Analysis of zz-www.sudokuoftheday.co.uk-20060518-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: .....8.......6....9634.2.7...8.1.7.6.9....5..3...9.28......6.4.48......2.57...3.. initial
Autosolve
position: .....8...8...6....963452.7...8.1.796.9....5..3...9.28..3.5.6.4748.....52.57...3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 3,7 => CTR => D1: 1,9 * DIS # G1: 4,9 => CTR => G1: 6 * DIS # H1: 6 => CTR => H1: 2,3 * DIS # G7: 9 => CTR => G7: 1,8 * DIS # I9: 9 => CTR => I9: 1,8 * DIS # A1: 2,5 => CTR => A1: 1,7 * DIS # F6: 4,7 => CTR => F6: 5 * PRF # D5: 6,7 => SOL * DIS # I5: 4 => CTR => I5: 1,3 * DIS # I5: 1,4 => CTR => I5: 3 * DIS # B6: 1,4 => CTR => B6: 7 * DIS # C7: 1,2 => CTR => C7: 9 * DIS # A1: 1,2 => CTR => A1: 5,7 * DIS # A5: 1,2 => CTR => A5: 6,7 * CNT 14 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 3,7 => CTR => D1: 1,9 * DIS D1: 1,9 # G1: 4,9 => CTR => G1: 6 * DIS D1: 1,9 + G1: 6 # E9: 2,8 => CTR => E9: 4 * PRF D1: 1,9 + G1: 6 + E9: 4 # D2: 1,9 => SOL * STA D1: 1,9 + G1: 6 + E9: 4 + D2: 1,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....8.......6....9634.2.7...8.1.7.6.9....5..3...9.28......6.4.48......2.57...3.. | initial |
| .....8...8...6....963452.7...8.1.796.9....5..3...9.28..3.5.6.4748.....52.57...3.. | autosolve |
| 714938625825167439963452178548213796692784513371695284139526847486371952257849361 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) E1: 3,7 G2: 4,9 H2: 2,3 G3: 1,8 I3: 1,8 A4: 2,5 B4: 2,4 D4: 2,3 F5: 4,7 D6: 6,7 H5: 1,3 I6: 1,4 A7: 1,2 E7: 2,8 E8: 3,7 H9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,I3: 1.. / G3 = 1 => 18 pairs (_) / I3 = 1 => 18 pairs (_) H5,H9: 1.. / H5 = 1 => 22 pairs (_) / H9 = 1 => 0 pairs (X) H1,H2: 2.. / H1 = 2 => 22 pairs (_) / H2 = 2 => 16 pairs (_) D4,F4: 3.. / D4 = 3 => 19 pairs (_) / F4 = 3 => 20 pairs (_) H5,I5: 3.. / H5 = 3 => 0 pairs (X) / I5 = 3 => 22 pairs (_) E1,E8: 3.. / E1 = 3 => 16 pairs (_) / E8 = 3 => 0 pairs (X) G1,G2: 4.. / G1 = 4 => 0 pairs (X) / G2 = 4 => 16 pairs (_) I5,I6: 4.. / I5 = 4 => 0 pairs (X) / I6 = 4 => 18 pairs (_) E9,F9: 4.. / E9 = 4 => 19 pairs (_) / F9 = 4 => 24 pairs (_) B4,F4: 4.. / B4 = 4 => 17 pairs (_) / F4 = 4 => 25 pairs (_) E5,E9: 4.. / E5 = 4 => 24 pairs (_) / E9 = 4 => 19 pairs (_) I1,I2: 5.. / I1 = 5 => 17 pairs (_) / I2 = 5 => 17 pairs (_) A4,C6: 5.. / A4 = 5 => 16 pairs (_) / C6 = 5 => 0 pairs (X) F4,F6: 5.. / F4 = 5 => 0 pairs (X) / F6 = 5 => 16 pairs (_) C2,I2: 5.. / C2 = 5 => 17 pairs (_) / I2 = 5 => 17 pairs (_) A4,F4: 5.. / A4 = 5 => 16 pairs (_) / F4 = 5 => 0 pairs (X) C6,F6: 5.. / C6 = 5 => 0 pairs (X) / F6 = 5 => 16 pairs (_) A1,A4: 5.. / A1 = 5 => 0 pairs (X) / A4 = 5 => 16 pairs (_) G1,H1: 6.. / G1 = 6 => 22 pairs (_) / H1 = 6 => 0 pairs (X) D5,D6: 6.. / D5 = 6 => 0 pairs (X) / D6 = 6 => 15 pairs (_) C8,A9: 6.. / C8 = 6 => 22 pairs (_) / A9 = 6 => 0 pairs (X) G8,H9: 6.. / G8 = 6 => 0 pairs (X) / H9 = 6 => 22 pairs (_) C6,D6: 6.. / C6 = 6 => 0 pairs (X) / D6 = 6 => 15 pairs (_) C8,G8: 6.. / C8 = 6 => 22 pairs (_) / G8 = 6 => 0 pairs (X) A9,H9: 6.. / A9 = 6 => 0 pairs (X) / H9 = 6 => 22 pairs (_) A5,A9: 6.. / A5 = 6 => 22 pairs (_) / A9 = 6 => 0 pairs (X) G1,G8: 6.. / G1 = 6 => 22 pairs (_) / G8 = 6 => 0 pairs (X) H1,H9: 6.. / H1 = 6 => 0 pairs (X) / H9 = 6 => 22 pairs (_) A5,B6: 7.. / A5 = 7 => 0 pairs (X) / B6 = 7 => 17 pairs (_) A1,A5: 7.. / A1 = 7 => 17 pairs (_) / A5 = 7 => 0 pairs (X) E1,E8: 7.. / E1 = 7 => 0 pairs (X) / E8 = 7 => 16 pairs (_) G3,I3: 8.. / G3 = 8 => 18 pairs (_) / I3 = 8 => 18 pairs (_) D5,E5: 8.. / D5 = 8 => 16 pairs (_) / E5 = 8 => 16 pairs (_) G7,I9: 8.. / G7 = 8 => 18 pairs (_) / I9 = 8 => 18 pairs (_) E7,G7: 8.. / E7 = 8 => 18 pairs (_) / G7 = 8 => 18 pairs (_) D5,D9: 8.. / D5 = 8 => 16 pairs (_) / D9 = 8 => 16 pairs (_) G3,G7: 8.. / G3 = 8 => 18 pairs (_) / G7 = 8 => 18 pairs (_) I3,I9: 8.. / I3 = 8 => 18 pairs (_) / I9 = 8 => 18 pairs (_) C7,C8: 9.. / C7 = 9 => 20 pairs (_) / C8 = 9 => 0 pairs (X) C7,G7: 9.. / C7 = 9 => 20 pairs (_) / G7 = 9 => 0 pairs (X) * DURATION: 0:00:45.333996 START: 23:13:54.823480 END: 23:14:40.157476 2019-04-30 * CP COUNT: (40) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B4,D4,D6,E1,E7,E8,F5,G2,G3,H2,H5,H9,I3,I6) * .....8...8...6....963452.7...8.1.796.9....5..3...9.28..3.5.6.4748.....52.57...3.. * PAIR E1: 3,7 BLK 2 D1: 3,7,1,9 # reduction candidate for 3,7 D1: 3,7 => CTR * ..4..8.6.87..6.423963452178.48.1.79679...453131..9.284.3.5.684748....652657.4.31. D1: 1,9 # 17 pairs D2: 3,7,1,9 # reduction candidate for 3,7 D2: 3,7 # 19 pairs F2: 3,7,1,9 # reduction candidate for 3,7 F2: 3,7 # 24 pairs * PAIR G2: 4,9 BLK 3 G1: 4,9,6 # reduction candidate for 4,9 G1: 4,9 => CTR * .....8.6.8...6..2.963452178..8.1.796.9....53.3...9.28..3952684748....652657...319 G1: 6 # 22 pairs * PAIR H2: 2,3 BLK 3 H1: 2,3,6 # reduction candidate for 2,3 H1: 6 => CTR * .....8.6.8...6..2.963452178..8.1.796.9....53.3...9.28..3952684748....652657...319 H1: 2,3 # 22 pairs * PAIR G3: 1,8 COL G G7: 1,8,9 # reduction candidate for 1,8 G7: 9 => CTR * .....8...8...6....963452871..8.1.796.9....5133...9.284.3.586947489....52.57...3.. G7: 1,8 # 20 pairs * PAIR I3: 1,8 COL I I9: 1,8,9 # reduction candidate for 1,8 I9: 9 => CTR * .....8...8...6....963452178..8.1.796.9....5..3...9.28..3952684748....652.57...3.9 I9: 1,8 # 22 pairs * PAIR A4: 2,5 COL A A1: 2,5,1,7 # reduction candidate for 2,5 A1: 2,5 => CTR * .....8.6.8...6..2.963452178.48.1.79679...453131..9.284132586.4748.....52657.4.31. A1: 1,7 # 17 pairs * PAIR B4: 2,4 BLK 4 C5: 2,4,1,6 # reduction candidate for 2,4 C5: 2,4 # 20 pairs C5: 1,6 # 17 pairs * PAIR B4: 2,4 COL B B1: 2,4,1,7 # reduction candidate for 2,4 B1: 2,4 # 19 pairs B2: 2,4,1,7 # reduction candidate for 2,4 B2: 2,4 # 20 pairs * PAIR F5: 4,7 BLK 5 F6: 4,7,5 # reduction candidate for 4,7 F6: 4,7 => CTR * 5....8...8...6...5963452.7.248315796796..45..315697284132586947489...652657.4.318 F6: 5 # 16 pairs * PAIR D6: 6,7 BLK 5 D5: 6,7,2,8 # reduction candidate for 6,7 D5: 6,7 => SOLVED * 714938625825167439963452178548213796692784513371695284139526847486371952257849361 D5: 2,8 # 16 pairs * PAIR H5: 1,3 BLK 6 I5: 1,3,4 # reduction candidate for 1,3 I5: 4 => CTR * .....8.6.8...6..2.963452178..8.1.796.9...753437.69.281.3.5.684748....652657.4.31. I5: 1,3 # 18 pairs * PAIR I6: 1,4 BLK 6 I5: 1,4,3 # reduction candidate for 1,4 I5: 1,4 => CTR * .....8.6.8...6..2.963452178..8.1.796.9....53.3...9.28..3952684748....652657...319 I5: 3 # 22 pairs * PAIR I6: 1,4 ROW 6 B6: 1,4,7 # reduction candidate for 1,4 B6: 1,4 => CTR * .....8.6.8...6..2.963452178.48.1.79679...453131..9.284.3.5.684748....652657.4.31. B6: 7 # 17 pairs C6: 1,4,5,6 # reduction candidate for 1,4 C6: 1,4 # 17 pairs * PAIR A7: 1,2 BLK 7 C7: 1,2,9 # reduction candidate for 1,2 C7: 1,2 => CTR * .....8...8...6....963452.7...8.1.796.9....5..3...9.28..3.5.6947489...652657...318 C7: 9 # 20 pairs A9: 1,2,6 # reduction candidate for 1,2 A9: 1,2 # 22 pairs * PAIR A7: 1,2 COL A A1: 1,2,5,7 # reduction candidate for 1,2 A1: 1,2 => CTR * .....8.6.8...6..2.96345217854821.79679...45..3...95284.3.5.6.4748.....52657.4.31. A1: 5,7 # 17 pairs A5: 1,2,6,7 # reduction candidate for 1,2 A5: 1,2 => CTR * 7...38.658.5.6..239634521785.8.1.796.96...53.37.69528..3952684748..7.652657...319 A5: 6,7 # 17 pairs * PAIR E7: 2,8 BLK 8 D9: 2,8,1,9 # reduction candidate for 2,8 D9: 2,8 # 19 pairs E9: 2,8,4 # reduction candidate for 2,8 E9: 2,8 # 24 pairs * PAIR E7: 2,8 COL E E5: 2,8,4 # reduction candidate for 2,8 E5: 4 # 24 pairs E5: 2,8 # 19 pairs * PAIR E8: 3,7 BLK 8 D8: 3,7,1,9 # reduction candidate for 3,7 D8: 3,7 # 18 pairs F8: 3,7,1,9 # reduction candidate for 3,7 F8: 3,7 # 22 pairs * PAIR H9: 1,6 BLK 9 G8: 1,6,9 # reduction candidate for 1,6 G8: 9 # 22 pairs G8: 1,6 # 21 pairs * PAIR H9: 1,6 ROW 9 A9: 1,6,2 # reduction candidate for 1,6 A9: 2 # 18 pairs A9: 1,6 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060518-absurd-base-pr-000.dot * REASONING * DIS # D1: 3,7 => CTR => D1: 1,9 * DIS # G1: 4,9 => CTR => G1: 6 * DIS # H1: 6 => CTR => H1: 2,3 * DIS # G7: 9 => CTR => G7: 1,8 * DIS # I9: 9 => CTR => I9: 1,8 * DIS # A1: 2,5 => CTR => A1: 1,7 * DIS # F6: 4,7 => CTR => F6: 5 * PRF # D5: 6,7 => SOL * DIS # I5: 4 => CTR => I5: 1,3 * DIS # I5: 1,4 => CTR => I5: 3 * DIS # B6: 1,4 => CTR => B6: 7 * DIS # C7: 1,2 => CTR => C7: 9 * DIS # A1: 1,2 => CTR => A1: 5,7 * DIS # A5: 1,2 => CTR => A5: 6,7 * CNT 14 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B4,D4,D6,E1,E7,E8,F5,G2,G3,H2,H5,H9,I3,I6) * .....8...8...6....963452.7...8.1.796.9....5..3...9.28..3.5.6.4748.....52.57...3.. * PAIR E1: 3,7 BLK 2 D1: 3,7,1,9 # reduction candidate for 3,7 D1: 3,7 => CTR * ..4..8.6.87..6.423963452178.48.1.79679...453131..9.284.3.5.684748....652657.4.31. D2: 3,7,1,9 # reduction candidate for 3,7 D2: 3,7 # 19 pairs F2: 3,7,1,9 # reduction candidate for 3,7 F2: 3,7 # 24 pairs * PAIR G2: 4,9 BLK 3 G1: 4,9,6 # reduction candidate for 4,9 G1: 4,9 => CTR * .....8.6.8...6..2.963452178..8.1.796.9....53.3...9.28..3952684748....652657...319 * PAIR E7: 2,8 BLK 8 D9: 2,8,9 # reduction candidate for 2,8 D9: 2,8 # 24 pairs E9: 2,8,4 # reduction candidate for 2,8 E9: 2,8 => CTR * 7.4.386258.576943.963452.7.5.8.1.79669..47513371695284.395.6.47486.7.952.57..436. * RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A7,A9,B1,B2,B4,C1,C2,C5,D1,D4,D8,D9,E5,E7,F2,F4,F5,F8,G3,G7,I1,I2,I3,I9) * 7...3862.8...6.43.963452.7.5.8.1.79669....513371695284.395.6.47486.7.952.57.4936. * PAIR D1: 1,9 BLK 2 D2: 1,9,7 # reduction candidate for 1,9 D2: 1,9 => SOLVED * 714938625825167439963452178548213796692784513371695284139526847486371952257849361 * DURATION: 0:00:07.182904 START: 23:15:07.599869 END: 23:15:14.782773 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060518-absurd-base-pr-001.dot * REASONING * DIS # D1: 3,7 => CTR => D1: 1,9 * DIS D1: 1,9 # G1: 4,9 => CTR => G1: 6 * DIS D1: 1,9 + G1: 6 # E9: 2,8 => CTR => E9: 4 * PRF D1: 1,9 + G1: 6 + E9: 4 # D2: 1,9 => SOL * STA D1: 1,9 + G1: 6 + E9: 4 + D2: 1,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060518, absurd
Solution
position: 714938625825167439963452178548213796692784513371695284139526847486371952257849361 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 # D1: 3,7 => CTR => D1: 1,9 * INC # D1: 1,9 => UNS * INC # D2: 3,7 => UNS * INC # F2: 3,7 => UNS * DIS # G1: 4,9 => CTR => G1: 6 * INC # G1: 6 => UNS * INC # H1: 2,3 => UNS * DIS # H1: 6 => CTR => H1: 2,3 * INC # G7: 1,8 => UNS * DIS # G7: 9 => CTR => G7: 1,8 * INC # I9: 1,8 => UNS * DIS # I9: 9 => CTR => I9: 1,8 * DIS # A1: 2,5 => CTR => A1: 1,7 * INC # A1: 1,7 => UNS * INC # C5: 2,4 => UNS * INC # C5: 1,6 => UNS * INC # B1: 2,4 => UNS * INC # B2: 2,4 => UNS * DIS # F6: 4,7 => CTR => F6: 5 * INC # F6: 5 => UNS * PRF # D5: 6,7 => SOL * INC # D5: 2,8 => UNS * INC # I5: 1,3 => UNS * DIS # I5: 4 => CTR => I5: 1,3 * DIS # I5: 1,4 => CTR => I5: 3 * INC # I5: 3 => UNS * DIS # B6: 1,4 => CTR => B6: 7 * INC # B6: 7 => UNS * INC # C6: 1,4 => UNS * DIS # C7: 1,2 => CTR => C7: 9 * INC # C7: 9 => UNS * INC # A9: 1,2 => UNS * DIS # A1: 1,2 => CTR => A1: 5,7 * INC # A1: 5,7 => UNS * DIS # A5: 1,2 => CTR => A5: 6,7 * INC # A5: 6,7 => UNS * INC # D9: 2,8 => UNS * INC # E9: 2,8 => UNS * INC # E5: 2,8 => UNS * INC # E5: 4 => UNS * INC # D8: 3,7 => UNS * INC # F8: 3,7 => UNS * INC # G8: 1,6 => UNS * INC # G8: 9 => UNS * INC # A9: 1,6 => UNS * INC # A9: 2 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 3,7 => CTR => D1: 1,9 * INC D1: 1,9 # D2: 3,7 => UNS * INC D1: 1,9 # F2: 3,7 => UNS * DIS D1: 1,9 # G1: 4,9 => CTR => G1: 6 * INC D1: 1,9 + G1: 6 # D9: 2,8 => UNS * DIS D1: 1,9 + G1: 6 # E9: 2,8 => CTR => E9: 4 * PRF D1: 1,9 + G1: 6 + E9: 4 # D2: 1,9 => SOL * STA D1: 1,9 + G1: 6 + E9: 4 + D2: 1,9 * CNT 7 HDP CHAINS / 7 HYP OPENED