Analysis of zz-www.sudokuoftheday.co.uk-20060906-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: ............534...658.1.........8.61....75.923......4.5..4.......2..67.9.6.2..... initial
Autosolve
position: ...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,9 => CTR => A1: 1,4,7 * DIS # B1: 2,9 => CTR => B1: 1,3,4,7 * DIS # G3: 2,9 => CTR => G3: 4 * DIS # I7: 3 => CTR => I7: 6,8 * DIS # H7: 2,3 => CTR => H7: 1,8 * DIS # I9: 8 => CTR => I9: 3,4 * PRF # C6: 6,9 => SOL * DIS # C6: 5 => CTR => C6: 6,9 * DIS # B8: 3 => CTR => B8: 4,8 * DIS # E9: 5 => CTR => E9: 8,9 * DIS # H8: 5,8 => CTR => H8: 3 * CNT 11 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,9 => CTR => A1: 1,4,7 * DIS A1: 1,4,7 # B1: 2,9 => CTR => B1: 1,3,4,7 * DIS A1: 1,4,7 + B1: 1,3,4,7 # G1: 1 => CTR => G1: 2,9 * DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 # G3: 2,9 => CTR => G3: 4 * DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 # B7: 8,9 => CTR => B7: 1,3,7 * PRF A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 # C6: 6,9 => SOL * STA A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 + C6: 6,9 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ............534...658.1.........8.61....75.923......4.5..4.......2..67.9.6.2..... | initial |
| ...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2..... | autosolve |
| 134862975297534618658719423725948361416375892389621547571493286842156739963287154 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) F1: 2,9 F3: 2,9 I2: 6,8 H3: 2,3 I3: 3,4 B6: 8,9 D4: 3,9 D5: 3,6 D6: 6,9 G4: 3,5 G5: 3,8 G6: 5,8 A8: 4,8 E7: 8,9 F7: 3,7 E8: 5,8 F9: 3,7 G9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 2.. / F1 = 2 => 19 pairs (_) / F3 = 2 => 0 pairs (X) A4,B4: 2.. / A4 = 2 => 19 pairs (_) / B4 = 2 => 19 pairs (_) G7,H7: 2.. / G7 = 2 => 20 pairs (_) / H7 = 2 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 15 pairs (_) / C1 = 3 => 0 pairs (X) H3,I3: 3.. / H3 = 3 => 0 pairs (X) / I3 = 3 => 15 pairs (_) D4,D5: 3.. / D4 = 3 => 0 pairs (X) / D5 = 3 => 0 pairs (_) G4,G5: 3.. / G4 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) F7,F9: 3.. / F7 = 3 => 18 pairs (_) / F9 = 3 => 17 pairs (_) D4,G4: 3.. / D4 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) D5,G5: 3.. / D5 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) B8,H8: 3.. / B8 = 3 => 0 pairs (X) / H8 = 3 => 14 pairs (_) G3,I3: 4.. / G3 = 4 => 15 pairs (_) / I3 = 4 => 0 pairs (X) A8,B8: 4.. / A8 = 4 => 21 pairs (_) / B8 = 4 => 14 pairs (_) G9,I9: 4.. / G9 = 4 => 0 pairs (X) / I9 = 4 => 15 pairs (_) C1,C5: 4.. / C1 = 4 => 19 pairs (_) / C5 = 4 => 0 pairs (X) G3,G9: 4.. / G3 = 4 => 15 pairs (_) / G9 = 4 => 0 pairs (X) I3,I9: 4.. / I3 = 4 => 0 pairs (X) / I9 = 4 => 15 pairs (_) C4,C6: 5.. / C4 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) G4,G6: 5.. / G4 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) E8,E9: 5.. / E8 = 5 => 19 pairs (_) / E9 = 5 => 0 pairs (X) H8,H9: 5.. / H8 = 5 => 0 pairs (X) / H9 = 5 => 19 pairs (_) C4,G4: 5.. / C4 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) C6,G6: 5.. / C6 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) E8,H8: 5.. / E8 = 5 => 19 pairs (_) / H8 = 5 => 0 pairs (X) E9,H9: 5.. / E9 = 5 => 0 pairs (X) / H9 = 5 => 19 pairs (_) G2,I2: 6.. / G2 = 6 => 19 pairs (_) / I2 = 6 => 0 pairs (X) C5,C6: 6.. / C5 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) D5,D6: 6.. / D5 = 6 => 0 pairs (X) / D6 = 6 => 0 pairs (_) G7,I7: 6.. / G7 = 6 => 0 pairs (X) / I7 = 6 => 19 pairs (_) C5,D5: 6.. / C5 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) C6,D6: 6.. / C6 = 6 => 0 pairs (X) / D6 = 6 => 0 pairs (_) G2,G7: 6.. / G2 = 6 => 19 pairs (_) / G7 = 6 => 0 pairs (X) I2,I7: 6.. / I2 = 6 => 0 pairs (X) / I7 = 6 => 19 pairs (_) H1,H2: 7.. / H1 = 7 => 18 pairs (_) / H2 = 7 => 22 pairs (_) F7,F9: 7.. / F7 = 7 => 17 pairs (_) / F9 = 7 => 18 pairs (_) H2,I2: 8.. / H2 = 8 => 0 pairs (X) / I2 = 8 => 19 pairs (_) G5,G6: 8.. / G5 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) B6,G6: 8.. / B6 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) F1,F3: 9.. / F1 = 9 => 0 pairs (X) / F3 = 9 => 19 pairs (_) D4,D6: 9.. / D4 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) E7,E9: 9.. / E7 = 9 => 18 pairs (_) / E9 = 9 => 18 pairs (_) F3,G3: 9.. / F3 = 9 => 19 pairs (_) / G3 = 9 => 0 pairs (X) * DURATION: 0:00:57.396888 START: 02:24:03.955667 END: 02:25:01.352555 2019-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B6,D4,D5,D6,E7,E8,F1,F3,F7,F9,G4,G5,G6,G9,H3,I2,I3) * ...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2..... * PAIR F1: 2,9 ROW 1 A1: 2,9,1,4,7 # reduction candidate for 2,9 A1: 2,9 => CTR * .4386.175...534...65871..34....48.61..46753923.6921.475..4......321.67.9.6.2..4.. A1: 1,4,7 # 18 pairs B1: 2,9,1,3,4,7 # reduction candidate for 2,9 B1: 2,9 => CTR * ..386...5...534...65871........48.61..46753923.6921.475..4.......21.67.9.6.2..... B1: 1,3,4,7 # 18 pairs G1: 2,9,1 # reduction candidate for 2,9 G1: 2,9 # 21 pairs * PAIR F3: 2,9 ROW 3 G3: 2,9,4 # reduction candidate for 2,9 G3: 2,9 => CTR * ..386...5...534...65871..34....48.61..46753923.6921.475..4......321.67.9.6.2..4.. G3: 4 # 15 pairs * PAIR I2: 6,8 COL I I7: 6,8,3 # reduction candidate for 6,8 I7: 3 => CTR * ..386...5...534.8665871..34....48.61..46753923.6921.475..4..623.321.67.9.6.2.3..8 I7: 6,8 # 20 pairs * PAIR H3: 2,3 COL H H7: 2,3,1,8 # reduction candidate for 2,3 H7: 2,3 => CTR * ..386...5...534...65871........48.61..46753923.6921.475..4......321.67.9.6.2..... H7: 1,8 # 21 pairs * PAIR I3: 3,4 COL I I9: 3,4,8 # reduction candidate for 3,4 I9: 8 => CTR * ..386...5...534.8665871..34....48.61..46753923.6921.475..4....3.321.67.9.6.2.34.8 I9: 3,4 # 20 pairs * PAIR B6: 8,9 COL B B7: 8,9,1,3,7 # reduction candidate for 8,9 B7: 8,9 # 23 pairs B7: 1,3,7 # 18 pairs * PAIR D6: 6,9 ROW 6 C6: 6,9,5 # reduction candidate for 6,9 C6: 6,9 => SOLVED * 134862975297534618658719423725948361416375892389621547571493286842156739963287154 C6: 5 => CTR * ...86...5...534...65871........48.61..6375892385.21.475..4.......21.67.9.6.2..... * PAIR A8: 4,8 BLK 7 B8: 4,8,3 # reduction candidate for 4,8 B8: 3 => CTR * ..386...5...534...65871........48.61..46753923.6921.475..4.....4321.67.9.6.2..... B8: 4,8 # 14 pairs * PAIR A8: 4,8 COL A A5: 4,8,1 # reduction candidate for 4,8 A5: 4,8 # 21 pairs A5: 1 # 21 pairs * PAIR E7: 8,9 BLK 8 E9: 8,9,5 # reduction candidate for 8,9 E9: 5 => CTR * ..386...5...534...65871........48.61..46753923.6921.475..49....432186759.6.25.... E9: 8,9 # 19 pairs * PAIR E7: 8,9 ROW 7 B7: 8,9,1,3,7 # reduction candidate for 8,9 B7: 8,9 # 23 pairs B7: 1,3,7 # 18 pairs * PAIR F7: 3,7 ROW 7 B7: 3,7,1,8,9 # reduction candidate for 3,7 B7: 3,7 # 22 pairs C7: 3,7,1,9 # reduction candidate for 3,7 C7: 3,7 # 21 pairs * PAIR E8: 5,8 BLK 8 E9: 5,8,9 # reduction candidate for 5,8 E9: 9 # 18 pairs E9: 5,8 # 18 pairs * PAIR E8: 5,8 ROW 8 H8: 5,8,3 # reduction candidate for 5,8 H8: 5,8 => CTR * ..386...5...534...65871........48.61..46753923.6921.475..4......321.67.9.6.2..... H8: 3 # 14 pairs * PAIR F9: 3,7 ROW 9 C9: 3,7,1,9 # reduction candidate for 3,7 C9: 3,7 # 20 pairs C9: 1,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060906-absurd-base-pr-000.dot * REASONING * DIS # A1: 2,9 => CTR => A1: 1,4,7 * DIS # B1: 2,9 => CTR => B1: 1,3,4,7 * DIS # G3: 2,9 => CTR => G3: 4 * DIS # I7: 3 => CTR => I7: 6,8 * DIS # H7: 2,3 => CTR => H7: 1,8 * DIS # I9: 8 => CTR => I9: 3,4 * PRF # C6: 6,9 => SOL * DIS # C6: 5 => CTR => C6: 6,9 * DIS # B8: 3 => CTR => B8: 4,8 * DIS # E9: 5 => CTR => E9: 8,9 * DIS # H8: 5,8 => CTR => H8: 3 * CNT 11 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B6,D4,D5,D6,E7,E8,F1,F3,F7,F9,G4,G5,G6,G9,H3,I2,I3) * ...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2..... * PAIR F1: 2,9 ROW 1 A1: 2,9,1,4,7 # reduction candidate for 2,9 A1: 2,9 => CTR * .4386.175...534...65871..34....48.61..46753923.6921.475..4......321.67.9.6.2..4.. B1: 2,9,1,3,4,7 # reduction candidate for 2,9 B1: 2,9 => CTR * ..386...5...534...65871........48.61..46753923.6921.475..4.......21.67.9.6.2..... G1: 2,9,1 # reduction candidate for 2,9 G1: 2,9 # 21 pairs * RESTART * PAIR F1: 2,9 ROW 1 G1: 2,9,1 # reduction candidate for 2,9 G1: 1 => CTR * ..3869125...534.78658712934....48.61..46753923.6921.475..4......321.67.9.6.2..4.. * PAIR RESTART * PAIR F3: 2,9 ROW 3 G3: 2,9,4 # reduction candidate for 2,9 G3: 2,9 => CTR * ..386...5...534...65871..34....48.61..46753923.6921.475..4...2..321.67.9.6.2..4.. * PAIR RESTART * PAIR B6: 8,9 COL B B7: 8,9,1,3,7 # reduction candidate for 8,9 B7: 8,9 => CTR * ..38629.5...5346.8658719423....48.61..46753923.6921.475.14.7236.321.67.9.6.2.31.4 * PAIR RESTART * PAIR D6: 6,9 ROW 6 C6: 6,9,5 # reduction candidate for 6,9 C6: 6,9 => SOLVED * 134862975297534618658719423725948361416375892389621547571493286842156739963287154 * DURATION: 0:00:09.786917 START: 02:25:25.173634 END: 02:25:34.960551 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060906-absurd-base-pr-001.dot * REASONING * DIS # A1: 2,9 => CTR => A1: 1,4,7 * DIS A1: 1,4,7 # B1: 2,9 => CTR => B1: 1,3,4,7 * DIS A1: 1,4,7 + B1: 1,3,4,7 # G1: 1 => CTR => G1: 2,9 * DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 # G3: 2,9 => CTR => G3: 4 * DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 # B7: 8,9 => CTR => B7: 1,3,7 * PRF A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 # C6: 6,9 => SOL * STA A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 + C6: 6,9 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060906, absurd
Solution
position: 134862975297534618658719423725948361416375892389621547571493286842156739963287154 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:
* DIS # A1: 2,9 => CTR => A1: 1,4,7 * INC # A1: 1,4,7 => UNS * DIS # B1: 2,9 => CTR => B1: 1,3,4,7 * INC # B1: 1,3,4,7 => UNS * INC # G1: 2,9 => UNS * DIS # G3: 2,9 => CTR => G3: 4 * INC # G3: 4 => UNS * INC # I7: 6,8 => UNS * DIS # I7: 3 => CTR => I7: 6,8 * DIS # H7: 2,3 => CTR => H7: 1,8 * INC # H7: 1,8 => UNS * INC # I9: 3,4 => UNS * DIS # I9: 8 => CTR => I9: 3,4 * INC # B7: 8,9 => UNS * INC # B7: 1,3,7 => UNS * PRF # C6: 6,9 => SOL * DIS # C6: 5 => CTR => C6: 6,9 * INC # B8: 4,8 => UNS * DIS # B8: 3 => CTR => B8: 4,8 * INC # A5: 4,8 => UNS * INC # A5: 1 => UNS * INC # E9: 8,9 => UNS * DIS # E9: 5 => CTR => E9: 8,9 * INC # B7: 8,9 => UNS * INC # B7: 1,3,7 => UNS * INC # B7: 3,7 => UNS * INC # C7: 3,7 => UNS * INC # E9: 5,8 => UNS * INC # E9: 9 => UNS * DIS # H8: 5,8 => CTR => H8: 3 * INC # H8: 3 => UNS * INC # C9: 3,7 => UNS * INC # C9: 1,9 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,9 => CTR => A1: 1,4,7 * DIS A1: 1,4,7 # B1: 2,9 => CTR => B1: 1,3,4,7 * INC A1: 1,4,7 + B1: 1,3,4,7 # G1: 2,9 => UNS * INC A1: 1,4,7 + B1: 1,3,4,7 # G1: 2,9 => UNS * DIS A1: 1,4,7 + B1: 1,3,4,7 # G1: 1 => CTR => G1: 2,9 * DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 # G3: 2,9 => CTR => G3: 4 * DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 # B7: 8,9 => CTR => B7: 1,3,7 * PRF A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 # C6: 6,9 => SOL * STA A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 + C6: 6,9 * CNT 8 HDP CHAINS / 8 HYP OPENED