Analysis of zz-www.sudokuoftheday.co.uk-20060504-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: ...5.6..8...41..57.2.......582...3......9.8....6..3..5.......4.1...876.9.6....... initial
Autosolve
position: ...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 3,9 => CTR => C2: 8 * DIS # D3: 3,7 => CTR => D3: 9 * DIS # F2: 8,9 => CTR => F2: 2 * DIS # A3: 8,9 => CTR => A3: 4,7 * PRF # E1: 7 => SOL * PRF # G1: 2,9 => SOL * DIS # F2: 8 => CTR => F2: 2,9 * DIS # F9: 2,9 => CTR => F9: 1,4 * DIS # I5: 4 => CTR => I5: 2,6 * PRF # D7: 2,6 => SOL * DIS # G6: 1 => CTR => G6: 2,4 * DIS # E9: 2,4 => CTR => E9: 3,5 * DIS # I5: 4,6 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # E4: 7 => CTR => E4: 4,6 * PRF # I3: 4,6 => SOL * DIS # I3: 3 => CTR => I3: 4,6 * DIS # H5: 6 => CTR => H5: 1,7 * PRF # D7: 2,3 => SOL * DIS # E7: 2,3 => CTR => E7: 5,6 * DIS # D9: 2,3 => CTR => D9: 1,9 * DIS # E9: 2,3 => CTR => E9: 4,5 * CNT 22 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 3,9 => CTR => C2: 8 * DIS C2: 8 # D3: 3,7 => CTR => D3: 9 * DIS C2: 8 + D3: 9 # H5: 7 => CTR => H5: 1,6 * DIS C2: 8 + D3: 9 + H5: 1,6 # I5: 4 => CTR => I5: 2,6 * PRF C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 # D7: 2,6 => SOL * STA C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 + D7: 2,6 * CNT 5 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5.6..8...41..57.2.......582...3......9.8....6..3..5.......4.1...876.9.6....... | initial |
| ...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8. | autosolve |
| 491576238638412957725938164582741396347695812916823475873269541154387629269154783 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B2: 3,9 E3: 3,7 F3: 8,9 H1: 2,3 G2: 2,9 H3: 1,6 F4: 1,4 D5: 2,6 E6: 2,4 I4: 4,6 H6: 1,7 D8: 2,3 G7: 5,7 H8: 2,3 G9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 19 pairs (_) / C1 = 1 => 16 pairs (_) G3,H3: 1.. / G3 = 1 => 19 pairs (_) / H3 = 1 => 0 pairs (X) D4,F4: 1.. / D4 = 1 => 0 pairs (X) / F4 = 1 => 16 pairs (_) I7,I9: 1.. / I7 = 1 => 18 pairs (_) / I9 = 1 => 16 pairs (_) C1,C5: 1.. / C1 = 1 => 16 pairs (_) / C5 = 1 => 19 pairs (_) G3,G6: 1.. / G3 = 1 => 19 pairs (_) / G6 = 1 => 0 pairs (X) E1,F2: 2.. / E1 = 2 => 0 pairs (X) / F2 = 2 => 21 pairs (_) D5,E6: 2.. / D5 = 2 => 0 pairs (X) / E6 = 2 => 0 pairs (_) I5,G6: 2.. / I5 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) A7,A9: 2.. / A7 = 2 => 0 pairs (X) / A9 = 2 => 16 pairs (_) F2,G2: 2.. / F2 = 2 => 21 pairs (_) / G2 = 2 => 0 pairs (X) D5,I5: 2.. / D5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) E6,G6: 2.. / E6 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) D8,H8: 2.. / D8 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) H1,H8: 2.. / H1 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) B2,C2: 3.. / B2 = 3 => 16 pairs (_) / C2 = 3 => 0 pairs (X) H1,I3: 3.. / H1 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) E1,H1: 3.. / E1 = 3 => 0 pairs (X) / H1 = 3 => 0 pairs (_) D8,H8: 3.. / D8 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) H1,H8: 3.. / H1 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 0 pairs (X) / F9 = 4 => 16 pairs (_) F4,F9: 4.. / F4 = 4 => 0 pairs (X) / F9 = 4 => 16 pairs (_) E7,E9: 5.. / E7 = 5 => 0 pairs (X) / E9 = 5 => 15 pairs (_) G7,G9: 5.. / G7 = 5 => 15 pairs (_) / G9 = 5 => 0 pairs (X) E7,G7: 5.. / E7 = 5 => 0 pairs (X) / G7 = 5 => 15 pairs (_) E9,G9: 5.. / E9 = 5 => 15 pairs (_) / G9 = 5 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 19 pairs (_) / I3 = 6 => 0 pairs (X) D7,E7: 6.. / D7 = 6 => 0 pairs (X) / E7 = 6 => 17 pairs (_) E4,E7: 6.. / E4 = 6 => 0 pairs (X) / E7 = 6 => 17 pairs (_) H3,H5: 6.. / H3 = 6 => 19 pairs (_) / H5 = 6 => 0 pairs (X) D4,E4: 7.. / D4 = 7 => 17 pairs (_) / E4 = 7 => 0 pairs (X) H5,H6: 7.. / H5 = 7 => 22 pairs (_) / H6 = 7 => 16 pairs (_) G7,G9: 7.. / G7 = 7 => 0 pairs (X) / G9 = 7 => 15 pairs (_) D3,D4: 7.. / D3 = 7 => 0 pairs (X) / D4 = 7 => 17 pairs (_) C2,A3: 8.. / C2 = 8 => 17 pairs (_) / A3 = 8 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 0 pairs (X) / F3 = 8 => 17 pairs (_) A7,C7: 8.. / A7 = 8 => 17 pairs (_) / C7 = 8 => 0 pairs (X) C2,F2: 8.. / C2 = 8 => 17 pairs (_) / F2 = 8 => 0 pairs (X) A3,F3: 8.. / A3 = 8 => 0 pairs (X) / F3 = 8 => 17 pairs (_) A3,A7: 8.. / A3 = 8 => 0 pairs (X) / A7 = 8 => 17 pairs (_) C2,C7: 8.. / C2 = 8 => 17 pairs (_) / C7 = 8 => 0 pairs (X) A6,B6: 9.. / A6 = 9 => 16 pairs (_) / B6 = 9 => 22 pairs (_) * DURATION: 0:00:48.047567 START: 22:53:20.259977 END: 22:54:08.307544 2019-04-30 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D5,D8,E3,E6,F3,F4,G2,G7,G9,H1,H3,H6,H8,I4) * ...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8. * PAIR B2: 3,9 BLK 1 C2: 3,9,8 # reduction candidate for 3,9 C2: 3,9 => CTR * ...5.6..86..418257825..9...582...39.....958.2..6823..5..8....4.154.87629.6.....8. C2: 8 # 17 pairs * PAIR B2: 3,9 COL B B7: 3,9,7 # reduction candidate for 3,9 B7: 7 # 17 pairs B7: 3,9 # 17 pairs * PAIR E3: 3,7 BLK 2 E1: 3,7,2 # reduction candidate for 3,7 E1: 3,7 # 21 pairs D3: 3,7,9 # reduction candidate for 3,7 D3: 3,7 => CTR * ...526.386..41.257.25......582...39....2958....68.3..5.......4.154.876.9.6.....8. D3: 9 # 21 pairs * PAIR F3: 8,9 BLK 2 F2: 8,9,2 # reduction candidate for 8,9 F2: 8,9 => CTR * ...526.386..41.257.25......582...39....2958....6843175.......4.154387629.6..5478. F2: 2 # 21 pairs * PAIR F3: 8,9 ROW 3 A3: 8,9,4,7 # reduction candidate for 8,9 A3: 8,9 => CTR * ...5.69386..41.257.25......582...39.....958.2..6823..5.......4.154.876.9.6.....8. A3: 4,7 # 19 pairs * PAIR H1: 2,3 ROW 1 E1: 2,3,7 # reduction candidate for 2,3 E1: 7 => SOLVED * 491576238638412957725938164582741396347695812916823475873269541154387629269154783 E1: 2,3 # 17 pairs * PAIR G2: 2,9 BLK 3 G1: 2,9,4 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 491576238638412957725938164582741396347695812916823475873269541154387629269154783 G1: 4 # 23 pairs * PAIR G2: 2,9 ROW 2 F2: 2,9,8 # reduction candidate for 2,9 F2: 8 => CTR * ...526.386..418257825..9...582...39....2958....6843175..8....4.154387629.6..5478. F2: 2,9 # 17 pairs * PAIR H3: 1,6 COL H H5: 1,6,7 # reduction candidate for 1,6 H5: 7 # 22 pairs H5: 1,6 # 16 pairs * PAIR F4: 1,4 COL F F9: 1,4,2,9 # reduction candidate for 1,4 F9: 2,9 => CTR * ...5.6..86..41..57.25......582..4396...6958.2..68234.5....61.4.154.876.9.6.....8. F9: 1,4 # 17 pairs * PAIR D5: 2,6 ROW 5 I5: 2,6,4 # reduction candidate for 2,6 I5: 4 => CTR * ...5.6..86..41..57.25......582...39....295864..68.3..5.......4.154.876.9.6.....8. I5: 2,6 # 19 pairs * PAIR D5: 2,6 COL D D7: 2,6,1,3,9 # reduction candidate for 2,6 D7: 2,6 => SOLVED * 491576238638412957725938164582741396347695812916823475873269541154387629269154783 D7: 1,3,9 # 17 pairs * PAIR E6: 2,4 ROW 6 G6: 2,4,1 # reduction candidate for 2,4 G6: 1 => CTR * ...5.6..86..41..57.25......582...39.....958.2..6823175.......4.154.87629.6.....8. G6: 2,4 # 19 pairs * PAIR E6: 2,4 COL E E9: 2,4,3,5 # reduction candidate for 2,4 E9: 2,4 => CTR * ...5.6..86..41..57.25......582.6.394...2958.6..68432.5...65.74.154387629.6....58. E9: 3,5 # 17 pairs * PAIR I4: 4,6 BLK 6 I5: 4,6,2 # reduction candidate for 4,6 I5: 4,6 => CTR * ...5.6..86..41..57.25......582...39....2958....68432.5.......4.154387629.6.....8. I5: 2 => SOLVED * 491576238638412957725938164582741396347695812916823475873269541154387629269154783 * PAIR I4: 4,6 ROW 4 E4: 4,6,7 # reduction candidate for 4,6 E4: 7 => CTR * ...5.6..86..41..57.2573....582.71394....958....68432.5....6.54.154.876.9.6..5478. E4: 4,6 # 17 pairs * PAIR I4: 4,6 COL I I3: 4,6,3 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 491576238638412957725938164582741396347695812916823475873269541154387629269154783 I3: 3 => CTR * ...536.286..412957.25.781635827.139.....958....68.32.58....9.4.1542876392693.4781 * PAIR H6: 1,7 BLK 6 H5: 1,7,6 # reduction candidate for 1,7 H5: 6 => CTR * ...5.6..86..41..57.25....16582...394...29586...68.3.75.......4.154.876.9.6.....8. H5: 1,7 # 19 pairs * PAIR H6: 1,7 ROW 6 B6: 1,7,4,9 # reduction candidate for 1,7 B6: 1,7 # 21 pairs B6: 4,9 # 17 pairs * PAIR D8: 2,3 BLK 8 D7: 2,3,1,6,9 # reduction candidate for 2,3 D7: 2,3 => SOLVED * 491576238638412957725938164582741396347695812916823475873269541154387629269154783 D7: 1,6,9 # 15 pairs E7: 2,3,5,6 # reduction candidate for 2,3 E7: 2,3 => CTR * ...5.6..86..41..57.25......582.6.394...2958.6..68432.5...6..54.154387629.6.....8. E7: 5,6 # 16 pairs D9: 2,3,1,9 # reduction candidate for 2,3 D9: 2,3 => CTR * ...5.6..86..412957.25..8...582...39....6958.2..6823..5.......4.154.876.9.6.....8. D9: 1,9 # 16 pairs E9: 2,3,4,5 # reduction candidate for 2,3 E9: 2,3 => CTR * ...5.6..86..41..57.25......582.61394...2958.6..68432.5...65.741154387629.6...458. E9: 4,5 # 16 pairs * PAIR H8: 2,3 BLK 9 I7: 2,3,1 # reduction candidate for 2,3 I7: 2,3 # 16 pairs I9: 2,3,1 # reduction candidate for 2,3 I9: 2,3 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060504-absurd-base-pr-000.dot * REASONING * DIS # C2: 3,9 => CTR => C2: 8 * DIS # D3: 3,7 => CTR => D3: 9 * DIS # F2: 8,9 => CTR => F2: 2 * DIS # A3: 8,9 => CTR => A3: 4,7 * PRF # E1: 7 => SOL * PRF # G1: 2,9 => SOL * DIS # F2: 8 => CTR => F2: 2,9 * DIS # F9: 2,9 => CTR => F9: 1,4 * DIS # I5: 4 => CTR => I5: 2,6 * PRF # D7: 2,6 => SOL * DIS # G6: 1 => CTR => G6: 2,4 * DIS # E9: 2,4 => CTR => E9: 3,5 * DIS # I5: 4,6 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # E4: 7 => CTR => E4: 4,6 * PRF # I3: 4,6 => SOL * DIS # I3: 3 => CTR => I3: 4,6 * DIS # H5: 6 => CTR => H5: 1,7 * PRF # D7: 2,3 => SOL * DIS # E7: 2,3 => CTR => E7: 5,6 * DIS # D9: 2,3 => CTR => D9: 1,9 * DIS # E9: 2,3 => CTR => E9: 4,5 * CNT 22 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D5,D8,E3,E6,F3,F4,G2,G7,G9,H1,H3,H6,H8,I4) * ...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8. * PAIR B2: 3,9 BLK 1 C2: 3,9,8 # reduction candidate for 3,9 C2: 3,9 => CTR * ...5.6..86..418257825..9...582...39.....958.2..6823..5..8....4.154.87629.6.....8. * PAIR E3: 3,7 BLK 2 E1: 3,7,2 # reduction candidate for 3,7 E1: 3,7 # 21 pairs D3: 3,7,9 # reduction candidate for 3,7 D3: 3,7 => CTR * ...5.6..8638419257.25..8...582...39.3...958.2..6823..58....2.4.15438762926.....8. * RESTART * PAIR H3: 1,6 COL H H5: 1,6,7 # reduction candidate for 1,6 H5: 7 => CTR * 9.7536.286384129574259781635827.139.341.9587.7968.3215873.29541154.876.9269.5478. * PAIR RESTART * PAIR D5: 2,6 ROW 5 I5: 2,6,4 # reduction candidate for 2,6 I5: 4 => CTR * ..15.6..8638412957.259.8...5827.139.3.7295864..68.3.75873..954.154.876.9269.5478. * PAIR D5: 2,6 COL D D7: 2,6,1 # reduction candidate for 2,6 D7: 2,6 => SOLVED * 491576238638412957725938164582741396347695812916823475873269541154387629269154783 * DURATION: 0:00:08.336363 START: 22:54:40.202013 END: 22:54:48.538376 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060504-absurd-base-pr-001.dot * REASONING * DIS # C2: 3,9 => CTR => C2: 8 * DIS C2: 8 # D3: 3,7 => CTR => D3: 9 * DIS C2: 8 + D3: 9 # H5: 7 => CTR => H5: 1,6 * DIS C2: 8 + D3: 9 + H5: 1,6 # I5: 4 => CTR => I5: 2,6 * PRF C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 # D7: 2,6 => SOL * STA C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 + D7: 2,6 * CNT 5 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060504, absurd
Solution
position: 491576238638412957725938164582741396347695812916823475873269541154387629269154783 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 # C2: 3,9 => CTR => C2: 8 * INC # C2: 8 => UNS * INC # B7: 3,9 => UNS * INC # B7: 7 => UNS * INC # E1: 3,7 => UNS * DIS # D3: 3,7 => CTR => D3: 9 * INC # D3: 9 => UNS * DIS # F2: 8,9 => CTR => F2: 2 * INC # F2: 2 => UNS * DIS # A3: 8,9 => CTR => A3: 4,7 * INC # A3: 4,7 => UNS * INC # E1: 2,3 => UNS * PRF # E1: 7 => SOL * PRF # G1: 2,9 => SOL * INC # G1: 4 => UNS * INC # F2: 2,9 => UNS * DIS # F2: 8 => CTR => F2: 2,9 * INC # H5: 1,6 => UNS * INC # H5: 7 => UNS * INC # F9: 1,4 => UNS * DIS # F9: 2,9 => CTR => F9: 1,4 * INC # I5: 2,6 => UNS * DIS # I5: 4 => CTR => I5: 2,6 * PRF # D7: 2,6 => SOL * INC # D7: 1,3,9 => UNS * INC # G6: 2,4 => UNS * DIS # G6: 1 => CTR => G6: 2,4 * DIS # E9: 2,4 => CTR => E9: 3,5 * INC # E9: 3,5 => UNS * DIS # I5: 4,6 => CTR => I5: 2 * PRF # I5: 2 => SOL * INC # E4: 4,6 => UNS * DIS # E4: 7 => CTR => E4: 4,6 * PRF # I3: 4,6 => SOL * DIS # I3: 3 => CTR => I3: 4,6 * INC # H5: 1,7 => UNS * DIS # H5: 6 => CTR => H5: 1,7 * INC # B6: 1,7 => UNS * INC # B6: 4,9 => UNS * PRF # D7: 2,3 => SOL * INC # D7: 1,6,9 => UNS * DIS # E7: 2,3 => CTR => E7: 5,6 * INC # E7: 5,6 => UNS * DIS # D9: 2,3 => CTR => D9: 1,9 * INC # D9: 1,9 => UNS * DIS # E9: 2,3 => CTR => E9: 4,5 * INC # E9: 4,5 => UNS * INC # I7: 2,3 => UNS * INC # I9: 2,3 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 3,9 => CTR => C2: 8 * INC C2: 8 # E1: 3,7 => UNS * DIS C2: 8 # D3: 3,7 => CTR => D3: 9 * INC C2: 8 + D3: 9 # H5: 1,6 => UNS * DIS C2: 8 + D3: 9 # H5: 7 => CTR => H5: 1,6 * INC C2: 8 + D3: 9 + H5: 1,6 # I5: 2,6 => UNS * DIS C2: 8 + D3: 9 + H5: 1,6 # I5: 4 => CTR => I5: 2,6 * PRF C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 # D7: 2,6 => SOL * STA C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 + D7: 2,6 * CNT 8 HDP CHAINS / 8 HYP OPENED