Analysis of xx-top500-032-base.sdk
Contents
Original Sudoku
level: medium
position: .5....2..6...1.......8......7.9............31......46....5..7.23...6....1........ initial
Autosolve
position: 7513..2..6.8.123..23.85.1..476931.2.58267493191328546786.5.371232.16....1...2.6.3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H2: 4,9 => SOL * DIS # I2: 4,9 => CTR => I2: 5 * DIS # H3: 4,9 => CTR => H3: 7 * PRF # H3: 7 => SOL * PRF # I3: 4,9 => SOL * DIS # H1: 4,9 => CTR => H1: 8 * PRF # F3: 6,9 => SOL * DIS # F3: 7 => CTR => F3: 6,9 * PRF # I1: 6,9 => SOL * DIS # H2: 4,7 => CTR => H2: 5,9 * PRF # H2: 5,9 => SOL * DIS # I8: 5,8 => CTR => I8: 4,9 * DIS # H8: 5,8 => CTR => H8: 4,9 * DIS # I8: 5,8 => CTR => I8: 4,9 * CNT 14 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H2: 4,9 => SOL * STA H2: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5....2..6...1.......8......7.9............31......46....5..7.23...6....1........ | initial |
| 7513..2..6.8.123..23.85.1..476931.2.58267493191328546786.5.371232.16....1...2.6.3 | autosolve |
| 751349286648712395239856174476931528582674931913285467864593712325167849197428653 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B2: 4,9 C3: 4,9 E1: 4,9 F1: 6,9 D2: 4,7 G4: 5,8 I4: 5,8 C7: 4,9 C8: 5,7 B9: 4,9 C9: 5,7 E7: 4,9 D9: 4,7 G8: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C3: 4.. / B2 = 4 => 0 pairs (*) / C3 = 4 => 0 pairs (X) E1,D2: 4.. / E1 = 4 => 0 pairs (*) / D2 = 4 => 0 pairs (X) C7,B9: 4.. / C7 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) E7,D9: 4.. / E7 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) H8,I8: 4.. / H8 = 4 => 16 pairs (_) / I8 = 4 => 18 pairs (_) C7,E7: 4.. / C7 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) B9,D9: 4.. / B9 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) B2,B9: 4.. / B2 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) C3,C7: 4.. / C3 = 4 => 0 pairs (X) / C7 = 4 => 0 pairs (_) D2,D9: 4.. / D2 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) E1,E7: 4.. / E1 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) H2,I2: 5.. / H2 = 5 => 0 pairs (X) / I2 = 5 => 14 pairs (_) G4,I4: 5.. / G4 = 5 => 13 pairs (_) / I4 = 5 => 0 pairs (X) C8,C9: 5.. / C8 = 5 => 0 pairs (*) / C9 = 5 => 0 pairs (X) C9,H9: 5.. / C9 = 5 => 14 pairs (_) / H9 = 5 => 0 pairs (*) G4,G8: 5.. / G4 = 5 => 13 pairs (_) / G8 = 5 => 0 pairs (X) F1,F3: 6.. / F1 = 6 => 14 pairs (_) / F3 = 6 => 0 pairs (*) I1,I3: 6.. / I1 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) F1,I1: 6.. / F1 = 6 => 14 pairs (_) / I1 = 6 => 0 pairs (*) F3,I3: 6.. / F3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) D2,F3: 7.. / D2 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) H2,H3: 7.. / H2 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) C8,C9: 7.. / C8 = 7 => 14 pairs (_) / C9 = 7 => 0 pairs (*) D2,H2: 7.. / D2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) F3,H3: 7.. / F3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) C8,F8: 7.. / C8 = 7 => 14 pairs (_) / F8 = 7 => 0 pairs (*) D2,D9: 7.. / D2 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) H1,I1: 8.. / H1 = 8 => 16 pairs (_) / I1 = 8 => 0 pairs (X) G4,I4: 8.. / G4 = 8 => 0 pairs (X) / I4 = 8 => 13 pairs (_) F8,F9: 8.. / F8 = 8 => 0 pairs (X) / F9 = 8 => 16 pairs (_) F9,H9: 8.. / F9 = 8 => 16 pairs (_) / H9 = 8 => 0 pairs (X) G4,G8: 8.. / G4 = 8 => 0 pairs (X) / G8 = 8 => 13 pairs (_) B2,C3: 9.. / B2 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) C7,B9: 9.. / C7 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) C7,E7: 9.. / C7 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) B2,B9: 9.. / B2 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) C3,C7: 9.. / C3 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) E1,E7: 9.. / E1 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) * DURATION: 0:01:31.818884 START: 03:44:46.820882 END: 03:46:18.639766 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B9,C3,C7,C8,C9,D2,D9,E1,E7,F1,G4,G8,I4) * 7513..2..6.8.123..23.85.1..476931.2.58267493191328546786.5.371232.16....1...2.6.3 * PAIR B2: 4,9 ROW 2 H2: 4,9,5,7 # reduction candidate for 4,9 H2: 4,9 => SOLVED * 751349286648712395239856174476931528582674931913285467864593712325167849197428653 H2: 5,7 # 15 pairs I2: 4,9,5 # reduction candidate for 4,9 I2: 4,9 => CTR * 75134.2986.871235.23.85.17.476931.2.58267493191328546786.5.371232716....1.5427683 I2: 5 # 14 pairs * PAIR C3: 4,9 ROW 3 H3: 4,9,7 # reduction candidate for 4,9 H3: 4,9 => CTR * 7513.62896.8.1237523.8571.647693152858267493191328546786.5.371232716.8541.5728693 H3: 7 => SOLVED * 751349286648712395239856174476931528582674931913285467864593712325167849197428653 I3: 4,9,6 # reduction candidate for 4,9 I3: 4,9 => SOLVED * 751349286648712395239856174476931528582674931913285467864593712325167849197428653 I3: 6 # 14 pairs * PAIR E1: 4,9 ROW 1 H1: 4,9,8 # reduction candidate for 4,9 H1: 4,9 => CTR * 7513.62.86.871235.2348591764769318255826749319132854678695.371232716.5..1.5.27683 H1: 8 # 16 pairs I1: 4,9,6,8 # reduction candidate for 4,9 I1: 4,9 # 17 pairs * PAIR F1: 6,9 BLK 2 F3: 6,9,7 # reduction candidate for 6,9 F3: 6,9 => SOLVED * 751349286648712395239856174476931528582674931913285467864593712325167849197428653 F3: 7 => CTR * 7513962..6.841237523485719647693152858267493191328546786954371232716.8..1.572.6.3 * PAIR F1: 6,9 ROW 1 I1: 6,9,4,8 # reduction candidate for 6,9 I1: 6,9 => SOLVED * 751349286648712395239856174476931528582674931913285467864593712325167849197428653 I1: 4,8 # 15 pairs * PAIR D2: 4,7 ROW 2 H2: 4,7,5,9 # reduction candidate for 4,7 H2: 4,7 => CTR * 7513..28.698.123.523485.1..47693152858267493191328546786954371232.1698.414.728693 H2: 5,9 => SOLVED * 751349286648712395239856174476931528582674931913285467864593712325167849197428653 * PAIR I4: 5,8 COL I I8: 5,8,4,9 # reduction candidate for 5,8 I8: 5,8 => CTR * 7513..28.698.1235423485.17.476931.2.58267493191328546786954371232.16..4.1...2.693 I8: 4,9 # 15 pairs * PAIR G8: 5,8 BLK 9 H8: 5,8,4,9 # reduction candidate for 5,8 H8: 5,8 => CTR * 7513..2..698.123.523485.17.47693152858267493191328546786954371232.1698541...2.693 H8: 4,9 # 15 pairs I8: 5,8,4,9 # reduction candidate for 5,8 I8: 5,8 => CTR * 7513..28.698.1235423485.17.476931.2.58267493191328546786954371232.16..4.1...2.693 I8: 4,9 # 15 pairs H9: 5,8,9 # reduction candidate for 5,8 H9: 5,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-032-base-pr-000.dot * REASONING * PRF # H2: 4,9 => SOL * DIS # I2: 4,9 => CTR => I2: 5 * DIS # H3: 4,9 => CTR => H3: 7 * PRF # H3: 7 => SOL * PRF # I3: 4,9 => SOL * DIS # H1: 4,9 => CTR => H1: 8 * PRF # F3: 6,9 => SOL * DIS # F3: 7 => CTR => F3: 6,9 * PRF # I1: 6,9 => SOL * DIS # H2: 4,7 => CTR => H2: 5,9 * PRF # H2: 5,9 => SOL * DIS # I8: 5,8 => CTR => I8: 4,9 * DIS # H8: 5,8 => CTR => H8: 4,9 * DIS # I8: 5,8 => CTR => I8: 4,9 * CNT 14 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B9,C3,C7,C8,C9,D2,D9,E1,E7,F1,G4,G8,I4) * 7513..2..6.8.123..23.85.1..476931.2.58267493191328546786.5.371232.16....1...2.6.3 * PAIR B2: 4,9 ROW 2 H2: 4,9,5,7 # reduction candidate for 4,9 H2: 4,9 => SOLVED * 751349286648712395239856174476931528582674931913285467864593712325167849197428653 * DURATION: 0:00:02.459007 START: 03:46:53.957441 END: 03:46:56.416448 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-032-base-pr-001.dot * REASONING * PRF # H2: 4,9 => SOL * STA H2: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 032 solution: 751349286648712395239856174476931528582674931913285467864593712325167849197428653 info: 1333 FNBTWXY S8.f 19751 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 751349286648712395239856174476931528582674931913285467864593712325167849197428653 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 # H2: 4,9 => SOL * INC # H2: 5,7 => UNS * DIS # I2: 4,9 => CTR => I2: 5 * INC # I2: 5 => UNS * DIS # H3: 4,9 => CTR => H3: 7 * PRF # H3: 7 => SOL * PRF # I3: 4,9 => SOL * INC # I3: 6 => UNS * DIS # H1: 4,9 => CTR => H1: 8 * INC # H1: 8 => UNS * INC # I1: 4,9 => UNS * PRF # F3: 6,9 => SOL * DIS # F3: 7 => CTR => F3: 6,9 * PRF # I1: 6,9 => SOL * INC # I1: 4,8 => UNS * DIS # H2: 4,7 => CTR => H2: 5,9 * PRF # H2: 5,9 => SOL * DIS # I8: 5,8 => CTR => I8: 4,9 * INC # I8: 4,9 => UNS * DIS # H8: 5,8 => CTR => H8: 4,9 * INC # H8: 4,9 => UNS * DIS # I8: 5,8 => CTR => I8: 4,9 * INC # I8: 4,9 => UNS * INC # H9: 5,8 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H2: 4,9 => SOL * STA H2: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED