Analysis of xx-top500-021-base.sdk
Contents
Original Sudoku
level: medium
position: 1......727..5........3........6..8.34...1...............3...5...2...4.......7..4. initial
Autosolve
position: 1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # H3: 6,9 => CTR => H3: 8 * PRF # H3: 8 => SOL * DIS # E1: 6,9 => CTR => E1: 8 * PRF # A3: 2,9 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * PRF # C6: 2,8 => SOL * PRF # C2: 6,9 => SOL * DIS # F6: 2,9 => CTR => F6: 8 * PRF # F6: 8 => SOL * DIS # D6: 7,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * DIS # H3: 6,9 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # H8: 6,9 => SOL * DIS # H8: 8 => CTR => H8: 6,9 * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # A9: 8,9 => CTR => A9: 6 * DIS # A3: 8,9 => CTR => A3: 2,6 * PRF # H8: 6 => SOL * DIS # D6: 7 => CTR => D6: 8,9 * PRF # H8: 6,9 => SOL * DIS # H8: 8 => CTR => H8: 6,9 * PRF # H8: 6 => SOL * DIS # A9: 8,9 => CTR => A9: 6 * DIS # I2: 6 => CTR => I2: 8,9 * CNT 28 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I2: 6,9 => SOL * STA I2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1......727..5........3........6..8.34...1...............3...5...2...4.......7..4. | initial |
| 1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534. | autosolve |
| 135489672786521439294367185971642853458713296362958714843196527527834961619275348 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) G1: 6,9 A4: 2,9 C5: 2,8 F4: 2,9 D5: 7,8 G5: 2,7 H5: 6,9 I5: 6,9 G6: 2,7 A7: 8,9 D8: 8,9 G8: 6,9 I9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,A3: 2.. / C2 = 2 => 0 pairs (X) / A3 = 2 => 0 pairs (_) E2,E3: 2.. / E2 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) G5,G6: 2.. / G5 = 2 => 12 pairs (_) / G6 = 2 => 0 pairs (X) C2,E2: 2.. / C2 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) A3,E3: 2.. / A3 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) A4,F4: 2.. / A4 = 2 => 0 pairs (X) / F4 = 2 => 0 pairs (_) C5,G5: 2.. / C5 = 2 => 0 pairs (X) / G5 = 2 => 12 pairs (_) A3,A4: 2.. / A3 = 2 => 0 pairs (*) / A4 = 2 => 0 pairs (X) B6,C6: 6.. / B6 = 6 => 18 pairs (_) / C6 = 6 => 15 pairs (_) H5,I5: 6.. / H5 = 6 => 0 pairs (X) / I5 = 6 => 14 pairs (_) A9,C9: 6.. / A9 = 6 => 14 pairs (_) / C9 = 6 => 0 pairs (X) E7,F7: 6.. / E7 = 6 => 17 pairs (_) / F7 = 6 => 15 pairs (_) G8,H8: 6.. / G8 = 6 => 19 pairs (_) / H8 = 6 => 0 pairs (*) A3,A9: 6.. / A3 = 6 => 0 pairs (X) / A9 = 6 => 14 pairs (_) F1,F7: 6.. / F1 = 6 => 17 pairs (_) / F7 = 6 => 15 pairs (_) G1,G8: 6.. / G1 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) I2,I5: 6.. / I2 = 6 => 0 pairs (X) / I5 = 6 => 14 pairs (_) D5,D6: 7.. / D5 = 7 => 12 pairs (_) / D6 = 7 => 0 pairs (X) G5,G6: 7.. / G5 = 7 => 0 pairs (X) / G6 = 7 => 12 pairs (_) D5,G5: 7.. / D5 = 7 => 12 pairs (_) / G5 = 7 => 0 pairs (X) D6,G6: 7.. / D6 = 7 => 0 pairs (X) / G6 = 7 => 12 pairs (_) E1,F1: 8.. / E1 = 8 => 15 pairs (_) / F1 = 8 => 0 pairs (X) I2,H3: 8.. / I2 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) H8,I9: 8.. / H8 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) C5,D5: 8.. / C5 = 8 => 12 pairs (_) / D5 = 8 => 0 pairs (X) D8,H8: 8.. / D8 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) E1,E7: 8.. / E1 = 8 => 15 pairs (_) / E7 = 8 => 0 pairs (X) H3,H8: 8.. / H3 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) I2,I9: 8.. / I2 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) H5,I5: 9.. / H5 = 9 => 14 pairs (_) / I5 = 9 => 0 pairs (X) A4,F4: 9.. / A4 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) D6,D8: 9.. / D6 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) G1,G8: 9.. / G1 = 9 => 19 pairs (_) / G8 = 9 => 0 pairs (*) * DURATION: 0:01:05.816725 START: 03:17:51.069939 END: 03:18:56.886664 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,C5,D5,D8,F4,G1,G5,G6,G8,H5,I5,I9) * 1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534. * PAIR G1: 6,9 BLK 3 I2: 6,9,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 I2: 8 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 H3: 6,9,8 # reduction candidate for 6,9 H3: 6,9 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 H3: 8 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 * PAIR G1: 6,9 ROW 1 E1: 6,9,8 # reduction candidate for 6,9 E1: 6,9 => CTR * 1354689727..5.1438..43.7165.7164.85345..13.963...5..14943186527527934681618275349 E1: 8 # 15 pairs F1: 6,9,8 # reduction candidate for 6,9 F1: 6,9 # 15 pairs * PAIR A4: 2,9 BLK 4 C6: 2,9,6,8 # reduction candidate for 2,9 C6: 2,9 # 16 pairs C6: 6,8 # 14 pairs * PAIR A4: 2,9 COL A A3: 2,9,6,8 # reduction candidate for 2,9 A3: 2,9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 A3: 6,8 => CTR * 1354..9727.25914386.43271.52716498534587132..3..852714.431..527527934681816275349 * PAIR C5: 2,8 BLK 4 C6: 2,8,6,9 # reduction candidate for 2,8 C6: 2,8 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 C6: 6,9 # 14 pairs * PAIR C5: 2,8 COL C C2: 2,8,6,9 # reduction candidate for 2,8 C2: 6,9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 C2: 2,8 # 16 pairs * PAIR F4: 2,9 BLK 5 F6: 2,9,8 # reduction candidate for 2,9 F6: 2,9 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 F6: 8 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 * PAIR D5: 7,8 BLK 5 D6: 7,8,9 # reduction candidate for 7,8 D6: 7,8 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 D6: 9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 * PAIR H5: 6,9 COL H H3: 6,9,8 # reduction candidate for 6,9 H3: 6,9 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 H3: 8 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 H8: 6,9,8 # reduction candidate for 6,9 H8: 6,9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 H8: 8 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 * PAIR I5: 6,9 COL I I2: 6,9,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 I2: 8 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 * PAIR A7: 8,9 BLK 7 A9: 8,9,6 # reduction candidate for 8,9 A9: 8,9 => CTR * 1354...727..5.143.6.43271.52716498534587132..369852714.431..527527934681816275349 A9: 6 # 14 pairs C9: 8,9,6 # reduction candidate for 8,9 C9: 8,9 # 14 pairs * PAIR A7: 8,9 ROW 7 E7: 8,9,6 # reduction candidate for 8,9 E7: 8,9 # 15 pairs F7: 8,9,6 # reduction candidate for 8,9 F7: 8,9 # 17 pairs * PAIR A7: 8,9 COL A A3: 8,9,2,6 # reduction candidate for 8,9 A3: 8,9 => CTR * 1354...727.25.143...43271.52716498534587132..3..852714.431..527527934681.1.27534. A3: 2,6 # 15 pairs * PAIR D8: 8,9 BLK 8 E7: 8,9,6 # reduction candidate for 8,9 E7: 8,9 # 15 pairs F7: 8,9,6 # reduction candidate for 8,9 F7: 8,9 # 17 pairs * PAIR D8: 8,9 ROW 8 H8: 8,9,6 # reduction candidate for 8,9 H8: 6 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 H8: 8,9 # 19 pairs * PAIR D8: 8,9 COL D D6: 8,9,7 # reduction candidate for 8,9 D6: 7 => CTR * 1354..9727..5.1438..43.7165.716428534528137963..7592149431..527527934681.1.275349 D6: 8,9 # 12 pairs * PAIR G8: 6,9 BLK 9 H8: 6,9,8 # reduction candidate for 6,9 H8: 6,9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 H8: 8 => CTR * 1354..9727..5.1438..43.7165.7164.85345..13.963...5..149431..527527934681618275349 * PAIR I9: 8,9 BLK 9 H8: 8,9,6 # reduction candidate for 8,9 H8: 6 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 H8: 8,9 # 19 pairs * PAIR I9: 8,9 ROW 9 A9: 8,9,6 # reduction candidate for 8,9 A9: 8,9 => CTR * 1354...727..5.143.6.43271.52716498534587132..369852714.431..527527934681816275349 A9: 6 # 14 pairs C9: 8,9,6 # reduction candidate for 8,9 C9: 8,9 # 14 pairs * PAIR I9: 8,9 COL I I2: 8,9,6 # reduction candidate for 8,9 I2: 6 => CTR * 13548697278.5.1436.94327185.7164.8534587132693..958714843169527527834691.1.275348 I2: 8,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-021-base-pr-000.dot * REASONING * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # H3: 6,9 => CTR => H3: 8 * PRF # H3: 8 => SOL * DIS # E1: 6,9 => CTR => E1: 8 * PRF # A3: 2,9 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * PRF # C6: 2,8 => SOL * PRF # C2: 6,9 => SOL * DIS # F6: 2,9 => CTR => F6: 8 * PRF # F6: 8 => SOL * DIS # D6: 7,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * DIS # H3: 6,9 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # H8: 6,9 => SOL * DIS # H8: 8 => CTR => H8: 6,9 * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # A9: 8,9 => CTR => A9: 6 * DIS # A3: 8,9 => CTR => A3: 2,6 * PRF # H8: 6 => SOL * DIS # D6: 7 => CTR => D6: 8,9 * PRF # H8: 6,9 => SOL * DIS # H8: 8 => CTR => H8: 6,9 * PRF # H8: 6 => SOL * DIS # A9: 8,9 => CTR => A9: 6 * DIS # I2: 6 => CTR => I2: 8,9 * CNT 28 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,C5,D5,D8,F4,G1,G5,G6,G8,H5,I5,I9) * 1354...727..5.143...43.71.5.7164.85345..13...3...5..14.431..527527.34..1.1.27534. * PAIR G1: 6,9 BLK 3 I2: 6,9,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 135489672786521439294367185971642853458713296362958714843196527527834961619275348 * DURATION: 0:00:02.255854 START: 03:19:51.879123 END: 03:19:54.134977 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-021-base-pr-001.dot * REASONING * PRF # I2: 6,9 => SOL * STA I2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 021 solution: 135489672786521439294367185971642853458713296362958714843196527527834961619275348 info: 1312 FNBTXY S8.f 24861 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 135489672786521439294367185971642853458713296362958714843196527527834961619275348 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 # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # H3: 6,9 => CTR => H3: 8 * PRF # H3: 8 => SOL * DIS # E1: 6,9 => CTR => E1: 8 * INC # E1: 8 => UNS * INC # F1: 6,9 => UNS * INC # C6: 2,9 => UNS * INC # C6: 6,8 => UNS * PRF # A3: 2,9 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * PRF # C6: 2,8 => SOL * INC # C6: 6,9 => UNS * INC # C2: 2,8 => UNS * PRF # C2: 6,9 => SOL * DIS # F6: 2,9 => CTR => F6: 8 * PRF # F6: 8 => SOL * DIS # D6: 7,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * DIS # H3: 6,9 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # H8: 6,9 => SOL * DIS # H8: 8 => CTR => H8: 6,9 * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # A9: 8,9 => CTR => A9: 6 * INC # A9: 6 => UNS * INC # C9: 8,9 => UNS * INC # E7: 8,9 => UNS * INC # F7: 8,9 => UNS * DIS # A3: 8,9 => CTR => A3: 2,6 * INC # A3: 2,6 => UNS * INC # E7: 8,9 => UNS * INC # F7: 8,9 => UNS * INC # H8: 8,9 => UNS * PRF # H8: 6 => SOL * INC # D6: 8,9 => UNS * DIS # D6: 7 => CTR => D6: 8,9 * PRF # H8: 6,9 => SOL * DIS # H8: 8 => CTR => H8: 6,9 * INC # H8: 8,9 => UNS * PRF # H8: 6 => SOL * DIS # A9: 8,9 => CTR => A9: 6 * INC # A9: 6 => UNS * INC # C9: 8,9 => UNS * INC # I2: 8,9 => UNS * DIS # I2: 6 => CTR => I2: 8,9 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I2: 6,9 => SOL * STA I2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED