6,9,2,5 # reduction candidate for 6,9 B4: 6,9 => CTR * ..71.24.8....785..6....47.27.....241...2...7332.4.7...584...3279..725184172843... B4: 2,5 # 9 pairs C4: 6,9,5,8 # reduction candidate for 6,9 C4: 6,9 # 12 pairs G4: 6,9,2,8 # reduction candidate for 6,9 G4: 6,9 => CTR * 8.71..4..2...785..6.....7.872.....414..2..8733..4.72..584...3279..725184172843... G4: 2,8 # 9 pairs * PAIR F4: 6,9 COL F F1: 6,9,2 # reduction candidate for 6,9 F1: 6,9 => SOLVED * 257196438419378562638452719726539841895214673341687295584961327963725184172843956 F1: 2 => CTR * 8.71.24..24..785..6....47.27......414..2...733..4.7...584...3279..725184172843... F7: 6,9,1 # reduction candidate for 6,9 F7: 6,9 => CTR * ..71.24.8....785..6....47.27......41...2.1.733..4.7...584.1.3279..725184172843... F7: 1 # 11 pairs * PAIR D7: 6,9 BLK 8 E7: 6,9,1 # reduction candidate for 6,9 E7: 6,9 # 11 pairs F7: 6,9,1 # reduction candidate for 6,9 F7: 6,9 => CTR * ..71.24.8....785..6....47.27......41...2.1.733..4.7...584.1.3279..725184172843... F7: 1 # 11 pairs * PAIR D7: 6,9 COL D D2: 6,9,3,4 # reduction candidate for 6,9 D2: 6,9 => CTR * ..71.24.8....785..6....47.27......41...2...733..4.7...584...3279..725184172843... D2: 3,4 # 10 pairs D4: 6,9,3,5 # reduction candidate for 6,9 D4: 6,9 => CTR * .5716.43....3785..6..5947127.5.3.841...251.733..4872..584.1.3279..725184172843... D4: 3,5 # 9 pairs D6: 6,9,4 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 257196438419378562638452719726539841895214673341687295584961327963725184172843956 D6: 4 => CTR * ..71.24.8....785..6....47.27......41...2...733..4.7...584...3279..725184172843... * PAIR G9: 6,9 BLK 9 H9: 6,9,5 # reduction candidate for 6,9 H9: 6,9 # 10 pairs I9: 6,9,5 # reduction candidate for 6,9 I9: 6,9 # 10 pairs * PAIR G9: 6,9 COL G G4: 6,9,2,8 # reduction candidate for 6,9 G4: 6,9 => CTR * 8.71..4..2...785..6.....7.872.....414..2..8733..4.72..584...3279..725184172843... G4: 2,8 # 9 pairs G5: 6,9,8 # reduction candidate for 6,9 G5: 6,9 # 11 pairs G6: 6,9,2,8 # reduction candidate for 6,9 G6: 6,9 => CTR * 8.71..4..24..785..6....47..7.....241...2..87332.4.7...584...3279..725184172843... G6: 2,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-416-base-pr-000.dot * REASONING * PRF # I1: 2,8 => SOL * DIS # I1: 6,9 => CTR => I1: 2,8 * DIS # D4: 6,9 => CTR => D4: 3,5 * DIS # E4: 6,9 => CTR => E4: 3,5,8 * DIS # E5: 6,9 => CTR => E5: 1,5,8 * DIS # F5: 6,9 => CTR => F5: 1,4 * PRF # D6: 6,9 => SOL * DIS # D6: 4 => CTR => D6: 6,9 * DIS # E6: 6,9 => CTR => E6: 1,8 * DIS # B4: 6,9 => CTR => B4: 2,5 * DIS # G4: 6,9 => CTR => G4: 2,8 * PRF # F1: 6,9 => SOL * DIS # F1: 2 => CTR => F1: 6,9 * DIS # F7: 6,9 => CTR => F7: 1 * DIS # F7: 6,9 => CTR => F7: 1 * DIS # D2: 6,9 => CTR => D2: 3,4 * DIS # D4: 6,9 => CTR => D4: 3,5 * PRF # D6: 6,9 => SOL * DIS # D6: 4 => CTR => D6: 6,9 * DIS # G4: 6,9 => CTR => G4: 2,8 * DIS # G6: 6,9 => CTR => G6: 2,8 * CNT 21 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A5,B8,C8,D7,F4,G9) * ..71..4......785..6.....7..7......41...2...733....7...584...3279..725184172843... * PAIR A1: 2,8 ROW 1 I1: 2,8,6,9 # reduction candidate for 2,8 I1: 2,8 => SOLVED * 257196438419378562638452719726539841895214673341687295584961327963725184172843956 * DURATION: 0:00:02.609072 START: 17:04:06.305713 END: 17:04:08.914785 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-416-base-pr-001.dot * REASONING * PRF # I1: 2,8 => SOL * STA I1: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 416 solution: 257196438419378562638452719726539841895214673341687295584961327963725184172843956 info: 95067 FNBXYK S8.f 14366 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 257196438419378562638452719726539841895214673341687295584961327963725184172843956 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:
* PRF # I1: 2,8 => SOL * DIS # I1: 6,9 => CTR => I1: 2,8 * DIS # D4: 6,9 => CTR => D4: 3,5 * INC # D4: 3,5 => UNS * DIS # E4: 6,9 => CTR => E4: 3,5,8 * INC # E4: 3,5,8 => UNS * DIS # E5: 6,9 => CTR => E5: 1,5,8 * INC # E5: 1,5,8 => UNS * DIS # F5: 6,9 => CTR => F5: 1,4 * INC # F5: 1,4 => UNS * PRF # D6: 6,9 => SOL * DIS # D6: 4 => CTR => D6: 6,9 * DIS # E6: 6,9 => CTR => E6: 1,8 * INC # E6: 1,8 => UNS * DIS # B4: 6,9 => CTR => B4: 2,5 * INC # B4: 2,5 => UNS * INC # C4: 6,9 => UNS * DIS # G4: 6,9 => CTR => G4: 2,8 * INC # G4: 2,8 => UNS * PRF # F1: 6,9 => SOL * DIS # F1: 2 => CTR => F1: 6,9 * DIS # F7: 6,9 => CTR => F7: 1 * INC # F7: 1 => UNS * INC # E7: 6,9 => UNS * DIS # F7: 6,9 => CTR => F7: 1 * INC # F7: 1 => UNS * DIS # D2: 6,9 => CTR => D2: 3,4 * INC # D2: 3,4 => UNS * DIS # D4: 6,9 => CTR => D4: 3,5 * INC # D4: 3,5 => UNS * PRF # D6: 6,9 => SOL * DIS # D6: 4 => CTR => D6: 6,9 * INC # H9: 6,9 => UNS * INC # I9: 6,9 => UNS * DIS # G4: 6,9 => CTR => G4: 2,8 * INC # G4: 2,8 => UNS * INC # G5: 6,9 => UNS * DIS # G6: 6,9 => CTR => G6: 2,8 * INC # G6: 2,8 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I1: 2,8 => SOL * STA I1: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED