Analysis of zz-www.sudokuoftheday.co.uk-20190426-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: .....92.4...5..3..3..8...6.641....8..7......128.........218.6..5.7.9...2.....5.9. initial
Autosolve
position: .....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 8 => CTR => A1: 1,7 * DIS # H1: 1,7 => CTR => H1: 5 * PRF # E5: 3,5 => SOL * DIS # E6: 3,5 => CTR => E6: 1,4,7 * DIS # H6: 3,5 => CTR => H6: 4,7 * PRF # H6: 4,7 => SOL * DIS # H6: 4,5 => CTR => H6: 3,7 * DIS # D9: 3,7 => CTR => D9: 2,4,6 * DIS # E9: 3,7 => CTR => E9: 2,4,6 * DIS # I7: 3,7 => CTR => I7: 5 * PRF # F6: 3,7 => SOL * DIS # I7: 3,7 => CTR => I7: 5 * DIS # D9: 3,7 => CTR => D9: 2,4,6 * DIS # E9: 3,7 => CTR => E9: 2,4,6 * DIS # I4: 5,9 => CTR => I4: 3,7 * CNT 15 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 8 => CTR => A1: 1,7 * DIS A1: 1,7 # H1: 1,7 => CTR => H1: 5 * DIS A1: 1,7 + H1: 5 # G3: 9 => CTR => G3: 1,7 * PRF A1: 1,7 + H1: 5 + G3: 1,7 # E5: 3,5 => SOL * STA A1: 1,7 + H1: 5 + G3: 1,7 + E5: 3,5 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....92.4...5..3..3..8...6.641....8..7......128.........218.6..5.7.9...2.....5.9. | initial |
| .....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9. | autosolve |
| 168739254729564318354821769641972583973658421285413976492187635517396842836245197 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 6,8 A2: 1,7 B2: 2,6 H2: 1,7 C5: 3,5 C6: 3,5 G5: 4,5 A9: 1,8 C9: 6,8 F7: 3,7 H8: 1,4 G9: 1,4 I9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E6,F6: 1.. / E6 = 1 => 19 pairs (_) / F6 = 1 => 16 pairs (_) H8,G9: 1.. / H8 = 1 => 0 pairs (X) / G9 = 1 => 18 pairs (_) A2,H2: 1.. / A2 = 1 => 18 pairs (_) / H2 = 1 => 16 pairs (_) B8,H8: 1.. / B8 = 1 => 18 pairs (_) / H8 = 1 => 0 pairs (X) F3,F6: 1.. / F3 = 1 => 19 pairs (_) / F6 = 1 => 16 pairs (_) G3,G9: 1.. / G3 = 1 => 0 pairs (X) / G9 = 1 => 18 pairs (_) B2,B3: 2.. / B2 = 2 => 16 pairs (_) / B3 = 2 => 0 pairs (X) D9,E9: 2.. / D9 = 2 => 13 pairs (_) / E9 = 2 => 19 pairs (_) D4,D9: 2.. / D4 = 2 => 19 pairs (_) / D9 = 2 => 13 pairs (_) D1,E1: 3.. / D1 = 3 => 17 pairs (_) / E1 = 3 => 19 pairs (_) C5,C6: 3.. / C5 = 3 => 12 pairs (_) / C6 = 3 => 0 pairs (X) I4,H6: 3.. / I4 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) B8,B9: 3.. / B8 = 3 => 0 pairs (X) / B9 = 3 => 17 pairs (_) H6,H7: 3.. / H6 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) E2,F2: 4.. / E2 = 4 => 14 pairs (_) / F2 = 4 => 16 pairs (_) H8,G9: 4.. / H8 = 4 => 18 pairs (_) / G9 = 4 => 0 pairs (X) H6,H8: 4.. / H6 = 4 => 0 pairs (X) / H8 = 4 => 18 pairs (_) B1,B3: 5.. / B1 = 5 => 0 pairs (X) / B3 = 5 => 18 pairs (_) C5,C6: 5.. / C5 = 5 => 0 pairs (X) / C6 = 5 => 12 pairs (_) H7,I7: 5.. / H7 = 5 => 0 pairs (X) / I7 = 5 => 15 pairs (_) B1,H1: 5.. / B1 = 5 => 0 pairs (X) / H1 = 5 => 18 pairs (_) D5,E5: 6.. / D5 = 6 => 15 pairs (_) / E5 = 6 => 15 pairs (_) C1,C9: 6.. / C1 = 6 => 0 pairs (X) / C9 = 6 => 15 pairs (_) F2,F8: 6.. / F2 = 6 => 15 pairs (_) / F8 = 6 => 16 pairs (_) A1,A2: 7.. / A1 = 7 => 18 pairs (_) / A2 = 7 => 16 pairs (_) A2,H2: 7.. / A2 = 7 => 16 pairs (_) / H2 = 7 => 18 pairs (_) A1,C1: 8.. / A1 = 8 => 0 pairs (X) / C1 = 8 => 15 pairs (_) A9,C9: 8.. / A9 = 8 => 15 pairs (_) / C9 = 8 => 0 pairs (X) A1,A9: 8.. / A1 = 8 => 0 pairs (X) / A9 = 8 => 15 pairs (_) C1,C9: 8.. / C1 = 8 => 15 pairs (_) / C9 = 8 => 0 pairs (X) G3,I3: 9.. / G3 = 9 => 0 pairs (X) / I3 = 9 => 13 pairs (_) D4,D6: 9.. / D4 = 9 => 14 pairs (_) / D6 = 9 => 13 pairs (_) D6,G6: 9.. / D6 = 9 => 13 pairs (_) / G6 = 9 => 14 pairs (_) I3,I4: 9.. / I3 = 9 => 13 pairs (_) / I4 = 9 => 0 pairs (X) * DURATION: 0:00:35.730048 START: 05:36:59.113232 END: 05:37:34.843280 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,C1,C5,C6,C9,F7,G5,G9,H2,H8,I9) * .....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9. * PAIR A2: 1,7 BLK 1 A1: 1,7,8 # reduction candidate for 1,7 A1: 8 => CTR * 8.6..92.47295..3183.48...6.641....8.97...8.2128......649218.6..517.9.8.2.....5.9. A1: 1,7 # 15 pairs * PAIR B2: 2,6 ROW 2 E2: 2,6,4 # reduction candidate for 2,6 E2: 2,6 # 16 pairs F2: 2,6,4 # reduction candidate for 2,6 F2: 2,6 # 14 pairs * PAIR H2: 1,7 BLK 3 H1: 1,7,5 # reduction candidate for 1,7 H1: 1,7 => CTR * .586392.4.695..3.8324871.6.641....8.973468521285.13..64921876..517396842836..5197 H1: 5 # 18 pairs G3: 1,7,5,9 # reduction candidate for 1,7 G3: 1,7 # 19 pairs * PAIR C5: 3,5 ROW 5 E5: 3,5,4,6 # reduction candidate for 3,5 E5: 3,5 => SOLVED * 168739254729564318354821769641972583973658421285413976492187635517396842836245197 E5: 4,6 # 14 pairs * PAIR C6: 3,5 ROW 6 E6: 3,5,1,4,7 # reduction candidate for 3,5 E6: 3,5 => CTR * .....92.4..95..3.83.48...6.641....8397...8.2128...1..64921836..537.9.812.....5497 E6: 1,4,7 # 13 pairs H6: 3,5,4,7 # reduction candidate for 3,5 H6: 3,5 => CTR * .586392.4.695..3.8324871.6.641....8.973468521285.13..64921876..517396842836..5197 H6: 4,7 => SOLVED * 168739254729564318354821769641972583973658421285413976492187635517396842836245197 * PAIR G5: 4,5 BLK 6 G6: 4,5,7,9 # reduction candidate for 4,5 G6: 4,5 # 23 pairs H6: 4,5,3,7 # reduction candidate for 4,5 H6: 4,5 => CTR * ..8..92.4..95.43.83.48.1.69641..2.8397...8.2128..13.56492187635517.9.842836245197 H6: 3,7 # 19 pairs * PAIR G5: 4,5 ROW 5 E5: 4,5,3,6 # reduction candidate for 4,5 E5: 4,5 # 14 pairs E5: 3,6 # 14 pairs * PAIR A9: 1,8 COL A A1: 1,8,7 # reduction candidate for 1,8 A1: 7 # 18 pairs A1: 1,8 # 16 pairs * PAIR F7: 3,7 BLK 8 D9: 3,7,2,4,6 # reduction candidate for 3,7 D9: 3,7 => CTR * ...7.92.4..95..3.83.48..1696412..98.97...85212859.174649218.6355.7.9.812....25497 D9: 2,4,6 # 13 pairs E9: 3,7,2,4,6 # reduction candidate for 3,7 E9: 3,7 => CTR * ....192541.95..3783548..169641.52.83973..8521285..1.464921876355.7.9.812...2.5497 E9: 2,4,6 # 13 pairs * PAIR F7: 3,7 ROW 7 H7: 3,7,5 # reduction candidate for 3,7 H7: 3,7 # 15 pairs I7: 3,7,5 # reduction candidate for 3,7 I7: 3,7 => CTR * .58.392.4.695423.8324871.6.641253.8.973..8.21285.14.36492187653517396842836425197 I7: 5 # 15 pairs * PAIR F7: 3,7 COL F F4: 3,7,2 # reduction candidate for 3,7 F4: 3,7 # 19 pairs F6: 3,7,1,4 # reduction candidate for 3,7 F6: 3,7 => SOLVED * 168739254729564318354821769641972583973658421285413976492187635517396842836245197 F6: 1,4 # 14 pairs * PAIR I9: 3,7 BLK 9 H7: 3,7,5 # reduction candidate for 3,7 H7: 3,7 # 15 pairs I7: 3,7,5 # reduction candidate for 3,7 I7: 3,7 => CTR * .58.392.4.695423.8324871.6.641253.8.973..8.21285.14.36492187653517396842836425197 I7: 5 # 15 pairs * PAIR I9: 3,7 ROW 9 D9: 3,7,2,4,6 # reduction candidate for 3,7 D9: 3,7 => CTR * ...7.92.4..95..3.83.48..1696412..98.97...85212859.174649218.6355.7.9.812....25497 D9: 2,4,6 # 13 pairs E9: 3,7,2,4,6 # reduction candidate for 3,7 E9: 3,7 => CTR * ....192541.95..3783548..169641.52.83973..8521285..1.464921876355.7.9.812...2.5497 E9: 2,4,6 # 13 pairs * PAIR I9: 3,7 COL I I4: 3,7,5,9 # reduction candidate for 3,7 I4: 5,9 => CTR * .58..92.4.695423.8324871.6.6412.3.8.973..8.21285.14.36492187653517.96842836425197 I4: 3,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190426-absurd-base-pr-000.dot * REASONING * DIS # A1: 8 => CTR => A1: 1,7 * DIS # H1: 1,7 => CTR => H1: 5 * PRF # E5: 3,5 => SOL * DIS # E6: 3,5 => CTR => E6: 1,4,7 * DIS # H6: 3,5 => CTR => H6: 4,7 * PRF # H6: 4,7 => SOL * DIS # H6: 4,5 => CTR => H6: 3,7 * DIS # D9: 3,7 => CTR => D9: 2,4,6 * DIS # E9: 3,7 => CTR => E9: 2,4,6 * DIS # I7: 3,7 => CTR => I7: 5 * PRF # F6: 3,7 => SOL * DIS # I7: 3,7 => CTR => I7: 5 * DIS # D9: 3,7 => CTR => D9: 2,4,6 * DIS # E9: 3,7 => CTR => E9: 2,4,6 * DIS # I4: 5,9 => CTR => I4: 3,7 * CNT 15 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,C1,C5,C6,C9,F7,G5,G9,H2,H8,I9) * .....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9. * PAIR A2: 1,7 BLK 1 A1: 1,7,8 # reduction candidate for 1,7 A1: 8 => CTR * 8.6..92.47295..3183.48...6.641....8.97...8.2128......649218.6..517.9.8.2.....5.9. * PAIR B2: 2,6 ROW 2 E2: 2,6,4 # reduction candidate for 2,6 E2: 2,6 # 17 pairs F2: 2,6,4 # reduction candidate for 2,6 F2: 2,6 # 16 pairs * PAIR H2: 1,7 BLK 3 H1: 1,7,5 # reduction candidate for 1,7 H1: 1,7 => CTR * .586392.4.695243.83248...6.641..2.8397346852128......649218.6..517396842836.45197 G3: 1,7,9 # reduction candidate for 1,7 G3: 1,7 # 18 pairs * RESTART * PAIR H2: 1,7 BLK 3 G3: 1,7,9 # reduction candidate for 1,7 G3: 9 => CTR * .68..9254.295..3183548..967641....8997...8.2128.9...364921836755.7.9.8.28.6..5.9. * PAIR C5: 3,5 ROW 5 E5: 3,5,4,6 # reduction candidate for 3,5 E5: 3,5 => SOLVED * 168739254729564318354821769641972583973658421285413976492187635517396842836245197 * DURATION: 0:00:06.639121 START: 05:37:58.461592 END: 05:38:05.100713 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190426-absurd-base-pr-001.dot * REASONING * DIS # A1: 8 => CTR => A1: 1,7 * DIS A1: 1,7 # H1: 1,7 => CTR => H1: 5 * DIS A1: 1,7 + H1: 5 # G3: 9 => CTR => G3: 1,7 * PRF A1: 1,7 + H1: 5 + G3: 1,7 # E5: 3,5 => SOL * STA A1: 1,7 + H1: 5 + G3: 1,7 + E5: 3,5 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190426, absurd
Solution
position: 168739254729564318354821769641972583973658421285413976492187635517396842836245197 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 # A1: 1,7 => UNS * DIS # A1: 8 => CTR => A1: 1,7 * INC # E2: 2,6 => UNS * INC # F2: 2,6 => UNS * DIS # H1: 1,7 => CTR => H1: 5 * INC # H1: 5 => UNS * INC # G3: 1,7 => UNS * PRF # E5: 3,5 => SOL * INC # E5: 4,6 => UNS * DIS # E6: 3,5 => CTR => E6: 1,4,7 * INC # E6: 1,4,7 => UNS * DIS # H6: 3,5 => CTR => H6: 4,7 * PRF # H6: 4,7 => SOL * INC # G6: 4,5 => UNS * DIS # H6: 4,5 => CTR => H6: 3,7 * INC # H6: 3,7 => UNS * INC # E5: 4,5 => UNS * INC # E5: 3,6 => UNS * INC # A1: 1,8 => UNS * INC # A1: 7 => UNS * DIS # D9: 3,7 => CTR => D9: 2,4,6 * INC # D9: 2,4,6 => UNS * DIS # E9: 3,7 => CTR => E9: 2,4,6 * INC # E9: 2,4,6 => UNS * INC # H7: 3,7 => UNS * DIS # I7: 3,7 => CTR => I7: 5 * INC # I7: 5 => UNS * INC # F4: 3,7 => UNS * PRF # F6: 3,7 => SOL * INC # F6: 1,4 => UNS * INC # H7: 3,7 => UNS * DIS # I7: 3,7 => CTR => I7: 5 * INC # I7: 5 => UNS * DIS # D9: 3,7 => CTR => D9: 2,4,6 * INC # D9: 2,4,6 => UNS * DIS # E9: 3,7 => CTR => E9: 2,4,6 * INC # E9: 2,4,6 => UNS * INC # I4: 3,7 => UNS * DIS # I4: 5,9 => CTR => I4: 3,7 * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 1,7 => UNS * DIS # A1: 8 => CTR => A1: 1,7 * INC A1: 1,7 # E2: 2,6 => UNS * INC A1: 1,7 # F2: 2,6 => UNS * DIS A1: 1,7 # H1: 1,7 => CTR => H1: 5 * INC A1: 1,7 + H1: 5 # G3: 1,7 => UNS * INC A1: 1,7 + H1: 5 # G3: 1,7 => UNS * DIS A1: 1,7 + H1: 5 # G3: 9 => CTR => G3: 1,7 * PRF A1: 1,7 + H1: 5 + G3: 1,7 # E5: 3,5 => SOL * STA A1: 1,7 + H1: 5 + G3: 1,7 + E5: 3,5 * CNT 9 HDP CHAINS / 9 HYP OPENED