Analysis of zz-www.sudokuoftheday.co.uk-20190205-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: .5..6..1..37...58...9..8.....8.........6...47.1..7................7.21.9..548.3.. initial
Autosolve
position: 85..6791..37...58...9..87....8...6.1...61.847.1.87.2.5..1..64.8.8.7.21.9..54813.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 2,4 => SOL * DIS # A3: 2,4 => CTR => A3: 1,6 * DIS # B3: 2,4 => CTR => B3: 6 * PRF # B3: 6 => SOL * PRF # D3: 2,3 => SOL * DIS # F4: 4,9 => CTR => F4: 3,5 * DIS # I3: 2,6 => CTR => I3: 3,4 * DIS # A3: 2,6 => CTR => A3: 1,4 * PRF # H9: 2,6 => SOL * DIS # A5: 2,9 => CTR => A5: 3,5 * DIS # B9: 2,9 => CTR => B9: 6,7 * DIS # A5: 2,3 => CTR => A5: 5,9 * DIS # E4: 4 => CTR => E4: 2,9 * DIS # D2: 2,9 => CTR => D2: 1 * DIS # A4: 3,9 => CTR => A4: 4,5,7 * DIS # F4: 3,9 => CTR => F4: 4,5 * DIS # A6: 3,9 => CTR => A6: 4,6 * DIS # F6: 3,9 => CTR => F6: 4 * DIS # A9: 2,7 => CTR => A9: 6,9 * PRF # B9: 2,7 => SOL * PRF # H7: 2,7 => SOL * PRF # H9: 2,6 => SOL * DIS # A9: 2,6 => CTR => A9: 7,9 * DIS # I3: 2,6 => CTR => I3: 3,4 * CNT 24 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 2,4 => SOL * STA A2: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5..6..1..37...58...9..8.....8.........6...47.1..7................7.21.9..548.3.. | initial |
| 85..6791..37...58...9..87....8...6.1...61.847.1.87.2.5..1..64.8.8.7.21.9..54813.. | autosolve |
| 854267913237149586169358724748925631592613847613874295321596478486732159975481362 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 2,4 D1: 2,3 F2: 4,9 H3: 2,6 B5: 2,9 C5: 2,3 D4: 2,9 H4: 3,9 H6: 3,9 B7: 2,7 E8: 3,5 H8: 5,6 I9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 0 pairs (X) / A3 = 1 => 13 pairs (_) D2,D3: 1.. / D2 = 1 => 13 pairs (_) / D3 = 1 => 0 pairs (X) A2,D2: 1.. / A2 = 1 => 0 pairs (X) / D2 = 1 => 13 pairs (_) A3,D3: 1.. / A3 = 1 => 13 pairs (_) / D3 = 1 => 0 pairs (X) D4,E4: 2.. / D4 = 2 => 16 pairs (_) / E4 = 2 => 19 pairs (_) C1,C5: 2.. / C1 = 2 => 16 pairs (_) / C5 = 2 => 18 pairs (_) I1,I3: 3.. / I1 = 3 => 15 pairs (_) / I3 = 3 => 14 pairs (_) H4,H6: 3.. / H4 = 3 => 12 pairs (_) / H6 = 3 => 0 pairs (X) D1,I1: 3.. / D1 = 3 => 14 pairs (_) / I1 = 3 => 15 pairs (_) A8,C8: 4.. / A8 = 4 => 14 pairs (_) / C8 = 4 => 16 pairs (_) C1,I1: 4.. / C1 = 4 => 18 pairs (_) / I1 = 4 => 16 pairs (_) B3,B4: 4.. / B3 = 4 => 0 pairs (X) / B4 = 4 => 18 pairs (_) D3,E3: 5.. / D3 = 5 => 14 pairs (_) / E3 = 5 => 0 pairs (*) A4,A5: 5.. / A4 = 5 => 0 pairs (X) / A5 = 5 => 14 pairs (_) F4,F5: 5.. / F4 = 5 => 14 pairs (_) / F5 = 5 => 0 pairs (X) H7,H8: 5.. / H7 = 5 => 20 pairs (_) / H8 = 5 => 0 pairs (*) A4,F4: 5.. / A4 = 5 => 0 pairs (X) / F4 = 5 => 14 pairs (_) A5,F5: 5.. / A5 = 5 => 14 pairs (_) / F5 = 5 => 0 pairs (X) E8,H8: 5.. / E8 = 5 => 20 pairs (_) / H8 = 5 => 0 pairs (*) D3,D7: 5.. / D3 = 5 => 14 pairs (_) / D7 = 5 => 0 pairs (*) A6,C6: 6.. / A6 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) A2,I2: 6.. / A2 = 6 => 0 pairs (X) / I2 = 6 => 16 pairs (_) B3,B9: 6.. / B3 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) C6,C8: 6.. / C6 = 6 => 14 pairs (_) / C8 = 6 => 0 pairs (*) A4,B4: 7.. / A4 = 7 => 15 pairs (_) / B4 = 7 => 0 pairs (X) H7,H9: 7.. / H7 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) H4,H6: 9.. / H4 = 9 => 0 pairs (X) / H6 = 9 => 12 pairs (_) A9,B9: 9.. / A9 = 9 => 13 pairs (_) / B9 = 9 => 0 pairs (X) D7,E7: 9.. / D7 = 9 => 15 pairs (_) / E7 = 9 => 20 pairs (_) * DURATION: 0:00:42.093473 START: 03:30:38.123315 END: 03:31:20.216788 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,C1,C5,D1,D4,E8,F2,H3,H4,H6,H8,I9) * 85..6791..37...58...9..87....8...6.1...61.847.1.87.2.5..1..64.8.8.7.21.9..54813.. * PAIR C1: 2,4 BLK 1 A2: 2,4,1,6 # reduction candidate for 2,4 A2: 2,4 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 A2: 1,6 # 14 pairs A3: 2,4,1,6 # reduction candidate for 2,4 A3: 2,4 => CTR * 852367914137.495864691587237489256315..61.847.1.8742.5..1596478.8.732159.75481362 A3: 1,6 # 14 pairs B3: 2,4,6 # reduction candidate for 2,4 B3: 2,4 => CTR * 85236791..37...58..49..872...8...6.1...61.847.1687.2.5..1..6458.84752169965481372 B3: 6 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 * PAIR C1: 2,4 ROW 1 I1: 2,4,3 # reduction candidate for 2,4 I1: 3 # 15 pairs I1: 2,4 # 14 pairs * PAIR D1: 2,3 BLK 2 D3: 2,3,1,5 # reduction candidate for 2,3 D3: 2,3 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 D3: 1,5 # 14 pairs E3: 2,3,4,5 # reduction candidate for 2,3 E3: 2,3 # 20 pairs * PAIR D1: 2,3 ROW 1 I1: 2,3,4 # reduction candidate for 2,3 I1: 2,3 # 18 pairs I1: 4 # 16 pairs * PAIR F2: 4,9 BLK 2 E2: 4,9,2 # reduction candidate for 4,9 E2: 4,9 # 18 pairs E2: 2 # 18 pairs * PAIR F2: 4,9 COL F F4: 4,9,3,5 # reduction candidate for 4,9 F4: 4,9 => CTR * 852367914.37...58664915872.578...631.9.615847.1.873295.21..64.8.8.7.21.9965481372 F4: 3,5 # 14 pairs F6: 4,9,3 # reduction candidate for 4,9 F6: 4,9 # 17 pairs * PAIR H3: 2,6 BLK 3 I2: 2,6,4 # reduction candidate for 2,6 I2: 2,6 # 16 pairs I3: 2,6,3,4 # reduction candidate for 2,6 I3: 2,6 => CTR * 85..67913.37...584..9.487...48...6.1...61.847.1.8742.5..1..64.848.7.21.9..54813.. I3: 3,4 # 14 pairs * PAIR H3: 2,6 ROW 3 A3: 2,6,1,4 # reduction candidate for 2,6 A3: 2,6 => CTR * 85..6791.137...586..9158723..8...6.1...61.847.1.87.2.5..1596478.8.732159..5481362 A3: 1,4 # 14 pairs B3: 2,6,4 # reduction candidate for 2,6 B3: 2,6 # 18 pairs * PAIR H3: 2,6 COL H H9: 2,6,7 # reduction candidate for 2,6 H9: 2,6 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 H9: 7 # 14 pairs * PAIR B5: 2,9 BLK 4 A5: 2,9,3,5 # reduction candidate for 2,9 A5: 2,9 => CTR * 852367914.37...58664915872.578...6.1.93615847.1.87.2.5.21..64.8.8.7.21.9965481372 A5: 3,5 # 14 pairs * PAIR B5: 2,9 COL B B9: 2,9,6,7 # reduction candidate for 2,9 B9: 2,9 => CTR * 85..6791..37..9586.695.872.748..5631...61.847.1.8742.5.71..6458.8.752169695481372 B9: 6,7 # 15 pairs * PAIR C5: 2,3 BLK 4 A5: 2,3,5,9 # reduction candidate for 2,3 A5: 2,3 => CTR * 852367914.37...58664915872.578...6.1.9.615847.1.87.2.5.21..64.8.8.7.21.9965481372 A5: 5,9 # 14 pairs * PAIR D4: 2,9 BLK 5 E4: 2,9,4 # reduction candidate for 2,9 E4: 4 => CTR * 852367914.37.24586649158723..824.6.1...61.847.1.87.2.5..1..64.8.8.7.21.9.654813.2 E4: 2,9 # 17 pairs * PAIR D4: 2,9 COL D D2: 2,9,1 # reduction candidate for 2,9 D2: 2,9 => CTR * 852367914137...586.69158723.48.2.6.1..361.847.16874235321596478684732159.75481362 D2: 1 # 13 pairs * PAIR H4: 3,9 ROW 4 A4: 3,9,4,5,7 # reduction candidate for 3,9 A4: 3,9 => CTR * 85..6791..37...58..49..87...78.456.159261.847.1.87.2.5.21..64.8.8.7.21.9..54813.. A4: 4,5,7 # 13 pairs F4: 3,9,4,5 # reduction candidate for 3,9 F4: 3,9 => CTR * 852367914.37.2458664915872.57824.6.1.9.615847.1.87.2.5.21..64.8.8.7.21.9965481372 F4: 4,5 # 14 pairs * PAIR H6: 3,9 ROW 6 A6: 3,9,4,6 # reduction candidate for 3,9 A6: 3,9 => CTR * 854267913237149586169538724.489256315926138473168742957.1..64.8.83752169..54813.2 A6: 4,6 # 14 pairs F6: 3,9,4 # reduction candidate for 3,9 F6: 3,9 => CTR * 852367914.37...586649158723..8...6.1..361.847.1.87.2.5..1..64.8.8.7.21.9.654813.2 F6: 4 # 18 pairs * PAIR B7: 2,7 BLK 7 A7: 2,7,3 # reduction candidate for 2,7 A7: 2,7 # 20 pairs A9: 2,7,6,9 # reduction candidate for 2,7 A9: 2,7 => CTR * 85..6791..37...58..69..872..48...6.1.2361.847.16874235271..64.8.8.7.21.9.954813.. A9: 6,9 # 14 pairs B9: 2,7,6,9 # reduction candidate for 2,7 B9: 2,7 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 B9: 6,9 # 14 pairs * PAIR B7: 2,7 ROW 7 H7: 2,7,5 # reduction candidate for 2,7 H7: 2,7 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 H7: 5 # 20 pairs * PAIR E8: 3,5 BLK 8 D7: 3,5,9 # reduction candidate for 3,5 D7: 3,5 # 20 pairs E7: 3,5,9 # reduction candidate for 3,5 E7: 3,5 # 15 pairs * PAIR E8: 3,5 COL E E3: 3,5,2,4 # reduction candidate for 3,5 E3: 3,5 # 20 pairs E3: 2,4 # 15 pairs * PAIR I9: 2,6 BLK 9 H9: 2,6,7 # reduction candidate for 2,6 H9: 2,6 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 H9: 7 # 14 pairs * PAIR I9: 2,6 ROW 9 A9: 2,6,7,9 # reduction candidate for 2,6 A9: 2,6 => CTR * 852367914.37..9586.69548723748...6.1.2361.847.16874235271..6458384752169695481372 A9: 7,9 # 14 pairs B9: 2,6,7,9 # reduction candidate for 2,6 B9: 2,6 # 15 pairs * PAIR I9: 2,6 COL I I2: 2,6,4 # reduction candidate for 2,6 I2: 2,6 # 16 pairs I3: 2,6,3,4 # reduction candidate for 2,6 I3: 2,6 => CTR * 85..67913.37...584..9.487...48...6.1...61.847.1.8742.5..1..64.848.7.21.9..54813.. I3: 3,4 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190205-absurd-base-pr-000.dot * REASONING * PRF # A2: 2,4 => SOL * DIS # A3: 2,4 => CTR => A3: 1,6 * DIS # B3: 2,4 => CTR => B3: 6 * PRF # B3: 6 => SOL * PRF # D3: 2,3 => SOL * DIS # F4: 4,9 => CTR => F4: 3,5 * DIS # I3: 2,6 => CTR => I3: 3,4 * DIS # A3: 2,6 => CTR => A3: 1,4 * PRF # H9: 2,6 => SOL * DIS # A5: 2,9 => CTR => A5: 3,5 * DIS # B9: 2,9 => CTR => B9: 6,7 * DIS # A5: 2,3 => CTR => A5: 5,9 * DIS # E4: 4 => CTR => E4: 2,9 * DIS # D2: 2,9 => CTR => D2: 1 * DIS # A4: 3,9 => CTR => A4: 4,5,7 * DIS # F4: 3,9 => CTR => F4: 4,5 * DIS # A6: 3,9 => CTR => A6: 4,6 * DIS # F6: 3,9 => CTR => F6: 4 * DIS # A9: 2,7 => CTR => A9: 6,9 * PRF # B9: 2,7 => SOL * PRF # H7: 2,7 => SOL * PRF # H9: 2,6 => SOL * DIS # A9: 2,6 => CTR => A9: 7,9 * DIS # I3: 2,6 => CTR => I3: 3,4 * CNT 24 HDP CHAINS / 63 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,C1,C5,D1,D4,E8,F2,H3,H4,H6,H8,I9) * 85..6791..37...58...9..87....8...6.1...61.847.1.87.2.5..1..64.8.8.7.21.9..54813.. * PAIR C1: 2,4 BLK 1 A2: 2,4,1,6 # reduction candidate for 2,4 A2: 2,4 => SOLVED * 854267913237149586169358724748925631592613847613874295321596478486732159975481362 * DURATION: 0:00:01.630749 START: 03:32:03.910907 END: 03:32:05.541656 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190205-absurd-base-pr-001.dot * REASONING * PRF # A2: 2,4 => SOL * STA A2: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190205, absurd
Solution
position: 854267913237149586169358724748925631592613847613874295321596478486732159975481362 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 # A2: 2,4 => SOL * INC # A2: 1,6 => UNS * DIS # A3: 2,4 => CTR => A3: 1,6 * INC # A3: 1,6 => UNS * DIS # B3: 2,4 => CTR => B3: 6 * PRF # B3: 6 => SOL * INC # I1: 2,4 => UNS * INC # I1: 3 => UNS * PRF # D3: 2,3 => SOL * INC # D3: 1,5 => UNS * INC # E3: 2,3 => UNS * INC # I1: 2,3 => UNS * INC # I1: 4 => UNS * INC # E2: 4,9 => UNS * INC # E2: 2 => UNS * DIS # F4: 4,9 => CTR => F4: 3,5 * INC # F4: 3,5 => UNS * INC # F6: 4,9 => UNS * INC # I2: 2,6 => UNS * DIS # I3: 2,6 => CTR => I3: 3,4 * INC # I3: 3,4 => UNS * DIS # A3: 2,6 => CTR => A3: 1,4 * INC # A3: 1,4 => UNS * INC # B3: 2,6 => UNS * PRF # H9: 2,6 => SOL * INC # H9: 7 => UNS * DIS # A5: 2,9 => CTR => A5: 3,5 * INC # A5: 3,5 => UNS * DIS # B9: 2,9 => CTR => B9: 6,7 * INC # B9: 6,7 => UNS * DIS # A5: 2,3 => CTR => A5: 5,9 * INC # A5: 5,9 => UNS * INC # E4: 2,9 => UNS * DIS # E4: 4 => CTR => E4: 2,9 * DIS # D2: 2,9 => CTR => D2: 1 * INC # D2: 1 => UNS * DIS # A4: 3,9 => CTR => A4: 4,5,7 * INC # A4: 4,5,7 => UNS * DIS # F4: 3,9 => CTR => F4: 4,5 * INC # F4: 4,5 => UNS * DIS # A6: 3,9 => CTR => A6: 4,6 * INC # A6: 4,6 => UNS * DIS # F6: 3,9 => CTR => F6: 4 * INC # F6: 4 => UNS * INC # A7: 2,7 => UNS * DIS # A9: 2,7 => CTR => A9: 6,9 * INC # A9: 6,9 => UNS * PRF # B9: 2,7 => SOL * INC # B9: 6,9 => UNS * PRF # H7: 2,7 => SOL * INC # H7: 5 => UNS * INC # D7: 3,5 => UNS * INC # E7: 3,5 => UNS * INC # E3: 3,5 => UNS * INC # E3: 2,4 => UNS * PRF # H9: 2,6 => SOL * INC # H9: 7 => UNS * DIS # A9: 2,6 => CTR => A9: 7,9 * INC # A9: 7,9 => UNS * INC # B9: 2,6 => UNS * INC # I2: 2,6 => UNS * DIS # I3: 2,6 => CTR => I3: 3,4 * INC # I3: 3,4 => UNS * CNT 63 HDP CHAINS / 63 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 2,4 => SOL * STA A2: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED