Analysis of zz-www.sudokuoftheday.co.uk-20060101-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2006
level: medium
position: ..548...1........46...2...9.92......5...1..7....3.28....3.......5.6.13.....7.3.1. initial
Autosolve
position: ..548...1....3...46..12...9.92...1..5...1..7....3.2895..32.8....5.6.13.....7.3.1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 3 => CTR => B3: 4,8 * DIS # F2: 5,9 => CTR => F2: 6,7 * DIS # F2: 5,7 => CTR => F2: 6,9 * DIS # B5: 6,8 => CTR => B5: 3 * PRF # B5: 3 => SOL * PRF # G5: 4,6 => SOL * DIS # G5: 2 => CTR => G5: 4,6 * DIS # H7: 4,6 => CTR => H7: 5 * DIS # I5: 3,6 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # E9: 4,9 => CTR => E9: 5 * DIS # A8: 4,9 => CTR => A8: 2,7,8 * PRF # C8: 4,9 => SOL * DIS # G9: 2,4 => CTR => G9: 5,6,9 * CNT 14 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 3 => CTR => B3: 4,8 * DIS B3: 4,8 # F2: 5,9 => CTR => F2: 6,7 * PRF B3: 4,8 + F2: 6,7 # G2: 2,6 => SOL * STA B3: 4,8 + F2: 6,7 + G2: 2,6 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..548...1........46...2...9.92......5...1..7....3.28....3.......5.6.13.....7.3.1. | initial |
| ..548...1....3...46..12...9.92...1..5...1..7....3.2895..32.8....5.6.13.....7.3.1. | autosolve |
| 325489761917536284684127539792865143538914672461372895173298456859641327246753918 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C3: 4,8 D2: 5,9 F3: 5,7 G3: 5,7 H3: 3,8 C5: 6,8 D4: 5,8 E4: 6,7 F4: 4,5 D5: 8,9 F5: 4,9 E6: 6,7 H4: 4,6 I4: 3,6 E8: 4,9 I7: 6,7 H8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,B7: 1.. / A7 = 1 => 18 pairs (_) / B7 = 1 => 18 pairs (_) C2,C6: 1.. / C2 = 1 => 17 pairs (_) / C6 = 1 => 18 pairs (_) G5,I5: 2.. / G5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) H1,H3: 3.. / H1 = 3 => 0 pairs (X) / H3 = 3 => 19 pairs (_) A4,B5: 3.. / A4 = 3 => 0 pairs (X) / B5 = 3 => 0 pairs (_) I4,I5: 3.. / I4 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) B3,H3: 3.. / B3 = 3 => 0 pairs (X) / H3 = 3 => 19 pairs (_) A4,I4: 3.. / A4 = 3 => 0 pairs (X) / I4 = 3 => 0 pairs (_) B5,I5: 3.. / B5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) A1,A4: 3.. / A1 = 3 => 0 pairs (*) / A4 = 3 => 0 pairs (X) B3,C3: 4.. / B3 = 4 => 20 pairs (_) / C3 = 4 => 17 pairs (_) F4,F5: 4.. / F4 = 4 => 0 pairs (X) / F5 = 4 => 0 pairs (_) H4,G5: 4.. / H4 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) F4,H4: 4.. / F4 = 4 => 0 pairs (X) / H4 = 4 => 0 pairs (_) F5,G5: 4.. / F5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) D4,F4: 5.. / D4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) E7,E9: 5.. / E7 = 5 => 0 pairs (X) / E9 = 5 => 18 pairs (_) F3,G3: 5.. / F3 = 5 => 0 pairs (X) / G3 = 5 => 17 pairs (_) E9,G9: 5.. / E9 = 5 => 18 pairs (_) / G9 = 5 => 0 pairs (X) D2,D4: 5.. / D2 = 5 => 0 pairs (*) / D4 = 5 => 0 pairs (X) H2,H7: 5.. / H2 = 5 => 0 pairs (X) / H7 = 5 => 18 pairs (_) F1,F2: 6.. / F1 = 6 => 0 pairs (X) / F2 = 6 => 18 pairs (_) E4,E6: 6.. / E4 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) E4,E6: 7.. / E4 = 7 => 18 pairs (_) / E6 = 7 => 0 pairs (*) I7,I8: 7.. / I7 = 7 => 17 pairs (_) / I8 = 7 => 0 pairs (*) F3,G3: 7.. / F3 = 7 => 17 pairs (_) / G3 = 7 => 0 pairs (X) A4,E4: 7.. / A4 = 7 => 0 pairs (*) / E4 = 7 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 19 pairs (_) / H3 = 8 => 0 pairs (X) D4,D5: 8.. / D4 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) I8,I9: 8.. / I8 = 8 => 17 pairs (_) / I9 = 8 => 18 pairs (_) A4,D4: 8.. / A4 = 8 => 0 pairs (X) / D4 = 8 => 0 pairs (_) D5,F5: 9.. / D5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) G7,G9: 9.. / G7 = 9 => 18 pairs (_) / G9 = 9 => 20 pairs (_) A1,F1: 9.. / A1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) D2,D5: 9.. / D2 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) * DURATION: 0:00:42.048708 START: 19:44:42.655300 END: 19:45:24.704008 2019-04-30 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C5,D2,D4,D5,E4,E6,E8,F3,F4,F5,G3,H3,H4,H8,I4,I7) * ..548...1....3...46..12...9.92...1..5...1..7....3.2895..32.8....5.6.13.....7.3.1. * PAIR C3: 4,8 BLK 1 B3: 4,8,3 # reduction candidate for 4,8 B3: 3 => CTR * ..548...1....3...463412..893928751465..914273...362895..32.8..7.5.6.1328...7.3.1. B3: 4,8 # 19 pairs * PAIR C3: 4,8 COL C C8: 4,8,7,9 # reduction candidate for 4,8 C8: 4,8 # 22 pairs C9: 4,8,6,9 # reduction candidate for 4,8 C9: 4,8 # 21 pairs * PAIR D2: 5,9 BLK 2 F2: 5,9,6,7 # reduction candidate for 5,9 F2: 5,9 => CTR * 9.5486..1....3...46..1275.93928751465..914273...362895..32.8.57.5.6.1328...753.1. F2: 6,7 # 18 pairs * PAIR F3: 5,7 BLK 2 F2: 5,7,6,9 # reduction candidate for 5,7 F2: 5,7 => CTR * ..5486..1...93...46..12...9.925.4163536819472...362895..32.8....5.6.13.....7.3.1. F2: 6,9 # 18 pairs * PAIR G3: 5,7 BLK 3 G2: 5,7,2,6 # reduction candidate for 5,7 G2: 5,7 # 20 pairs G2: 2,6 # 18 pairs * PAIR H3: 3,8 ROW 3 B3: 3,8,4 # reduction candidate for 3,8 B3: 4 # 20 pairs B3: 3,8 # 17 pairs * PAIR C5: 6,8 BLK 4 B5: 6,8,3 # reduction candidate for 6,8 B5: 6,8 => CTR * ..548...1....3...46..12...93928751465..914273...362895..32.8..7.5.6.1328...7.3.1. B5: 3 => SOLVED * 325489761917536284684127539792865143538914672461372895173298456859641327246753918 * PAIR C5: 6,8 COL C C9: 6,8,4,9 # reduction candidate for 6,8 C9: 6,8 # 20 pairs C9: 4,9 # 19 pairs * PAIR E6: 6,7 ROW 6 B6: 6,7,1,4 # reduction candidate for 6,7 B6: 6,7 # 20 pairs C6: 6,7,1,4 # reduction candidate for 6,7 C6: 6,7 # 20 pairs * PAIR H4: 4,6 BLK 6 G5: 4,6,2 # reduction candidate for 4,6 G5: 4,6 => SOLVED * 325489761917536284684127539792865143538914672461372895173298456859641327246753918 G5: 2 => CTR * ..548...1....3...46..12...9.92...14.5...1427....3.2895..32.8....5.6.132....7.3.1. * PAIR H4: 4,6 COL H H7: 4,6,5 # reduction candidate for 4,6 H7: 4,6 => CTR * ..548...1....3..546..125789.925.4163536819472...362895..32.8.4..5.6.132....7.3.1. H7: 5 # 18 pairs * PAIR I4: 3,6 BLK 6 I5: 3,6,2 # reduction candidate for 3,6 I5: 3,6 => CTR * ..548...1....3...46..12...9.92...14.5...1427....3.2895..32.8....5.6.132....7.3.1. I5: 2 => SOLVED * 325489761917536284684127539792865143538914672461372895173298456859641327246753918 * PAIR E8: 4,9 BLK 8 E7: 4,9,5 # reduction candidate for 4,9 E7: 4,9 # 18 pairs E9: 4,9,5 # reduction candidate for 4,9 E9: 4,9 => CTR * ..548...1....3..546..125789.925.4163536819472...362895..325894..5.6.132....7.351. E9: 5 # 18 pairs * PAIR E8: 4,9 ROW 8 A8: 4,9,2,7,8 # reduction candidate for 4,9 A8: 4,9 => CTR * 375489261219536.846..127539.92865143538914672...372895..32.8.5..576.132882.753.16 A8: 2,7,8 # 17 pairs C8: 4,9,7,8 # reduction candidate for 4,9 C8: 4,9 => SOLVED * 325489761917536284684127539792865143538914672461372895173298456859641327246753918 C8: 7,8 # 18 pairs * PAIR I7: 6,7 ROW 7 B7: 6,7,1,4 # reduction candidate for 6,7 B7: 6,7 # 20 pairs B7: 1,4 # 19 pairs * PAIR H8: 2,4 BLK 9 G9: 2,4,5,6,9 # reduction candidate for 2,4 G9: 2,4 => CTR * 3.5489.61...536.84684127539792865143538914672.463728951.324895..5.69132....75341. G9: 5,6,9 # 17 pairs * PAIR H8: 2,4 ROW 8 A8: 2,4,7,8,9 # reduction candidate for 2,4 A8: 2,4 # 21 pairs A8: 7,8,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060101-absurd-base-pr-000.dot * REASONING * DIS # B3: 3 => CTR => B3: 4,8 * DIS # F2: 5,9 => CTR => F2: 6,7 * DIS # F2: 5,7 => CTR => F2: 6,9 * DIS # B5: 6,8 => CTR => B5: 3 * PRF # B5: 3 => SOL * PRF # G5: 4,6 => SOL * DIS # G5: 2 => CTR => G5: 4,6 * DIS # H7: 4,6 => CTR => H7: 5 * DIS # I5: 3,6 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # E9: 4,9 => CTR => E9: 5 * DIS # A8: 4,9 => CTR => A8: 2,7,8 * PRF # C8: 4,9 => SOL * DIS # G9: 2,4 => CTR => G9: 5,6,9 * CNT 14 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C5,D2,D4,D5,E4,E6,E8,F3,F4,F5,G3,H3,H4,H8,I4,I7) * ..548...1....3...46..12...9.92...1..5...1..7....3.2895..32.8....5.6.13.....7.3.1. * PAIR C3: 4,8 BLK 1 B3: 4,8,3 # reduction candidate for 4,8 B3: 3 => CTR * ..548...1....3...463412..893928751465..914273...362895..32.8..7.5.6.1328...7.3.1. * PAIR C3: 4,8 COL C C8: 4,8,7,9 # reduction candidate for 4,8 C8: 4,8 # 22 pairs C9: 4,8,6,9 # reduction candidate for 4,8 C9: 4,8 # 23 pairs * PAIR D2: 5,9 BLK 2 F2: 5,9,6,7 # reduction candidate for 5,9 F2: 5,9 => CTR * ..5486.21....3.6846..127539.92...163536819472...362895..32.895.25.6.13.....753.1. * PAIR G3: 5,7 BLK 3 G2: 5,7,2,6 # reduction candidate for 5,7 G2: 2,6 => SOLVED * 325489761917536284684127539792865143538914672461372895173298456859641327246753918 * DURATION: 0:00:06.259431 START: 19:45:48.181066 END: 19:45:54.440497 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060101-absurd-base-pr-001.dot * REASONING * DIS # B3: 3 => CTR => B3: 4,8 * DIS B3: 4,8 # F2: 5,9 => CTR => F2: 6,7 * PRF B3: 4,8 + F2: 6,7 # G2: 2,6 => SOL * STA B3: 4,8 + F2: 6,7 + G2: 2,6 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2006, 20060101, absurd
Solution
position: 325489761917536284684127539792865143538914672461372895173298456859641327246753918 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 # B3: 4,8 => UNS * DIS # B3: 3 => CTR => B3: 4,8 * INC # C8: 4,8 => UNS * INC # C9: 4,8 => UNS * DIS # F2: 5,9 => CTR => F2: 6,7 * INC # F2: 6,7 => UNS * DIS # F2: 5,7 => CTR => F2: 6,9 * INC # F2: 6,9 => UNS * INC # G2: 5,7 => UNS * INC # G2: 2,6 => UNS * INC # B3: 3,8 => UNS * INC # B3: 4 => UNS * DIS # B5: 6,8 => CTR => B5: 3 * PRF # B5: 3 => SOL * INC # C9: 6,8 => UNS * INC # C9: 4,9 => UNS * INC # B6: 6,7 => UNS * INC # C6: 6,7 => UNS * PRF # G5: 4,6 => SOL * DIS # G5: 2 => CTR => G5: 4,6 * DIS # H7: 4,6 => CTR => H7: 5 * INC # H7: 5 => UNS * DIS # I5: 3,6 => CTR => I5: 2 * PRF # I5: 2 => SOL * INC # E7: 4,9 => UNS * DIS # E9: 4,9 => CTR => E9: 5 * INC # E9: 5 => UNS * DIS # A8: 4,9 => CTR => A8: 2,7,8 * INC # A8: 2,7,8 => UNS * PRF # C8: 4,9 => SOL * INC # C8: 7,8 => UNS * INC # B7: 6,7 => UNS * INC # B7: 1,4 => UNS * DIS # G9: 2,4 => CTR => G9: 5,6,9 * INC # G9: 5,6,9 => UNS * INC # A8: 2,4 => UNS * INC # A8: 7,8,9 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 4,8 => UNS * DIS # B3: 3 => CTR => B3: 4,8 * INC B3: 4,8 # C8: 4,8 => UNS * INC B3: 4,8 # C9: 4,8 => UNS * DIS B3: 4,8 # F2: 5,9 => CTR => F2: 6,7 * INC B3: 4,8 + F2: 6,7 # G2: 5,7 => UNS * PRF B3: 4,8 + F2: 6,7 # G2: 2,6 => SOL * STA B3: 4,8 + F2: 6,7 + G2: 2,6 * CNT 7 HDP CHAINS / 7 HYP OPENED