Analysis of zz-www.sudokuoftheday.co.uk-20190403-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: ...14.8.52.....9.1..1.25.4...8...16.4....2..8.39.7....57..8.........6..29..5..... initial
Autosolve
position: ..714.8252.....9.1..1.25.4.728.5.16.4....2..8.39.7.25457.28.........65.29.25..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 7 => CTR => D3: 3,9 * PRF # F7: 3,9 => SOL * DIS # D2: 3,6 => CTR => D2: 7,8 * PRF # E5: 3,6 => SOL * DIS # G3: 3,7 => CTR => G3: 6 * PRF # D2: 3,7 => SOL * DIS # F2: 3,7 => CTR => F2: 8 * PRF # F2: 8 => SOL * DIS # H5: 3,7 => CTR => H5: 9 * DIS # H9: 3,7 => CTR => H9: 1,8 * DIS # B5: 5,6 => CTR => B5: 1 * PRF # B5: 1 => SOL * DIS # B5: 5 => CTR => B5: 1,6 * PRF # D2: 3,7 => SOL * DIS # H5: 7 => CTR => H5: 3,9 * PRF # D4: 3,9 => SOL * DIS # I7: 6 => CTR => I7: 3,9 * DIS # H5: 3,7 => CTR => H5: 9 * DIS # G3: 3,7 => CTR => G3: 6 * DIS # H8: 1,8 => CTR => H8: 3,7,9 * DIS # C7: 3,4 => CTR => C7: 6 * PRF # D8: 3,4 => SOL * DIS # E8: 1,3 => CTR => E8: 9 * DIS # F9: 1,3 => CTR => F9: 4,7 * DIS # H9: 1,3 => CTR => H9: 7,8 * DIS # E5: 6,9 => CTR => E5: 1,3 * CNT 26 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 7 => CTR => D3: 3,9 * PRF D3: 3,9 # F7: 3,9 => SOL * STA D3: 3,9 + F7: 3,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...14.8.52.....9.1..1.25.4...8...16.4....2..8.39.7....57..8.........6..29..5..... | initial |
| ..714.8252.....9.1..1.25.4.728.5.16.4....2..8.39.7.25457.28.........65.29.25..... | autosolve |
| 367149825254768931891325647728954163415632798639871254576283419183496572942517386 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 3,6 B1: 6,9 B2: 4,5 C2: 4,5 A3: 3,8 B3: 8,9 F1: 3,9 E2: 3,6 H2: 3,7 C5: 5,6 A6: 1,6 D6: 6,8 F6: 1,8 I4: 3,9 G5: 3,7 A8: 1,8 C8: 3,4 E9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,A6: 1.. / B5 = 1 => 0 pairs (*) / A6 = 1 => 0 pairs (X) E5,F6: 1.. / E5 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) B5,E5: 1.. / B5 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) A6,F6: 1.. / A6 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) F7,H7: 1.. / F7 = 1 => 0 pairs (X) / H7 = 1 => 20 pairs (_) A6,A8: 1.. / A6 = 1 => 0 pairs (X) / A8 = 1 => 0 pairs (_) A1,A3: 3.. / A1 = 3 => 0 pairs (*) / A3 = 3 => 0 pairs (X) C7,C8: 3.. / C7 = 3 => 0 pairs (X) / C8 = 3 => 19 pairs (_) A1,F1: 3.. / A1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) B2,C2: 4.. / B2 = 4 => 0 pairs (X) / C2 = 4 => 20 pairs (_) D4,F4: 4.. / D4 = 4 => 22 pairs (_) / F4 = 4 => 0 pairs (*) G7,G9: 4.. / G7 = 4 => 21 pairs (_) / G9 = 4 => 19 pairs (_) D4,D8: 4.. / D4 = 4 => 22 pairs (_) / D8 = 4 => 0 pairs (*) B2,C2: 5.. / B2 = 5 => 20 pairs (_) / C2 = 5 => 0 pairs (X) B5,C5: 5.. / B5 = 5 => 0 pairs (X) / C5 = 5 => 20 pairs (_) B2,B5: 5.. / B2 = 5 => 20 pairs (_) / B5 = 5 => 0 pairs (X) C2,C5: 5.. / C2 = 5 => 0 pairs (X) / C5 = 5 => 20 pairs (_) A1,B1: 6.. / A1 = 6 => 0 pairs (X) / B1 = 6 => 0 pairs (_) D2,E2: 6.. / D2 = 6 => 0 pairs (X) / E2 = 6 => 17 pairs (_) G3,I3: 6.. / G3 = 6 => 20 pairs (_) / I3 = 6 => 0 pairs (X) C7,B9: 6.. / C7 = 6 => 20 pairs (_) / B9 = 6 => 0 pairs (X) A6,D6: 6.. / A6 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) A1,A6: 6.. / A1 = 6 => 0 pairs (X) / A6 = 6 => 0 pairs (_) C5,C7: 6.. / C5 = 6 => 0 pairs (X) / C7 = 6 => 20 pairs (_) E2,E5: 6.. / E2 = 6 => 17 pairs (_) / E5 = 6 => 0 pairs (X) G5,H5: 7.. / G5 = 7 => 19 pairs (_) / H5 = 7 => 0 pairs (X) D8,F9: 7.. / D8 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) D8,H8: 7.. / D8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) F2,F9: 7.. / F2 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) I3,I9: 7.. / I3 = 7 => 23 pairs (_) / I9 = 7 => 0 pairs (X) A3,B3: 8.. / A3 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) D2,F2: 8.. / D2 = 8 => 0 pairs (X) / F2 = 8 => 0 pairs (_) D6,F6: 8.. / D6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) H8,H9: 8.. / H8 = 8 => 0 pairs (X) / H9 = 8 => 18 pairs (_) B9,H9: 8.. / B9 = 8 => 0 pairs (X) / H9 = 8 => 18 pairs (_) A3,A8: 8.. / A3 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) D2,D6: 8.. / D2 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) F2,F6: 8.. / F2 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) B1,B3: 9.. / B1 = 9 => 0 pairs (X) / B3 = 9 => 0 pairs (_) F1,D3: 9.. / F1 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) I4,H5: 9.. / I4 = 9 => 0 pairs (X) / H5 = 9 => 23 pairs (_) B1,F1: 9.. / B1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) B3,D3: 9.. / B3 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) E5,E8: 9.. / E5 = 9 => 0 pairs (X) / E8 = 9 => 18 pairs (_) I4,I7: 9.. / I4 = 9 => 0 pairs (X) / I7 = 9 => 23 pairs (_) * DURATION: 0:00:55.189863 START: 05:01:59.199227 END: 05:02:54.389090 2019-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,A8,B1,B2,B3,C2,C5,C8,D6,E2,E9,F1,F6,G5,H2,I4) * ..714.8252.....9.1..1.25.4.728.5.16.4....2..8.39.7.25457.28.........65.29.25..... * PAIR F1: 3,9 BLK 2 D3: 3,9,7 # reduction candidate for 3,9 D3: 7 => CTR * ..71498252.....9.1.91725.4.728.5.16.4....2..8.39.7.25457.28.........65729.25.7.8. D3: 3,9 # 23 pairs * PAIR F1: 3,9 COL F F4: 3,9,4 # reduction candidate for 3,9 F4: 3,9 # 22 pairs F7: 3,9,1,4 # reduction candidate for 3,9 F7: 3,9 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 F7: 1,4 # 19 pairs * PAIR E2: 3,6 BLK 2 D2: 3,6,7,8 # reduction candidate for 3,6 D2: 3,6 => CTR * ..714.8252....8971..1725.4.728.5.16.4....27.8.3987125457.28..1.1....65.29.2517... D2: 7,8 # 18 pairs * PAIR E2: 3,6 COL E E5: 3,6,1,9 # reduction candidate for 3,6 E5: 3,6 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 E5: 1,9 # 18 pairs * PAIR H2: 3,7 BLK 3 G3: 3,7,6 # reduction candidate for 3,7 G3: 3,7 => CTR * ..714.8252..867931..1.257467284531694...1237813967825457.28...38.37.65.29.253...7 G3: 6 # 20 pairs I3: 3,7,6 # reduction candidate for 3,7 I3: 3,7 # 20 pairs * PAIR H2: 3,7 ROW 2 D2: 3,7,6,8 # reduction candidate for 3,7 D2: 3,7 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 D2: 6,8 # 21 pairs F2: 3,7,8 # reduction candidate for 3,7 F2: 3,7 => CTR * 6971438252..867931381925.4.728.5.16.4..31279813967825457.28..1981.7.65.29.25..... F2: 8 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 * PAIR H2: 3,7 COL H H5: 3,7,9 # reduction candidate for 3,7 H5: 3,7 => CTR * 3671498252..8679318.1.25.4.7284531694....2378.39.7825457.28149....7965.29.2534... H5: 9 # 23 pairs H8: 3,7,1,8,9 # reduction candidate for 3,7 H8: 3,7 # 28 pairs H9: 3,7,1,8 # reduction candidate for 3,7 H9: 3,7 => CTR * 367149825254..7931891325.4.728.5.16.4....2..8.39.7.25457628..191437965829825..... H9: 1,8 # 19 pairs * PAIR C5: 5,6 BLK 4 B5: 5,6,1 # reduction candidate for 5,6 B5: 5,6 => CTR * 6971438252..867931381925.4.728.591634..31279813967825457.28.319813.965.29.253..8. B5: 1 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 * PAIR A6: 1,6 BLK 4 B5: 1,6,5 # reduction candidate for 1,6 B5: 5 => CTR * 697143825245867931381925746728.59163456.12..813967825457.28....8...965.296253..87 B5: 1,6 # 20 pairs * PAIR D6: 6,8 COL D D2: 6,8,3,7 # reduction candidate for 6,8 D2: 3,7 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 D2: 6,8 # 21 pairs * PAIR I4: 3,9 BLK 6 H5: 3,9,7 # reduction candidate for 3,9 H5: 7 => CTR * 3671498252..8679318.1.25.4.7284531694....2378.39.7825457.28.......7.65.29.25..... H5: 3,9 # 19 pairs * PAIR I4: 3,9 ROW 4 D4: 3,9,4 # reduction candidate for 3,9 D4: 3,9 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 D4: 4 # 22 pairs F4: 3,9,4 # reduction candidate for 3,9 F4: 3,9 # 22 pairs * PAIR I4: 3,9 COL I I7: 3,9,6 # reduction candidate for 3,9 I7: 6 => CTR * 6971438252...6.9313819256477283541694.6..2..8.39.7.25457.28...6.....65.29625...8. I7: 3,9 # 21 pairs * PAIR G5: 3,7 BLK 6 H5: 3,7,9 # reduction candidate for 3,7 H5: 3,7 => CTR * 3671498252..8679318.1.25.4.7284531694....2378.39.7825457.28149....7965.29.2534... H5: 9 # 23 pairs * PAIR G5: 3,7 COL G G3: 3,7,6 # reduction candidate for 3,7 G3: 3,7 => CTR * ..714.8252..867931..1.257467284531694...1237813967825457.28...38.37.65.29.253...7 G3: 6 # 20 pairs G9: 3,7,4,6 # reduction candidate for 3,7 G9: 3,7 # 23 pairs * PAIR A8: 1,8 BLK 7 B8: 1,8,4 # reduction candidate for 1,8 B8: 1,8 # 23 pairs B9: 1,8,4,6 # reduction candidate for 1,8 B9: 1,8 # 24 pairs * PAIR A8: 1,8 ROW 8 H8: 1,8,3,7,9 # reduction candidate for 1,8 H8: 1,8 => CTR * 697143825254867931381925.4.7284591634...12..813967825457.28....843796512912534.8. H8: 3,7,9 # 20 pairs * PAIR C8: 3,4 BLK 7 C7: 3,4,6 # reduction candidate for 3,4 C7: 3,4 => CTR * 6971438252.5867931381925.4.728.5.16.45631279813967825457.28..1981.7.65.29625...8. C7: 6 # 20 pairs * PAIR C8: 3,4 ROW 8 D8: 3,4,7,9 # reduction candidate for 3,4 D8: 3,4 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 D8: 7,9 # 23 pairs * PAIR E9: 1,3 BLK 8 F7: 1,3,4,9 # reduction candidate for 1,3 F7: 1,3 # 21 pairs E8: 1,3,9 # reduction candidate for 1,3 E8: 1,3 => CTR * ..714.8252...689.1891.25.4.728.5.169415692..863987125457.28..1.1...365929.251..8. E8: 9 # 18 pairs F9: 1,3,4,7 # reduction candidate for 1,3 F9: 1,3 => CTR * ..714.8252..867931..1.25.4.72845.16.4...12..813967825457.284.198..7.65.29.25..... F9: 4,7 # 19 pairs * PAIR E9: 1,3 ROW 9 H9: 1,3,7,8 # reduction candidate for 1,3 H9: 1,3 => CTR * 367149825254..7931891325.4.72845.16.4....2..8.39.7.25457628....1437965829825..... H9: 7,8 # 19 pairs * PAIR E9: 1,3 COL E E5: 1,3,6,9 # reduction candidate for 1,3 E5: 6,9 => CTR * 367149825254.38971891725.4.728.5.16.415.6279863987125457628..191.34965829.251.... E5: 1,3 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190403-absurd-base-pr-000.dot * REASONING * DIS # D3: 7 => CTR => D3: 3,9 * PRF # F7: 3,9 => SOL * DIS # D2: 3,6 => CTR => D2: 7,8 * PRF # E5: 3,6 => SOL * DIS # G3: 3,7 => CTR => G3: 6 * PRF # D2: 3,7 => SOL * DIS # F2: 3,7 => CTR => F2: 8 * PRF # F2: 8 => SOL * DIS # H5: 3,7 => CTR => H5: 9 * DIS # H9: 3,7 => CTR => H9: 1,8 * DIS # B5: 5,6 => CTR => B5: 1 * PRF # B5: 1 => SOL * DIS # B5: 5 => CTR => B5: 1,6 * PRF # D2: 3,7 => SOL * DIS # H5: 7 => CTR => H5: 3,9 * PRF # D4: 3,9 => SOL * DIS # I7: 6 => CTR => I7: 3,9 * DIS # H5: 3,7 => CTR => H5: 9 * DIS # G3: 3,7 => CTR => G3: 6 * DIS # H8: 1,8 => CTR => H8: 3,7,9 * DIS # C7: 3,4 => CTR => C7: 6 * PRF # D8: 3,4 => SOL * DIS # E8: 1,3 => CTR => E8: 9 * DIS # F9: 1,3 => CTR => F9: 4,7 * DIS # H9: 1,3 => CTR => H9: 7,8 * DIS # E5: 6,9 => CTR => E5: 1,3 * CNT 26 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,A8,B1,B2,B3,C2,C5,C8,D6,E2,E9,F1,F6,G5,H2,I4) * ..714.8252.....9.1..1.25.4.728.5.16.4....2..8.39.7.25457.28.........65.29.25..... * PAIR F1: 3,9 BLK 2 D3: 3,9,7 # reduction candidate for 3,9 D3: 7 => CTR * ..71498252.....9.1.91725.4.728.5.16.4....2..8.39.7.25457.28.........65729.25.7.8. * PAIR F1: 3,9 COL F F4: 3,9,4 # reduction candidate for 3,9 F4: 3,9 # 26 pairs F7: 3,9,1,4 # reduction candidate for 3,9 F7: 3,9 => SOLVED * 367149825254768931891325647728954163415632798639871254576283419183496572942517386 * DURATION: 0:00:03.623509 START: 05:03:31.758390 END: 05:03:35.381899 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190403-absurd-base-pr-001.dot * REASONING * DIS # D3: 7 => CTR => D3: 3,9 * PRF D3: 3,9 # F7: 3,9 => SOL * STA D3: 3,9 + F7: 3,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190403, absurd
Solution
position: 367149825254768931891325647728954163415632798639871254576283419183496572942517386 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 # D3: 3,9 => UNS * DIS # D3: 7 => CTR => D3: 3,9 * INC # F4: 3,9 => UNS * PRF # F7: 3,9 => SOL * INC # F7: 1,4 => UNS * DIS # D2: 3,6 => CTR => D2: 7,8 * INC # D2: 7,8 => UNS * PRF # E5: 3,6 => SOL * INC # E5: 1,9 => UNS * DIS # G3: 3,7 => CTR => G3: 6 * INC # G3: 6 => UNS * INC # I3: 3,7 => UNS * PRF # D2: 3,7 => SOL * INC # D2: 6,8 => UNS * DIS # F2: 3,7 => CTR => F2: 8 * PRF # F2: 8 => SOL * DIS # H5: 3,7 => CTR => H5: 9 * INC # H5: 9 => UNS * INC # H8: 3,7 => UNS * DIS # H9: 3,7 => CTR => H9: 1,8 * INC # H9: 1,8 => UNS * DIS # B5: 5,6 => CTR => B5: 1 * PRF # B5: 1 => SOL * INC # B5: 1,6 => UNS * DIS # B5: 5 => CTR => B5: 1,6 * INC # D2: 6,8 => UNS * PRF # D2: 3,7 => SOL * INC # H5: 3,9 => UNS * DIS # H5: 7 => CTR => H5: 3,9 * PRF # D4: 3,9 => SOL * INC # D4: 4 => UNS * INC # F4: 3,9 => UNS * INC # I7: 3,9 => UNS * DIS # I7: 6 => CTR => I7: 3,9 * DIS # H5: 3,7 => CTR => H5: 9 * INC # H5: 9 => UNS * DIS # G3: 3,7 => CTR => G3: 6 * INC # G3: 6 => UNS * INC # G9: 3,7 => UNS * INC # B8: 1,8 => UNS * INC # B9: 1,8 => UNS * DIS # H8: 1,8 => CTR => H8: 3,7,9 * INC # H8: 3,7,9 => UNS * DIS # C7: 3,4 => CTR => C7: 6 * INC # C7: 6 => UNS * PRF # D8: 3,4 => SOL * INC # D8: 7,9 => UNS * INC # F7: 1,3 => UNS * DIS # E8: 1,3 => CTR => E8: 9 * INC # E8: 9 => UNS * DIS # F9: 1,3 => CTR => F9: 4,7 * INC # F9: 4,7 => UNS * DIS # H9: 1,3 => CTR => H9: 7,8 * INC # H9: 7,8 => UNS * INC # E5: 1,3 => UNS * DIS # E5: 6,9 => CTR => E5: 1,3 * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 3,9 => UNS * DIS # D3: 7 => CTR => D3: 3,9 * INC D3: 3,9 # F4: 3,9 => UNS * PRF D3: 3,9 # F7: 3,9 => SOL * STA D3: 3,9 + F7: 3,9 * CNT 4 HDP CHAINS / 4 HYP OPENED