Analysis of zz-www.sudokuoftheday.co.uk-20190411-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: 2.9....4...7..68......1..9....18.46.42.6.............7............435..63...6.5.1 initial
Autosolve
position: 219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 3,4 => CTR => B3: 6,8 * DIS # C3: 6,8 => CTR => C3: 3,4 * DIS # A6: 6,8 => CTR => A6: 9 * PRF # D1: 5,7 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * PRF # D1: 3,5 => SOL * DIS # F9: 7,8 => CTR => F9: 9 * DIS # B3: 3,4 => CTR => B3: 6,8 * PRF # D1: 3,5 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * DIS # D2: 2,3 => CTR => D2: 9 * DIS # A6: 6,8 => CTR => A6: 9 * DIS # C3: 6,8 => CTR => C3: 3,4 * DIS # C7: 6,8 => CTR => C7: 2,5 * DIS # E7: 7,9 => CTR => E7: 2 * PRF # E7: 2 => SOL * DIS # F9: 8 => CTR => F9: 7,9 * PRF # D1: 3,5 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * DIS # C7: 2,8 => CTR => C7: 5,6 * PRF # C9: 2,8 => SOL * DIS # C9: 4 => CTR => C9: 2,8 * DIS # D7: 2,9 => CTR => D7: 7,8 * DIS # B8: 7,8 => CTR => B8: 9 * DIS # B9: 7,8 => CTR => B9: 4,9 * PRF # D9: 7,8 => SOL * DIS # D9: 2,9 => CTR => D9: 7,8 * DIS # F9: 7,8 => CTR => F9: 9 * CNT 28 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 3,4 => CTR => B3: 6,8 * DIS B3: 6,8 # A6: 6,8 => CTR => A6: 9 * PRF B3: 6,8 + A6: 9 # D1: 5,7 => SOL * STA B3: 6,8 + A6: 9 + D1: 5,7 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.9....4...7..68......1..9....18.46.42.6.............7............435..63...6.5.1 | initial |
| 219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1 | autosolve |
| 219578643537946812864213795753182469421697358986354127675821934198435276342769581 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) B2: 3,4 A3: 6,8 E1: 5,7 F1: 7,8 D3: 2,5 F3: 3,4 I1: 3,5 I2: 2,3 I3: 2,5 B4: 3,5 C4: 3,5 C6: 6,8 E5: 7,9 F5: 7,9 D6: 3,5 E6: 4,5 F6: 3,4 C8: 2,8 G7: 2,9 G8: 2,9 H8: 7,8 H9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 2.. / I2 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) G7,G8: 2.. / G7 = 2 => 0 pairs (X) / G8 = 2 => 21 pairs (_) D3,I3: 2.. / D3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) C8,G8: 2.. / C8 = 2 => 0 pairs (X) / G8 = 2 => 21 pairs (_) C9,D9: 2.. / C9 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E2,E7: 2.. / E2 = 2 => 0 pairs (X) / E7 = 2 => 0 pairs (_) I1,I2: 3.. / I1 = 3 => 0 pairs (*) / I2 = 3 => 0 pairs (X) B4,C4: 3.. / B4 = 3 => 0 pairs (X) / C4 = 3 => 20 pairs (_) D6,F6: 3.. / D6 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) D1,I1: 3.. / D1 = 3 => 0 pairs (X) / I1 = 3 => 0 pairs (_) C3,C4: 3.. / C3 = 3 => 0 pairs (X) / C4 = 3 => 20 pairs (_) F3,F6: 3.. / F3 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) E2,F3: 4.. / E2 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) E6,F6: 4.. / E6 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) B9,C9: 4.. / B9 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) B2,E2: 4.. / B2 = 4 => 0 pairs (X) / E2 = 4 => 0 pairs (_) C3,C9: 4.. / C3 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) E2,E6: 4.. / E2 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) F3,F6: 4.. / F3 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) I1,I3: 5.. / I1 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) B4,C4: 5.. / B4 = 5 => 20 pairs (_) / C4 = 5 => 0 pairs (X) D6,E6: 5.. / D6 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) B7,C7: 5.. / B7 = 5 => 0 pairs (X) / C7 = 5 => 20 pairs (_) D3,I3: 5.. / D3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) B4,B7: 5.. / B4 = 5 => 20 pairs (_) / B7 = 5 => 0 pairs (X) C4,C7: 5.. / C4 = 5 => 0 pairs (X) / C7 = 5 => 20 pairs (_) E1,E6: 5.. / E1 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) E5,F5: 7.. / E5 = 7 => 0 pairs (X) / F5 = 7 => 21 pairs (_) H8,H9: 7.. / H8 = 7 => 23 pairs (_) / H9 = 7 => 0 pairs (X) B8,H8: 7.. / B8 = 7 => 0 pairs (X) / H8 = 7 => 23 pairs (_) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 22 pairs (_) H8,H9: 8.. / H8 = 8 => 0 pairs (X) / H9 = 8 => 23 pairs (_) F1,F9: 8.. / F1 = 8 => 22 pairs (_) / F9 = 8 => 0 pairs (X) D2,E2: 9.. / D2 = 9 => 23 pairs (_) / E2 = 9 => 0 pairs (X) A6,B6: 9.. / A6 = 9 => 24 pairs (_) / B6 = 9 => 0 pairs (X) E5,F5: 9.. / E5 = 9 => 21 pairs (_) / F5 = 9 => 0 pairs (X) G7,G8: 9.. / G7 = 9 => 21 pairs (_) / G8 = 9 => 0 pairs (X) B8,G8: 9.. / B8 = 9 => 21 pairs (_) / G8 = 9 => 0 pairs (X) A6,A7: 9.. / A6 = 9 => 24 pairs (_) / A7 = 9 => 0 pairs (X) F5,F9: 9.. / F5 = 9 => 0 pairs (X) / F9 = 9 => 21 pairs (_) * DURATION: 0:00:53.361764 START: 05:12:36.434518 END: 05:13:29.796282 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B2,B4,C4,C6,C8,D3,D6,E1,E5,E6,F1,F3,F5,F6,G7,G8,H8,H9,I1,I2,I3) * 219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1 * PAIR B2: 3,4 BLK 1 B3: 3,4,6,8 # reduction candidate for 3,4 B3: 3,4 => CTR * 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341.24359.63.426.5.1 B3: 6,8 # 24 pairs C3: 3,4,6,8 # reduction candidate for 3,4 C3: 3,4 # 24 pairs * PAIR A3: 6,8 BLK 1 B3: 6,8,3,4 # reduction candidate for 6,8 B3: 6,8 # 24 pairs C3: 6,8,3,4 # reduction candidate for 6,8 C3: 6,8 => CTR * 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341..435..63.426.5.1 C3: 3,4 # 24 pairs * PAIR A3: 6,8 COL A A6: 6,8,9 # reduction candidate for 6,8 A6: 6,8 => CTR * 219..864.5.7926813...5147927..18246942169.358.9....1279....12341.24359.63..2695.1 A6: 9 # 24 pairs A7: 6,8,9 # reduction candidate for 6,8 A7: 6,8 # 24 pairs * PAIR E1: 5,7 BLK 2 D1: 5,7,3,8 # reduction candidate for 5,7 D1: 5,7 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 D1: 3,8 # 28 pairs * PAIR F1: 7,8 BLK 2 D1: 7,8,3,5 # reduction candidate for 7,8 D1: 7,8 => CTR * 219.58643547396812...2147957..1824694216793589..543127...821934198435276372.6.581 D1: 3,5 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 * PAIR F1: 7,8 COL F F9: 7,8,9 # reduction candidate for 7,8 F9: 7,8 => CTR * 219.58643547396812...2147957..1824694216793589..543127...82193419843527637296.581 F9: 9 # 21 pairs * PAIR F3: 3,4 ROW 3 B3: 3,4,6,8 # reduction candidate for 3,4 B3: 3,4 => CTR * 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341.24359.63.426.5.1 B3: 6,8 # 24 pairs C3: 3,4,6,8 # reduction candidate for 3,4 C3: 3,4 # 24 pairs * PAIR I1: 3,5 ROW 1 D1: 3,5,7,8 # reduction candidate for 3,5 D1: 3,5 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 D1: 7,8 => CTR * 219.58643547396812...2147957..1824694216793589..543127...821934198435276372.6.581 * PAIR I2: 2,3 ROW 2 D2: 2,3,9 # reduction candidate for 2,3 D2: 2,3 => CTR * 219...64.5.7.9681.....1479.7..182469421679358....43127....2193419.435..63...6.5.1 D2: 9 # 23 pairs * PAIR C6: 6,8 BLK 4 A6: 6,8,9 # reduction candidate for 6,8 A6: 6,8 => CTR * 219..864.5.7926813...5147927..18246942169.358.9....1279....12341.24359.63..2695.1 A6: 9 # 24 pairs B6: 6,8,9 # reduction candidate for 6,8 B6: 6,8 # 24 pairs * PAIR C6: 6,8 COL C C3: 6,8,3,4 # reduction candidate for 6,8 C3: 6,8 => CTR * 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341..435..63.426.5.1 C3: 3,4 # 24 pairs C7: 6,8,2,5 # reduction candidate for 6,8 C7: 6,8 => CTR * 219...64.5.7..681...3.1479.7351824694216..358....43127.5...1.341..435..63.426.5.1 C7: 2,5 # 23 pairs * PAIR E5: 7,9 COL E E7: 7,9,2 # reduction candidate for 7,9 E7: 7,9 => CTR * 219...64.5.7.26813...5147927..1824694216..358...3..127.....1.341..435..63...6.5.1 E7: 2 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 * PAIR F5: 7,9 COL F F9: 7,9,8 # reduction candidate for 7,9 F9: 8 => CTR * 2198.76435.7..6812...21.7957..182469421679358...543127...7219341..435..63...68571 F9: 7,9 # 22 pairs * PAIR D6: 3,5 COL D D1: 3,5,7,8 # reduction candidate for 3,5 D1: 3,5 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 D1: 7,8 => CTR * 219.58643547396812...2147957..1824694216793589..543127...821934198435276372.6.581 * PAIR C8: 2,8 BLK 7 C7: 2,8,5,6 # reduction candidate for 2,8 C7: 2,8 => CTR * 219...64.5.7..681...3.1479.7351824694216..358..6.4312765...1.341..435..63.426.5.1 C7: 5,6 # 23 pairs C9: 2,8,4 # reduction candidate for 2,8 C9: 2,8 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 C9: 4 => CTR * 219...64.5.7.26813...5147927..1824694216..358...3..127.....1.341..435..63.426.5.1 * PAIR G7: 2,9 ROW 7 D7: 2,9,7,8 # reduction candidate for 2,9 D7: 2,9 => CTR * 2197586435.7..6812...21.7957..1824694216.7358...54.127.....1.341..435.863...6.571 D7: 7,8 # 23 pairs E7: 2,9,7 # reduction candidate for 2,9 E7: 2,9 # 26 pairs * PAIR H8: 7,8 ROW 8 B8: 7,8,9 # reduction candidate for 7,8 B8: 7,8 => CTR * 219...64.5.7.26813...5147927..1824694216..358...3..127.....12341.24359.63..26.5.1 B8: 9 # 21 pairs * PAIR H9: 7,8 ROW 9 B9: 7,8,4,9 # reduction candidate for 7,8 B9: 7,8 => CTR * 219..864.5.7926813...5147927..18246942169.358......127.....1.341..435..63.42695.1 B9: 4,9 # 23 pairs D9: 7,8,2,9 # reduction candidate for 7,8 D9: 7,8 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 D9: 2,9 => CTR * 219.58643547396812...2147957..1824694216793589..543127...82193419843527637296.581 F9: 7,8,9 # reduction candidate for 7,8 F9: 7,8 => CTR * 219.58643547396812...2147957..1824694216793589..543127...82193419843527637296.581 F9: 9 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190411-absurd-base-pr-000.dot * REASONING * DIS # B3: 3,4 => CTR => B3: 6,8 * DIS # C3: 6,8 => CTR => C3: 3,4 * DIS # A6: 6,8 => CTR => A6: 9 * PRF # D1: 5,7 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * PRF # D1: 3,5 => SOL * DIS # F9: 7,8 => CTR => F9: 9 * DIS # B3: 3,4 => CTR => B3: 6,8 * PRF # D1: 3,5 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * DIS # D2: 2,3 => CTR => D2: 9 * DIS # A6: 6,8 => CTR => A6: 9 * DIS # C3: 6,8 => CTR => C3: 3,4 * DIS # C7: 6,8 => CTR => C7: 2,5 * DIS # E7: 7,9 => CTR => E7: 2 * PRF # E7: 2 => SOL * DIS # F9: 8 => CTR => F9: 7,9 * PRF # D1: 3,5 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * DIS # C7: 2,8 => CTR => C7: 5,6 * PRF # C9: 2,8 => SOL * DIS # C9: 4 => CTR => C9: 2,8 * DIS # D7: 2,9 => CTR => D7: 7,8 * DIS # B8: 7,8 => CTR => B8: 9 * DIS # B9: 7,8 => CTR => B9: 4,9 * PRF # D9: 7,8 => SOL * DIS # D9: 2,9 => CTR => D9: 7,8 * DIS # F9: 7,8 => CTR => F9: 9 * CNT 28 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B2,B4,C4,C6,C8,D3,D6,E1,E5,E6,F1,F3,F5,F6,G7,G8,H8,H9,I1,I2,I3) * 219...64.5.7..681.....1.79.7..1824694216..358......127.....1.341..435..63...6.5.1 * PAIR B2: 3,4 BLK 1 B3: 3,4,6,8 # reduction candidate for 3,4 B3: 3,4 => CTR * 219...64.5.7.26813.3.5147927531824694216..358...3..127..5..1.341.24359.63.426.5.1 * RESTART * PAIR A3: 6,8 COL A A6: 6,8,9 # reduction candidate for 6,8 A6: 6,8 => CTR * 219..864.5.7926813..351479273518246942169.358.9....1279....12341.24359.63..2695.1 * RESTART * PAIR RESTART * PAIR E1: 5,7 BLK 2 D1: 5,7,3,8 # reduction candidate for 5,7 D1: 5,7 => SOLVED * 219578643537946812864213795753182469421697358986354127675821934198435276342769581 * DURATION: 0:00:03.484174 START: 05:14:08.089319 END: 05:14:11.573493 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190411-absurd-base-pr-001.dot * REASONING * DIS # B3: 3,4 => CTR => B3: 6,8 * DIS B3: 6,8 # A6: 6,8 => CTR => A6: 9 * PRF B3: 6,8 + A6: 9 # D1: 5,7 => SOL * STA B3: 6,8 + A6: 9 + D1: 5,7 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190411, absurd
Solution
position: 219578643537946812864213795753182469421697358986354127675821934198435276342769581 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 # B3: 3,4 => CTR => B3: 6,8 * INC # B3: 6,8 => UNS * INC # C3: 3,4 => UNS * INC # B3: 6,8 => UNS * DIS # C3: 6,8 => CTR => C3: 3,4 * INC # C3: 3,4 => UNS * DIS # A6: 6,8 => CTR => A6: 9 * INC # A6: 9 => UNS * INC # A7: 6,8 => UNS * PRF # D1: 5,7 => SOL * INC # D1: 3,8 => UNS * DIS # D1: 7,8 => CTR => D1: 3,5 * PRF # D1: 3,5 => SOL * DIS # F9: 7,8 => CTR => F9: 9 * INC # F9: 9 => UNS * DIS # B3: 3,4 => CTR => B3: 6,8 * INC # B3: 6,8 => UNS * INC # C3: 3,4 => UNS * PRF # D1: 3,5 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * DIS # D2: 2,3 => CTR => D2: 9 * INC # D2: 9 => UNS * DIS # A6: 6,8 => CTR => A6: 9 * INC # A6: 9 => UNS * INC # B6: 6,8 => UNS * DIS # C3: 6,8 => CTR => C3: 3,4 * INC # C3: 3,4 => UNS * DIS # C7: 6,8 => CTR => C7: 2,5 * INC # C7: 2,5 => UNS * DIS # E7: 7,9 => CTR => E7: 2 * PRF # E7: 2 => SOL * INC # F9: 7,9 => UNS * DIS # F9: 8 => CTR => F9: 7,9 * PRF # D1: 3,5 => SOL * DIS # D1: 7,8 => CTR => D1: 3,5 * DIS # C7: 2,8 => CTR => C7: 5,6 * INC # C7: 5,6 => UNS * PRF # C9: 2,8 => SOL * DIS # C9: 4 => CTR => C9: 2,8 * DIS # D7: 2,9 => CTR => D7: 7,8 * INC # D7: 7,8 => UNS * INC # E7: 2,9 => UNS * DIS # B8: 7,8 => CTR => B8: 9 * INC # B8: 9 => UNS * DIS # B9: 7,8 => CTR => B9: 4,9 * INC # B9: 4,9 => UNS * PRF # D9: 7,8 => SOL * DIS # D9: 2,9 => CTR => D9: 7,8 * DIS # F9: 7,8 => CTR => F9: 9 * INC # F9: 9 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 3,4 => CTR => B3: 6,8 * DIS B3: 6,8 # A6: 6,8 => CTR => A6: 9 * PRF B3: 6,8 + A6: 9 # D1: 5,7 => SOL * STA B3: 6,8 + A6: 9 + D1: 5,7 * CNT 3 HDP CHAINS / 3 HYP OPENED