Analysis of zz-www.sudokuoftheday.co.uk-20060604-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: 1..93...8.256........751.2...6..92..8......5..9..2346.........5.8..9....7...8..1. initial
Autosolve
position: 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 4 => CTR => A3: 3,9 * DIS # G2: 3,9 => CTR => G2: 1,7 * DIS # I2: 3,9 => CTR => I2: 1 * DIS # B4: 3,4 => CTR => B4: 7 * DIS # G2: 3,9 => CTR => G2: 1,7 * DIS # I2: 3,9 => CTR => I2: 1 * DIS # A3: 4 => CTR => A3: 3,9 * DIS # G5: 3,9 => CTR => G5: 1 * PRF # G9: 3,9 => SOL * DIS # G9: 6 => CTR => G9: 3,9 * DIS # B4: 3,4 => CTR => B4: 7 * DIS # B4: 4 => CTR => B4: 3,7 * DIS # E5: 1,7 => CTR => E5: 6 * DIS # E5: 1 => CTR => E5: 6,7 * DIS # F7: 6,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # I5: 1,3 => CTR => I5: 9 * DIS # I2: 9 => CTR => I2: 1,3 * PRF # C9: 3,4 => SOL * DIS # F7: 6,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # E5: 1 => CTR => E5: 6,7 * DIS # F7: 7 => CTR => F7: 4,6 * PRF # G9: 3,9 => SOL * DIS # G9: 6 => CTR => G9: 3,9 * PRF # C7: 3,9 => SOL * DIS # C7: 4 => CTR => C7: 3,9 * DIS # H2: 7 => CTR => H2: 3,9 * DIS # G8: 3,7 => CTR => G8: 6 * PRF # G8: 6 => SOL * PRF # H2: 9 => SOL * CNT 31 HDP CHAINS / 58 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 4 => CTR => A3: 3,9 * DIS A3: 3,9 # G2: 3,9 => CTR => G2: 1,7 * DIS A3: 3,9 + G2: 1,7 # I2: 3,9 => CTR => I2: 1 * PRF A3: 3,9 + G2: 1,7 + I2: 1 # G9: 3,9 => SOL * STA A3: 3,9 + G2: 1,7 + I2: 1 + G9: 3,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..93...8.256........751.2...6..92..8......5..9..2346.........5.8..9....7...8..1. | initial |
| 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1. | autosolve |
| 167932548325648791948751326476519283832467159591823467619274835283195674754386912 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 3,9 B3: 3,4 G3: 3,9 A4: 3,4 B5: 3,7 E4: 1,7 F5: 6,7 I4: 1,3 A7: 2,6 A8: 2,6 C8: 3,4 D7: 2,3 E7: 6,7 D9: 2,3 F9: 4,6 H7: 3,9 H8: 3,7 I8: 2,4 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I2: 1.. / G2 = 1 => 0 pairs (X) / I2 = 1 => 16 pairs (_) E4,E5: 1.. / E4 = 1 => 19 pairs (_) / E5 = 1 => 0 pairs (X) E4,I4: 1.. / E4 = 1 => 19 pairs (_) / I4 = 1 => 0 pairs (X) G2,G5: 1.. / G2 = 1 => 0 pairs (X) / G5 = 1 => 16 pairs (_) A7,A8: 2.. / A7 = 2 => 0 pairs (X) / A8 = 2 => 0 pairs (_) D7,D9: 2.. / D7 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) I8,I9: 2.. / I8 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) A7,D7: 2.. / A7 = 2 => 0 pairs (X) / D7 = 2 => 0 pairs (_) A8,I8: 2.. / A8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) D9,I9: 2.. / D9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) D7,D9: 3.. / D7 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) A3,B3: 4.. / A3 = 4 => 0 pairs (X) / B3 = 4 => 19 pairs (_) A4,B4: 4.. / A4 = 4 => 19 pairs (_) / B4 = 4 => 0 pairs (X) F7,F9: 4.. / F7 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) I8,I9: 4.. / I8 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) C7,F7: 4.. / C7 = 4 => 0 pairs (X) / F7 = 4 => 0 pairs (_) C8,I8: 4.. / C8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) A3,A4: 4.. / A3 = 4 => 0 pairs (X) / A4 = 4 => 19 pairs (_) B3,B4: 4.. / B3 = 4 => 19 pairs (_) / B4 = 4 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 17 pairs (_) / F5 = 6 => 0 pairs (X) A7,A8: 6.. / A7 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) G8,G9: 6.. / G8 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) A8,G8: 6.. / A8 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) F9,G9: 6.. / F9 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) E5,E7: 6.. / E5 = 6 => 17 pairs (_) / E7 = 6 => 0 pairs (X) G2,H2: 7.. / G2 = 7 => 17 pairs (_) / H2 = 7 => 0 pairs (X) B4,B5: 7.. / B4 = 7 => 19 pairs (_) / B5 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 17 pairs (_) / F7 = 7 => 0 pairs (X) G8,H8: 7.. / G8 = 7 => 0 pairs (X) / H8 = 7 => 17 pairs (_) B4,E4: 7.. / B4 = 7 => 19 pairs (_) / E4 = 7 => 0 pairs (X) F5,F7: 7.. / F5 = 7 => 17 pairs (_) / F7 = 7 => 0 pairs (X) G2,G8: 7.. / G2 = 7 => 17 pairs (_) / G8 = 7 => 0 pairs (X) H2,H8: 7.. / H2 = 7 => 0 pairs (X) / H8 = 7 => 17 pairs (_) A2,A3: 9.. / A2 = 9 => 22 pairs (_) / A3 = 9 => 21 pairs (_) G5,I5: 9.. / G5 = 9 => 0 pairs (X) / I5 = 9 => 21 pairs (_) C7,C9: 9.. / C7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) H7,G9: 9.. / H7 = 9 => 21 pairs (_) / G9 = 9 => 0 pairs (*) A3,G3: 9.. / A3 = 9 => 21 pairs (_) / G3 = 9 => 22 pairs (_) C7,H7: 9.. / C7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) C9,G9: 9.. / C9 = 9 => 21 pairs (_) / G9 = 9 => 0 pairs (*) H2,H7: 9.. / H2 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) I2,I5: 9.. / I2 = 9 => 0 pairs (X) / I5 = 9 => 21 pairs (_) * DURATION: 0:00:53.751966 START: 23:36:48.855000 END: 23:37:42.606966 2019-04-30 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A7,A8,B3,B5,C8,D7,D9,E4,E7,F5,F9,G3,H7,H8,I4,I8,I9) * 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1. * PAIR A2: 3,9 BLK 1 A3: 3,9,4 # reduction candidate for 3,9 A3: 4 => CTR * 167932548925648...438751926346579281872416359591823467.1..6789568.195732759.8..1. A3: 3,9 # 19 pairs * PAIR A2: 3,9 ROW 2 G2: 3,9,1,7 # reduction candidate for 3,9 G2: 3,9 => CTR * 167932548.25648.71..8751.26..65192838324..159591823467.1....895.8.19573.75938.612 G2: 1,7 # 20 pairs H2: 3,9,7 # reduction candidate for 3,9 H2: 3,9 # 17 pairs I2: 3,9,1 # reduction candidate for 3,9 I2: 3,9 => CTR * 167932548.2564817...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612 I2: 1 # 16 pairs * PAIR B3: 3,4 BLK 1 A3: 3,4,9 # reduction candidate for 3,4 A3: 3,4 # 22 pairs A3: 9 # 21 pairs * PAIR B3: 3,4 COL B B4: 3,4,7 # reduction candidate for 3,4 B4: 3,4 => CTR * 167932548.25648.....8751.26..6579281872416.5.591823467.1..678.568.195..275.284.1. B4: 7 # 19 pairs * PAIR G3: 3,9 BLK 3 G2: 3,9,1,7 # reduction candidate for 3,9 G2: 3,9 => CTR * 167932548.25648.71..8751.26..65192838324..159591823467.1....895.8.19573.75938.612 G2: 1,7 # 20 pairs H2: 3,9,7 # reduction candidate for 3,9 H2: 3,9 # 17 pairs I2: 3,9,1 # reduction candidate for 3,9 I2: 3,9 => CTR * 167932548.2564817...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612 I2: 1 # 16 pairs * PAIR G3: 3,9 ROW 3 A3: 3,9,4 # reduction candidate for 3,9 A3: 4 => CTR * 167932548925648...438751926346579281872416359591823467.1..6789568.195732759.8..1. A3: 3,9 # 19 pairs * PAIR G3: 3,9 COL G G5: 3,9,1 # reduction candidate for 3,9 G5: 3,9 => CTR * 167932548.2564817...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612 G5: 1 # 16 pairs G9: 3,9,6 # reduction candidate for 3,9 G9: 3,9 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 G9: 6 => CTR * 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....895.8.195...75938.612 * PAIR A4: 3,4 BLK 4 B4: 3,4,7 # reduction candidate for 3,4 B4: 3,4 => CTR * 167932548.25648.....8751.26..6579281872416.5.591823467.1..678.568.195..275.284.1. B4: 7 # 19 pairs * PAIR A4: 3,4 COL A A3: 3,4,9 # reduction candidate for 3,4 A3: 3,4 # 22 pairs A3: 9 # 21 pairs * PAIR B5: 3,7 BLK 4 B4: 3,7,4 # reduction candidate for 3,7 B4: 4 => CTR * 167932548.25648.....8751.26.46579281872416.5.591823467.1..678.568.195..275.284.1. B4: 3,7 # 19 pairs * PAIR E4: 1,7 BLK 5 E5: 1,7,6 # reduction candidate for 1,7 E5: 1,7 => CTR * 167932548.25648.....8751.26..65.928.8.24.6.5.591823467.1..678.568.195..275.284.1. E5: 6 # 17 pairs * PAIR F5: 6,7 BLK 5 E5: 6,7,1 # reduction candidate for 6,7 E5: 1 => CTR * 167932548.25648.....8751.26..65.928.8.2416.5.591823467.1..678.568.195..275.284.1. E5: 6,7 # 19 pairs * PAIR F5: 6,7 COL F F7: 6,7,4 # reduction candidate for 6,7 F7: 6,7 => CTR * 167932548.25648.....8751.26..65.928.8.24...5.591823467.14...895.83195.74759.84.1. F7: 4 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 * PAIR I4: 1,3 BLK 6 G5: 1,3,9 # reduction candidate for 1,3 G5: 1,3 # 21 pairs I5: 1,3,9 # reduction candidate for 1,3 I5: 1,3 => CTR * 167932548.25648..99487513264.65.928.8.24..95.591823467.1....895.8.195.3.75938.612 I5: 9 # 21 pairs * PAIR I4: 1,3 COL I I2: 1,3,9 # reduction candidate for 1,3 I2: 9 => CTR * 167932548.256481799487513264.65.928.8.24..95.591823467.1....895.8.19573.75938.612 I2: 1,3 # 21 pairs * PAIR C8: 3,4 BLK 7 C7: 3,4,9 # reduction candidate for 3,4 C7: 3,4 # 21 pairs C9: 3,4,9 # reduction candidate for 3,4 C9: 3,4 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 C9: 9 # 21 pairs * PAIR E7: 6,7 BLK 8 F7: 6,7,4 # reduction candidate for 6,7 F7: 6,7 => CTR * 167932548.25648.....8751.26..65.928.8.24...5.591823467.14...895.83195.74759.84.1. F7: 4 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 * PAIR E7: 6,7 COL E E5: 6,7,1 # reduction candidate for 6,7 E5: 1 => CTR * 167932548.25648.....8751.26..65.928.8.2416.5.591823467.1..678.568.195..275.284.1. E5: 6,7 # 19 pairs * PAIR F9: 4,6 BLK 8 F7: 4,6,7 # reduction candidate for 4,6 F7: 7 => CTR * 167932548.25648.....8751.26..65.928.8.24...5.591823467.14..7895.83195.74759.84.1. F7: 4,6 # 17 pairs * PAIR H7: 3,9 BLK 9 G9: 3,9,6 # reduction candidate for 3,9 G9: 3,9 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 G9: 6 => CTR * 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....895.8.195...75938.612 * PAIR H7: 3,9 ROW 7 C7: 3,9,4 # reduction candidate for 3,9 C7: 3,9 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 C7: 4 => CTR * 167932548.25648.....8751.26..65.928.8.24...5.591823467.14...895.83195.74759.84.1. * PAIR H7: 3,9 COL H H2: 3,9,7 # reduction candidate for 3,9 H2: 7 => CTR * 167932548.25648.7...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612 H2: 3,9 # 17 pairs * PAIR H8: 3,7 BLK 9 G8: 3,7,6 # reduction candidate for 3,7 G8: 3,7 => CTR * 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.568.195..275.28.614 G8: 6 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 * PAIR H8: 3,7 COL H H2: 3,7,9 # reduction candidate for 3,7 H2: 9 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 H2: 3,7 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060604-absurd-base-pr-000.dot * REASONING * DIS # A3: 4 => CTR => A3: 3,9 * DIS # G2: 3,9 => CTR => G2: 1,7 * DIS # I2: 3,9 => CTR => I2: 1 * DIS # B4: 3,4 => CTR => B4: 7 * DIS # G2: 3,9 => CTR => G2: 1,7 * DIS # I2: 3,9 => CTR => I2: 1 * DIS # A3: 4 => CTR => A3: 3,9 * DIS # G5: 3,9 => CTR => G5: 1 * PRF # G9: 3,9 => SOL * DIS # G9: 6 => CTR => G9: 3,9 * DIS # B4: 3,4 => CTR => B4: 7 * DIS # B4: 4 => CTR => B4: 3,7 * DIS # E5: 1,7 => CTR => E5: 6 * DIS # E5: 1 => CTR => E5: 6,7 * DIS # F7: 6,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # I5: 1,3 => CTR => I5: 9 * DIS # I2: 9 => CTR => I2: 1,3 * PRF # C9: 3,4 => SOL * DIS # F7: 6,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # E5: 1 => CTR => E5: 6,7 * DIS # F7: 7 => CTR => F7: 4,6 * PRF # G9: 3,9 => SOL * DIS # G9: 6 => CTR => G9: 3,9 * PRF # C7: 3,9 => SOL * DIS # C7: 4 => CTR => C7: 3,9 * DIS # H2: 7 => CTR => H2: 3,9 * DIS # G8: 3,7 => CTR => G8: 6 * PRF # G8: 6 => SOL * PRF # H2: 9 => SOL * CNT 31 HDP CHAINS / 58 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A7,A8,B3,B5,C8,D7,D9,E4,E7,F5,F9,G3,H7,H8,I4,I8,I9) * 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1. * PAIR A2: 3,9 BLK 1 A3: 3,9,4 # reduction candidate for 3,9 A3: 4 => CTR * 167932548925648...438751926346579281872416359591823467.1..6789568.195732759.8..1. * PAIR A2: 3,9 ROW 2 G2: 3,9,1,7 # reduction candidate for 3,9 G2: 3,9 => CTR * 167932548.25648.71.48751.264.65192838324..159591823467.1....895.8.19573.75938.612 H2: 3,9,7 # reduction candidate for 3,9 H2: 3,9 # 17 pairs I2: 3,9,1 # reduction candidate for 3,9 I2: 3,9 => CTR * 167932548.2564817..48751.264.65.928.8.24...5.591823467.1....895.8.19573.75938.612 * RESTART * PAIR RESTART * PAIR G3: 3,9 COL G G9: 3,9,6 # reduction candidate for 3,9 G9: 3,9 => SOLVED * 167932548325648791948751326476519283832467159591823467619274835283195674754386912 * DURATION: 0:00:05.638925 START: 23:38:24.516019 END: 23:38:30.154944 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060604-absurd-base-pr-001.dot * REASONING * DIS # A3: 4 => CTR => A3: 3,9 * DIS A3: 3,9 # G2: 3,9 => CTR => G2: 1,7 * DIS A3: 3,9 + G2: 1,7 # I2: 3,9 => CTR => I2: 1 * PRF A3: 3,9 + G2: 1,7 + I2: 1 # G9: 3,9 => SOL * STA A3: 3,9 + G2: 1,7 + I2: 1 + G9: 3,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060604, absurd
Solution
position: 167932548325648791948751326476519283832467159591823467619274835283195674754386912 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 # A3: 3,9 => UNS * DIS # A3: 4 => CTR => A3: 3,9 * DIS # G2: 3,9 => CTR => G2: 1,7 * INC # G2: 1,7 => UNS * INC # H2: 3,9 => UNS * DIS # I2: 3,9 => CTR => I2: 1 * INC # I2: 1 => UNS * INC # A3: 3,4 => UNS * INC # A3: 9 => UNS * DIS # B4: 3,4 => CTR => B4: 7 * INC # B4: 7 => UNS * DIS # G2: 3,9 => CTR => G2: 1,7 * INC # G2: 1,7 => UNS * INC # H2: 3,9 => UNS * DIS # I2: 3,9 => CTR => I2: 1 * INC # I2: 1 => UNS * INC # A3: 3,9 => UNS * DIS # A3: 4 => CTR => A3: 3,9 * DIS # G5: 3,9 => CTR => G5: 1 * INC # G5: 1 => UNS * PRF # G9: 3,9 => SOL * DIS # G9: 6 => CTR => G9: 3,9 * DIS # B4: 3,4 => CTR => B4: 7 * INC # B4: 7 => UNS * INC # A3: 3,4 => UNS * INC # A3: 9 => UNS * INC # B4: 3,7 => UNS * DIS # B4: 4 => CTR => B4: 3,7 * DIS # E5: 1,7 => CTR => E5: 6 * INC # E5: 6 => UNS * INC # E5: 6,7 => UNS * DIS # E5: 1 => CTR => E5: 6,7 * DIS # F7: 6,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * INC # G5: 1,3 => UNS * DIS # I5: 1,3 => CTR => I5: 9 * INC # I5: 9 => UNS * INC # I2: 1,3 => UNS * DIS # I2: 9 => CTR => I2: 1,3 * INC # C7: 3,4 => UNS * PRF # C9: 3,4 => SOL * INC # C9: 9 => UNS * DIS # F7: 6,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * INC # E5: 6,7 => UNS * DIS # E5: 1 => CTR => E5: 6,7 * INC # F7: 4,6 => UNS * DIS # F7: 7 => CTR => F7: 4,6 * PRF # G9: 3,9 => SOL * DIS # G9: 6 => CTR => G9: 3,9 * PRF # C7: 3,9 => SOL * DIS # C7: 4 => CTR => C7: 3,9 * INC # H2: 3,9 => UNS * DIS # H2: 7 => CTR => H2: 3,9 * DIS # G8: 3,7 => CTR => G8: 6 * PRF # G8: 6 => SOL * INC # H2: 3,7 => UNS * PRF # H2: 9 => SOL * CNT 58 HDP CHAINS / 58 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 3,9 => UNS * DIS # A3: 4 => CTR => A3: 3,9 * DIS A3: 3,9 # G2: 3,9 => CTR => G2: 1,7 * INC A3: 3,9 + G2: 1,7 # H2: 3,9 => UNS * DIS A3: 3,9 + G2: 1,7 # I2: 3,9 => CTR => I2: 1 * PRF A3: 3,9 + G2: 1,7 + I2: 1 # G9: 3,9 => SOL * STA A3: 3,9 + G2: 1,7 + I2: 1 + G9: 3,9 * CNT 6 HDP CHAINS / 6 HYP OPENED