Analysis of zz-www.sudokuoftheday.co.uk-20190430-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: ..92.8....359..2..4..7.....15..9......4..5.39....8...5..7....1......6..45.3....76 initial
Autosolve
position: ..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 6,7 => CTR => B1: 1 * DIS # A5: 6,7 => CTR => A5: 2,8 * PRF # F6: 1,4 => SOL * DIS # F9: 1,4 => CTR => F9: 2,9 * DIS # E3: 1,3 => CTR => E3: 5,6 * DIS # I3: 8 => CTR => I3: 1,3 * DIS # A5: 2,6 => CTR => A5: 7,8 * DIS # B5: 2,6 => CTR => B5: 7,8 * DIS # C3: 2,6 => CTR => C3: 1,8 * DIS # G5: 8 => CTR => G5: 1,6 * DIS # F6: 1,2 => CTR => F6: 4,7 * DIS # E9: 4 => CTR => E9: 1,2 * DIS # G7: 8,9 => CTR => G7: 3,5 * DIS # G8: 8,9 => CTR => G8: 3,5 * DIS # G3: 8,9 => CTR => G3: 3,5,6 * CNT 15 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 6,7 => CTR => B1: 1 * DIS B1: 1 # A2: 8 => CTR => A2: 6,7 * DIS B1: 1 + A2: 6,7 # C4: 8 => CTR => C4: 2,6 * PRF B1: 1 + A2: 6,7 + C4: 2,6 # E1: 4,6 => SOL * STA B1: 1 + A2: 6,7 + C4: 2,6 + E1: 4,6 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..92.8....359..2..4..7.....15..9......4..5.39....8...5..7....1......6..45.3....76 | initial |
| ..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76 | autosolve |
| 719268453635941287428753691156397842874625139392184765267439518981576324543812976 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 6,7 F2: 1,4 F3: 1,3 C6: 2,6 D5: 1,6 E5: 1,2 G9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,G6: 1.. / G5 = 1 => 20 pairs (_) / G6 = 1 => 11 pairs (_) C3,C8: 1.. / C3 = 1 => 0 pairs (X) / C8 = 1 => 8 pairs (_) B3,C3: 2.. / B3 = 2 => 9 pairs (_) / C3 = 2 => 0 pairs (X) I7,H8: 2.. / I7 = 2 => 9 pairs (_) / H8 = 2 => 16 pairs (_) I4,I7: 2.. / I4 = 2 => 16 pairs (_) / I7 = 2 => 9 pairs (_) D4,F4: 3.. / D4 = 3 => 8 pairs (_) / F4 = 3 => 0 pairs (X) D8,G8: 3.. / D8 = 3 => 0 pairs (X) / G8 = 3 => 8 pairs (_) B7,B9: 4.. / B7 = 4 => 0 pairs (X) / B9 = 4 => 12 pairs (_) E1,E3: 5.. / E1 = 5 => 0 pairs (X) / E3 = 5 => 7 pairs (_) D7,D8: 5.. / D7 = 5 => 7 pairs (_) / D8 = 5 => 8 pairs (_) D7,G7: 5.. / D7 = 5 => 7 pairs (_) / G7 = 5 => 8 pairs (_) A7,B7: 6.. / A7 = 6 => 0 pairs (X) / B7 = 6 => 13 pairs (_) A5,B5: 7.. / A5 = 7 => 0 pairs (X) / B5 = 7 => 8 pairs (_) F4,F6: 7.. / F4 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) A2,I2: 7.. / A2 = 7 => 20 pairs (_) / I2 = 7 => 11 pairs (_) F6,G6: 7.. / F6 = 7 => 7 pairs (_) / G6 = 7 => 0 pairs (*) B1,B5: 7.. / B1 = 7 => 0 pairs (X) / B5 = 7 => 8 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (X) / H3 = 9 => 7 pairs (_) A7,A8: 9.. / A7 = 9 => 0 pairs (X) / A8 = 9 => 7 pairs (_) F7,F9: 9.. / F7 = 9 => 6 pairs (_) / F9 = 9 => 0 pairs (X) F9,G9: 9.. / F9 = 9 => 0 pairs (X) / G9 = 9 => 6 pairs (_) H3,H8: 9.. / H3 = 9 => 7 pairs (_) / H8 = 9 => 0 pairs (X) * DURATION: 0:00:19.711048 START: 05:42:36.610627 END: 05:42:56.321675 2019-05-01 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C6,D5,E5,F2,F3,G9) * ..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76 * PAIR A1: 6,7 BLK 1 B1: 6,7,1 # reduction candidate for 6,7 B1: 6,7 => CTR * ..92.8..38359..2..4..7.3..815.39......4..5.3939..8...5..7.3..12....763.45.3....76 B1: 1 # 9 pairs A2: 6,7,8 # reduction candidate for 6,7 A2: 6,7 # 20 pairs * PAIR A1: 6,7 ROW 1 G1: 6,7,3,4,5 # reduction candidate for 6,7 G1: 6,7 # 15 pairs G1: 3,4,5 # 8 pairs * PAIR A1: 6,7 COL A A5: 6,7,2,8 # reduction candidate for 6,7 A5: 6,7 => CTR * .192.8..38359..2.7426753..115839...267412583939268.145267439518981576324543....76 A5: 2,8 # 9 pairs * PAIR F2: 1,4 BLK 2 E1: 1,4,3,5,6 # reduction candidate for 1,4 E1: 1,4 # 11 pairs E2: 1,4,6 # reduction candidate for 1,4 E2: 1,4 # 14 pairs * PAIR F2: 1,4 COL F F6: 1,4,2,7 # reduction candidate for 1,4 F6: 1,4 => SOLVED * 719268453635941287428753691156397842874625139392184765267439518981576324543812976 F6: 2,7 # 8 pairs F9: 1,4,2,9 # reduction candidate for 1,4 F9: 1,4 => CTR * ..92.87537359.124848.7...9.158392..7..4615839396487125..7.395129..5763845.3124976 F9: 2,9 # 8 pairs * PAIR F3: 1,3 BLK 2 E1: 1,3,4,5,6 # reduction candidate for 1,3 E1: 1,3 # 19 pairs E3: 1,3,5,6 # reduction candidate for 1,3 E3: 1,3 => CTR * ..9258....359642814..7....315..9......4..5.3939..8...5..7.3..1.....763.45.3.4..76 E3: 5,6 # 8 pairs * PAIR F3: 1,3 ROW 3 I3: 1,3,8 # reduction candidate for 1,3 I3: 8 => CTR * .792.8.518359..2.74.17...9815..93782.84..5.3939..87..5..75..8139183765245.38..976 I3: 1,3 # 11 pairs * PAIR C6: 2,6 BLK 4 C4: 2,6,8 # reduction candidate for 2,6 C4: 2,6 # 20 pairs A5: 2,6,7,8 # reduction candidate for 2,6 A5: 2,6 => CTR * ..924875373596124848.75.69.158.92467274615839396487125..7..9.129...76.845.3124976 A5: 7,8 # 20 pairs B5: 2,6,7,8 # reduction candidate for 2,6 B5: 2,6 => CTR * 6792.8...8359..2.74..7...98158.9.7.27.4..583939648.1.5..7....1.....76..45.3...976 B5: 7,8 # 8 pairs * PAIR C6: 2,6 ROW 6 H6: 2,6,4 # reduction candidate for 2,6 H6: 4 # 21 pairs H6: 2,6 # 9 pairs * PAIR C6: 2,6 COL C C3: 2,6,1,8 # reduction candidate for 2,6 C3: 2,6 => CTR * ..924875373596124848275.69.158.92467274615839396487125..7..9.12921.76.845.3124976 C3: 1,8 # 12 pairs * PAIR D5: 1,6 BLK 5 D6: 1,6,4 # reduction candidate for 1,6 D6: 1,6 # 18 pairs D6: 4 # 12 pairs * PAIR D5: 1,6 ROW 5 G5: 1,6,8 # reduction candidate for 1,6 G5: 8 => CTR * ..924875373596124848.75.69.158.92467274615839396487125..7..9.129...76.845.3124976 G5: 1,6 # 20 pairs * PAIR E5: 1,2 BLK 5 F6: 1,2,4,7 # reduction candidate for 1,2 F6: 1,2 => CTR * .192.8..3.359142.7462753..1158397..27.462513939.4817.5.47.3..1...1.763.45.314..76 F6: 4,7 # 8 pairs * PAIR E5: 1,2 COL E E9: 1,2,4 # reduction candidate for 1,2 E9: 4 => CTR * 7.92.8...8359.42674..7...9.15..9....274.15.3939..8...5647....1.9...76..45.3.4..76 E9: 1,2 # 10 pairs * PAIR G9: 8,9 BLK 9 G7: 8,9,3,5 # reduction candidate for 8,9 G7: 8,9 => CTR * ..92.8.5..359..2..42.75.69.15..93..2..462513939218746526754.8139..376524543812976 G7: 3,5 # 8 pairs G8: 8,9,3,5 # reduction candidate for 8,9 G8: 8,9 => CTR * ..92.8....359..2..4..7.1.9.15..93.....4.25.3939..87..5..7549312...376.545.38.2976 G8: 3,5 # 8 pairs H8: 8,9,2,5 # reduction candidate for 8,9 H8: 8,9 # 14 pairs * PAIR G9: 8,9 COL G G3: 8,9,3,5,6 # reduction candidate for 8,9 G3: 8,9 => CTR * ..92.8....359..2..42.7..89.15..9......4.25.3939..8...5.67..9.1.9.8.76.24543812976 G3: 3,5,6 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190430-absurd-base-pr-000.dot * REASONING * DIS # B1: 6,7 => CTR => B1: 1 * DIS # A5: 6,7 => CTR => A5: 2,8 * PRF # F6: 1,4 => SOL * DIS # F9: 1,4 => CTR => F9: 2,9 * DIS # E3: 1,3 => CTR => E3: 5,6 * DIS # I3: 8 => CTR => I3: 1,3 * DIS # A5: 2,6 => CTR => A5: 7,8 * DIS # B5: 2,6 => CTR => B5: 7,8 * DIS # C3: 2,6 => CTR => C3: 1,8 * DIS # G5: 8 => CTR => G5: 1,6 * DIS # F6: 1,2 => CTR => F6: 4,7 * DIS # E9: 4 => CTR => E9: 1,2 * DIS # G7: 8,9 => CTR => G7: 3,5 * DIS # G8: 8,9 => CTR => G8: 3,5 * DIS # G3: 8,9 => CTR => G3: 3,5,6 * CNT 15 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C6,D5,E5,F2,F3,G9) * ..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76 * PAIR A1: 6,7 BLK 1 B1: 6,7,1 # reduction candidate for 6,7 B1: 6,7 => CTR * ..92.8..38359..2..4..7.3..815.39......4..5.3939..8...5..7.3..12....763.45.3....76 A2: 6,7,8 # reduction candidate for 6,7 A2: 6,7 # 20 pairs * RESTART * PAIR A1: 6,7 BLK 1 A2: 6,7,8 # reduction candidate for 6,7 A2: 8 => CTR * 7192.8..38359..2.74..7....1158.9...2.74..583939..8.1.5..7....18..1.76.245.3...976 * PAIR A1: 6,7 ROW 1 G1: 6,7,3,4,5 # reduction candidate for 6,7 G1: 6,7 # 25 pairs G1: 3,4,5 # 21 pairs * PAIR C6: 2,6 BLK 4 C4: 2,6,8 # reduction candidate for 2,6 C4: 8 => CTR * .192.8....359..2..4..7.....158.9....274.1583939648...5.67....1...1.76..4543....76 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A2,D4,D8,E2,E7,F2,F3,F6,G1,G6,G8,H2,H4,I1,I3,I7) * .192.8.5..359..2..42875.69.156.9...287462513939218..65267..9.1.981.76.24543812976 * PAIR E2: 4,6 BLK 2 E1: 4,6,3 # reduction candidate for 4,6 E1: 4,6 => SOLVED * 719268453635941287428753691156397842874625139392184765267439518981576324543812976 * DURATION: 0:00:07.218837 START: 05:43:18.725820 END: 05:43:25.944657 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190430-absurd-base-pr-001.dot * REASONING * DIS # B1: 6,7 => CTR => B1: 1 * DIS B1: 1 # A2: 8 => CTR => A2: 6,7 * DIS B1: 1 + A2: 6,7 # C4: 8 => CTR => C4: 2,6 * PRF B1: 1 + A2: 6,7 + C4: 2,6 # E1: 4,6 => SOL * STA B1: 1 + A2: 6,7 + C4: 2,6 + E1: 4,6 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190430, absurd
Solution
position: 719268453635941287428753691156397842874625139392184765267439518981576324543812976 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 # B1: 6,7 => CTR => B1: 1 * INC # B1: 1 => UNS * INC # A2: 6,7 => UNS * INC # G1: 6,7 => UNS * INC # G1: 3,4,5 => UNS * DIS # A5: 6,7 => CTR => A5: 2,8 * INC # A5: 2,8 => UNS * INC # E1: 1,4 => UNS * INC # E2: 1,4 => UNS * PRF # F6: 1,4 => SOL * INC # F6: 2,7 => UNS * DIS # F9: 1,4 => CTR => F9: 2,9 * INC # F9: 2,9 => UNS * INC # E1: 1,3 => UNS * DIS # E3: 1,3 => CTR => E3: 5,6 * INC # E3: 5,6 => UNS * INC # I3: 1,3 => UNS * DIS # I3: 8 => CTR => I3: 1,3 * INC # C4: 2,6 => UNS * DIS # A5: 2,6 => CTR => A5: 7,8 * INC # A5: 7,8 => UNS * DIS # B5: 2,6 => CTR => B5: 7,8 * INC # B5: 7,8 => UNS * INC # H6: 2,6 => UNS * INC # H6: 4 => UNS * DIS # C3: 2,6 => CTR => C3: 1,8 * INC # C3: 1,8 => UNS * INC # D6: 1,6 => UNS * INC # D6: 4 => UNS * INC # G5: 1,6 => UNS * DIS # G5: 8 => CTR => G5: 1,6 * DIS # F6: 1,2 => CTR => F6: 4,7 * INC # F6: 4,7 => UNS * INC # E9: 1,2 => UNS * DIS # E9: 4 => CTR => E9: 1,2 * DIS # G7: 8,9 => CTR => G7: 3,5 * INC # G7: 3,5 => UNS * DIS # G8: 8,9 => CTR => G8: 3,5 * INC # G8: 3,5 => UNS * INC # H8: 8,9 => UNS * DIS # G3: 8,9 => CTR => G3: 3,5,6 * INC # G3: 3,5,6 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 6,7 => CTR => B1: 1 * INC B1: 1 # A2: 6,7 => UNS * INC B1: 1 # A2: 6,7 => UNS * DIS B1: 1 # A2: 8 => CTR => A2: 6,7 * INC B1: 1 + A2: 6,7 # G1: 6,7 => UNS * INC B1: 1 + A2: 6,7 # G1: 3,4,5 => UNS * INC B1: 1 + A2: 6,7 # C4: 2,6 => UNS * DIS B1: 1 + A2: 6,7 # C4: 8 => CTR => C4: 2,6 * PRF B1: 1 + A2: 6,7 + C4: 2,6 # E1: 4,6 => SOL * STA B1: 1 + A2: 6,7 + C4: 2,6 + E1: 4,6 * CNT 9 HDP CHAINS / 9 HYP OPENED