Analysis of zz-www.sudokuoftheday.co.uk-20060515-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6.24.91...5....9........ initial
Autosolve
position: 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 7 => CTR => E2: 4,9 * DIS # H4: 3,4 => CTR => H4: 6,9 * DIS # B5: 1,9 => CTR => B5: 2,3,5,8 * DIS # C5: 1,9 => CTR => C5: 2,3,5,8 * DIS # H5: 3,8 => CTR => H5: 4,6,9 * DIS # B6: 3,8 => CTR => B6: 2,9 * DIS # B5: 3,8 => CTR => B5: 1,2,5,9 * DIS # B6: 3,8 => CTR => B6: 2,9 * DIS # C9: 2 => CTR => C9: 4,8 * DIS # G3: 3,8 => CTR => G3: 9 * CNT 10 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 7 => CTR => E2: 4,9 * PRF E2: 4,9 # I8: 6 => SOL * STA E2: 4,9 + I8: 6 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6.24.91...5....9........ | initial |
| 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1.. | autosolve |
| 615298743729345681843167952371586294458921367296734518587612439132459876964873125 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) E1: 4,9 D3: 1,9 F3: 1,7 A4: 3,4 D5: 1,9 I6: 3,8 B7: 3,8 D8: 4,8 D9: 4,8 E9: 3,7 F9: 3,7 G8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 19 pairs (_) / F3 = 1 => 0 pairs (X) I1,I2: 1.. / I1 = 1 => 13 pairs (_) / I2 = 1 => 14 pairs (_) C4,F4: 1.. / C4 = 1 => 0 pairs (*) / F4 = 1 => 0 pairs (X) D3,D5: 1.. / D3 = 1 => 19 pairs (_) / D5 = 1 => 0 pairs (X) E5,E6: 2.. / E5 = 2 => 13 pairs (_) / E6 = 2 => 0 pairs (X) H8,H9: 2.. / H8 = 2 => 16 pairs (_) / H9 = 2 => 13 pairs (_) E9,F9: 3.. / E9 = 3 => 0 pairs (X) / F9 = 3 => 19 pairs (_) E1,E2: 4.. / E1 = 4 => 12 pairs (_) / E2 = 4 => 0 pairs (*) A4,A5: 4.. / A4 = 4 => 16 pairs (_) / A5 = 4 => 16 pairs (_) C8,C9: 4.. / C8 = 4 => 16 pairs (_) / C9 = 4 => 12 pairs (_) D8,D9: 4.. / D8 = 4 => 12 pairs (_) / D9 = 4 => 16 pairs (_) A5,H5: 4.. / A5 = 4 => 16 pairs (_) / H5 = 4 => 16 pairs (_) C8,D8: 4.. / C8 = 4 => 16 pairs (_) / D8 = 4 => 12 pairs (_) C9,D9: 4.. / C9 = 4 => 12 pairs (_) / D9 = 4 => 16 pairs (_) B5,C5: 5.. / B5 = 5 => 12 pairs (_) / C5 = 5 => 12 pairs (_) H9,I9: 5.. / H9 = 5 => 20 pairs (_) / I9 = 5 => 12 pairs (_) C3,H3: 5.. / C3 = 5 => 13 pairs (_) / H3 = 5 => 12 pairs (_) B1,B5: 5.. / B1 = 5 => 12 pairs (_) / B5 = 5 => 12 pairs (_) I1,I9: 5.. / I1 = 5 => 20 pairs (_) / I9 = 5 => 12 pairs (_) F4,F5: 6.. / F4 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) B8,B9: 6.. / B8 = 6 => 16 pairs (_) / B9 = 6 => 13 pairs (_) F5,H5: 6.. / F5 = 6 => 13 pairs (_) / H5 = 6 => 0 pairs (*) A2,A3: 7.. / A2 = 7 => 19 pairs (_) / A3 = 7 => 0 pairs (X) E2,F3: 7.. / E2 = 7 => 0 pairs (X) / F3 = 7 => 19 pairs (_) C7,C8: 7.. / C7 = 7 => 18 pairs (_) / C8 = 7 => 14 pairs (_) E9,F9: 7.. / E9 = 7 => 19 pairs (_) / F9 = 7 => 0 pairs (X) H7,H8: 7.. / H7 = 7 => 14 pairs (_) / H8 = 7 => 18 pairs (_) A2,E2: 7.. / A2 = 7 => 19 pairs (_) / E2 = 7 => 0 pairs (X) A3,F3: 7.. / A3 = 7 => 0 pairs (X) / F3 = 7 => 19 pairs (_) C7,H7: 7.. / C7 = 7 => 18 pairs (_) / H7 = 7 => 14 pairs (_) C8,H8: 7.. / C8 = 7 => 14 pairs (_) / H8 = 7 => 18 pairs (_) E2,E9: 7.. / E2 = 7 => 0 pairs (X) / E9 = 7 => 19 pairs (_) F3,F9: 7.. / F3 = 7 => 19 pairs (_) / F9 = 7 => 0 pairs (X) D8,D9: 8.. / D8 = 8 => 16 pairs (_) / D9 = 8 => 12 pairs (_) C4,H4: 9.. / C4 = 9 => 0 pairs (X) / H4 = 9 => 19 pairs (_) B6,E6: 9.. / B6 = 9 => 19 pairs (_) / E6 = 9 => 0 pairs (X) D3,D5: 9.. / D3 = 9 => 0 pairs (X) / D5 = 9 => 19 pairs (_) G3,G5: 9.. / G3 = 9 => 19 pairs (_) / G5 = 9 => 0 pairs (X) * DURATION: 0:00:42.806747 START: 23:09:42.958210 END: 23:10:25.764957 2019-04-30 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,D3,D5,D8,D9,E1,E9,F3,F9,G8,I6) * 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1.. * PAIR E1: 4,9 BLK 2 E2: 4,9,7 # reduction candidate for 4,9 E2: 7 => CTR * 6..2487.....3756..74.961..2.7158.29....1....7..67.451.5..6124.91...59...9...371.. E2: 4,9 # 19 pairs * PAIR E1: 4,9 ROW 1 H1: 4,9,3,5 # reduction candidate for 4,9 H1: 4,9 # 13 pairs H1: 3,5 # 13 pairs * PAIR A4: 3,4 BLK 4 A5: 3,4,2,8 # reduction candidate for 3,4 A5: 2,8 # 17 pairs A5: 3,4 # 16 pairs * PAIR A4: 3,4 ROW 4 H4: 3,4,6,9 # reduction candidate for 3,4 H4: 3,4 => CTR * 6..2.87.....3.56...4..6...2.795812.6...9.6..7..67.451.5..6124.91...59...9....31.. H4: 6,9 # 13 pairs I4: 3,4,6 # reduction candidate for 3,4 I4: 3,4 # 16 pairs * PAIR D5: 1,9 ROW 5 B5: 1,9,2,3,5,8 # reduction candidate for 1,9 B5: 1,9 => CTR * 65.2.873.7..3.568..4.167952473581296.159.6.47.967.451.5386124.91...59...9...731.5 B5: 2,3,5,8 # 12 pairs C5: 1,9,2,3,5,8 # reduction candidate for 1,9 C5: 1,9 => CTR * 6..2.87..7..3.568.348167952473581296.519.6.47.967.451.5876124391...59...9...731.. C5: 2,3,5,8 # 12 pairs * PAIR I6: 3,8 BLK 6 G5: 3,8,9 # reduction candidate for 3,8 G5: 3,8 # 19 pairs H5: 3,8,4,6,9 # reduction candidate for 3,8 H5: 3,8 => CTR * 6..2.87.....3.56...4..6...237.5812..4..9.6..7.967.451.5..6124.91...59...9.....1.. H5: 4,6,9 # 12 pairs * PAIR I6: 3,8 ROW 6 A6: 3,8,2 # reduction candidate for 3,8 A6: 3,8 # 15 pairs B6: 3,8,2,9 # reduction candidate for 3,8 B6: 3,8 => CTR * 6..2487.....3756..74.961..2.7158.29....12...72.679451.5..6124.91...59...9...371.. B6: 2,9 # 13 pairs * PAIR I6: 3,8 COL I I8: 3,8,6 # reduction candidate for 3,8 I8: 3,8 # 18 pairs I8: 6 # 17 pairs * PAIR B7: 3,8 BLK 7 C7: 3,8,7 # reduction candidate for 3,8 C7: 3,8 # 14 pairs B8: 3,8,2,6 # reduction candidate for 3,8 B8: 3,8 # 17 pairs C8: 3,8,2,4,7 # reduction candidate for 3,8 C8: 3,8 # 16 pairs * PAIR B7: 3,8 ROW 7 H7: 3,8,7 # reduction candidate for 3,8 H7: 3,8 # 18 pairs H7: 7 # 14 pairs * PAIR B7: 3,8 COL B B5: 3,8,1,2,5,9 # reduction candidate for 3,8 B5: 3,8 => CTR * 65.2.8731.1.3.5648.4.167952.715862944.5921867.967.451.5..6124.91...59..696....1.5 B5: 1,2,5,9 # 12 pairs B6: 3,8,2,9 # reduction candidate for 3,8 B6: 3,8 => CTR * 6..2487.....3756..74.961..2.7158.29....12...72.679451.5..6124.91...59...9...371.. B6: 2,9 # 13 pairs * PAIR D8: 4,8 ROW 8 C8: 4,8,2,3,7 # reduction candidate for 4,8 C8: 4,8 # 20 pairs C8: 2,3,7 # 12 pairs * PAIR D9: 4,8 ROW 9 C9: 4,8,2 # reduction candidate for 4,8 C9: 2 => CTR * 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91.4859376962...1.. C9: 4,8 # 15 pairs * PAIR G8: 3,8 BLK 9 H7: 3,8,7 # reduction candidate for 3,8 H7: 3,8 # 18 pairs H8: 3,8,2,6,7 # reduction candidate for 3,8 H8: 3,8 # 16 pairs I8: 3,8,6 # reduction candidate for 3,8 I8: 3,8 # 18 pairs * PAIR G8: 3,8 ROW 8 B8: 3,8,2,6 # reduction candidate for 3,8 B8: 3,8 # 17 pairs C8: 3,8,2,4,7 # reduction candidate for 3,8 C8: 3,8 # 16 pairs * PAIR G8: 3,8 COL G G3: 3,8,9 # reduction candidate for 3,8 G3: 3,8 => CTR * 6..2487.....3756..74.961..2.7.58.2........9.7..679451.5..6124.91...59...9.....1.. G3: 9 # 19 pairs G5: 3,8,9 # reduction candidate for 3,8 G5: 3,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060515-absurd-base-pr-000.dot * REASONING * DIS # E2: 7 => CTR => E2: 4,9 * DIS # H4: 3,4 => CTR => H4: 6,9 * DIS # B5: 1,9 => CTR => B5: 2,3,5,8 * DIS # C5: 1,9 => CTR => C5: 2,3,5,8 * DIS # H5: 3,8 => CTR => H5: 4,6,9 * DIS # B6: 3,8 => CTR => B6: 2,9 * DIS # B5: 3,8 => CTR => B5: 1,2,5,9 * DIS # B6: 3,8 => CTR => B6: 2,9 * DIS # C9: 2 => CTR => C9: 4,8 * DIS # G3: 3,8 => CTR => G3: 9 * CNT 10 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,D3,D5,D8,D9,E1,E9,F3,F9,G8,I6) * 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1.. * PAIR E1: 4,9 BLK 2 E2: 4,9,7 # reduction candidate for 4,9 E2: 7 => CTR * 6..2487.....3756..74.961..2.7158.29....1....7..67.451.5..6124.91...59...9...371.. * PAIR I6: 3,8 COL I I8: 3,8,6 # reduction candidate for 3,8 I8: 6 => SOLVED * 615298743729345681843167952371586294458921367296734518587612439132459876964873125 * DURATION: 0:00:04.181131 START: 23:10:50.049009 END: 23:10:54.230140 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060515-absurd-base-pr-001.dot * REASONING * DIS # E2: 7 => CTR => E2: 4,9 * PRF E2: 4,9 # I8: 6 => SOL * STA E2: 4,9 + I8: 6 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060515, absurd
Solution
position: 615298743729345681843167952371586294458921367296734518587612439132459876964873125 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 # E2: 4,9 => UNS * DIS # E2: 7 => CTR => E2: 4,9 * INC # H1: 4,9 => UNS * INC # H1: 3,5 => UNS * INC # A5: 3,4 => UNS * INC # A5: 2,8 => UNS * DIS # H4: 3,4 => CTR => H4: 6,9 * INC # H4: 6,9 => UNS * INC # I4: 3,4 => UNS * DIS # B5: 1,9 => CTR => B5: 2,3,5,8 * INC # B5: 2,3,5,8 => UNS * DIS # C5: 1,9 => CTR => C5: 2,3,5,8 * INC # C5: 2,3,5,8 => UNS * INC # G5: 3,8 => UNS * DIS # H5: 3,8 => CTR => H5: 4,6,9 * INC # H5: 4,6,9 => UNS * INC # A6: 3,8 => UNS * DIS # B6: 3,8 => CTR => B6: 2,9 * INC # B6: 2,9 => UNS * INC # I8: 3,8 => UNS * INC # I8: 6 => UNS * INC # C7: 3,8 => UNS * INC # B8: 3,8 => UNS * INC # C8: 3,8 => UNS * INC # H7: 3,8 => UNS * INC # H7: 7 => UNS * DIS # B5: 3,8 => CTR => B5: 1,2,5,9 * INC # B5: 1,2,5,9 => UNS * DIS # B6: 3,8 => CTR => B6: 2,9 * INC # B6: 2,9 => UNS * INC # C8: 4,8 => UNS * INC # C8: 2,3,7 => UNS * INC # C9: 4,8 => UNS * DIS # C9: 2 => CTR => C9: 4,8 * INC # H7: 3,8 => UNS * INC # H8: 3,8 => UNS * INC # I8: 3,8 => UNS * INC # B8: 3,8 => UNS * INC # C8: 3,8 => UNS * DIS # G3: 3,8 => CTR => G3: 9 * INC # G3: 9 => UNS * INC # G5: 3,8 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 4,9 => UNS * DIS # E2: 7 => CTR => E2: 4,9 * INC E2: 4,9 # I8: 3,8 => UNS * PRF E2: 4,9 # I8: 6 => SOL * STA E2: 4,9 + I8: 6 * CNT 4 HDP CHAINS / 4 HYP OPENED