Analysis of zz-www.sudokuoftheday.co.uk-20060603-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: ....5...2..51..87..74..8.9..4.291......76.........46..72......3.8....951......... initial
Autosolve
position: ....57..2..51..87..74..8.9..4.291......76.........46..72....4.3.8..72951......... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D1: 3,6 => SOL * DIS # F2: 3,6 => CTR => F2: 9 * DIS # D9: 3,6 => CTR => D9: 4,8,9 * DIS # E2: 2,3 => CTR => E2: 4 * PRF # E2: 4 => SOL * DIS # H1: 1,3 => CTR => H1: 4,6 * DIS # C1: 1,3 => CTR => C1: 6,8,9 * DIS # G5: 1,3 => CTR => G5: 2,5 * DIS # H1: 1,3 => CTR => H1: 4,6 * DIS # D6: 8 => CTR => D6: 3,5 * PRF # G5: 3,5 => SOL * PRF # E9: 3,8 => SOL * DIS # H5: 3,8 => CTR => H5: 1,2,4 * DIS # A4: 3,8 => CTR => A4: 5,6 * DIS # C4: 3,8 => CTR => C4: 6,7 * PRF # A8: 3,6 => SOL * PRF # D8: 4 => SOL * DIS # E9: 1,8 => CTR => E9: 3,4 * DIS # I9: 6,8 => CTR => I9: 7 * CNT 19 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:
* PRF # D1: 3,6 => SOL * STA D1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....5...2..51..87..74..8.9..4.291......76.........46..72......3.8....951......... | initial |
| ....57..2..51..87..74..8.9..4.291......76.........46..72....4.3.8..72951......... | autosolve |
| 968357142235149876174628395546291738892763514317584629729815463683472951451936287 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) D3: 3,6 E3: 2,3 G1: 1,3 I2: 4,6 I3: 5,6 F5: 3,5 E6: 3,8 H4: 3,8 C8: 3,6 E7: 1,8 H7: 6,8 G9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,E9: 1.. / E7 = 1 => 12 pairs (_) / E9 = 1 => 0 pairs (X) A3,G3: 1.. / A3 = 1 => 13 pairs (_) / G3 = 1 => 15 pairs (_) C7,E7: 1.. / C7 = 1 => 0 pairs (X) / E7 = 1 => 12 pairs (_) A2,A3: 2.. / A2 = 2 => 12 pairs (_) / A3 = 2 => 0 pairs (X) E2,E3: 2.. / E2 = 2 => 0 pairs (X) / E3 = 2 => 12 pairs (_) C5,C6: 2.. / C5 = 2 => 17 pairs (_) / C6 = 2 => 0 pairs (X) G9,H9: 2.. / G9 = 2 => 17 pairs (_) / H9 = 2 => 0 pairs (X) A2,E2: 2.. / A2 = 2 => 12 pairs (_) / E2 = 2 => 0 pairs (X) A3,E3: 2.. / A3 = 2 => 0 pairs (X) / E3 = 2 => 12 pairs (_) C6,H6: 2.. / C6 = 2 => 0 pairs (X) / H6 = 2 => 17 pairs (_) G5,G9: 2.. / G5 = 2 => 0 pairs (X) / G9 = 2 => 17 pairs (_) D1,E2: 4.. / D1 = 4 => 0 pairs (X) / E2 = 4 => 0 pairs (_) H1,I2: 4.. / H1 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) H5,I5: 4.. / H5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) A8,A9: 4.. / A8 = 4 => 15 pairs (_) / A9 = 4 => 0 pairs (*) D1,H1: 4.. / D1 = 4 => 0 pairs (X) / H1 = 4 => 0 pairs (_) E2,I2: 4.. / E2 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) A8,D8: 4.. / A8 = 4 => 15 pairs (_) / D8 = 4 => 0 pairs (*) E2,E9: 4.. / E2 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) H1,H5: 4.. / H1 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) I2,I5: 4.. / I2 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) G3,I3: 5.. / G3 = 5 => 0 pairs (X) / I3 = 5 => 17 pairs (_) F5,D6: 5.. / F5 = 5 => 14 pairs (_) / D6 = 5 => 14 pairs (_) A9,B9: 5.. / A9 = 5 => 16 pairs (_) / B9 = 5 => 12 pairs (_) D7,F7: 5.. / D7 = 5 => 14 pairs (_) / F7 = 5 => 14 pairs (_) D6,D7: 5.. / D6 = 5 => 14 pairs (_) / D7 = 5 => 14 pairs (_) F5,F7: 5.. / F5 = 5 => 14 pairs (_) / F7 = 5 => 14 pairs (_) A4,C4: 6.. / A4 = 6 => 14 pairs (_) / C4 = 6 => 21 pairs (_) C4,C6: 7.. / C4 = 7 => 0 pairs (X) / C6 = 7 => 17 pairs (_) G9,I9: 7.. / G9 = 7 => 0 pairs (X) / I9 = 7 => 17 pairs (_) C6,I6: 7.. / C6 = 7 => 17 pairs (_) / I6 = 7 => 0 pairs (X) G4,G9: 7.. / G4 = 7 => 17 pairs (_) / G9 = 7 => 0 pairs (X) A1,C1: 8.. / A1 = 8 => 20 pairs (_) / C1 = 8 => 12 pairs (_) D6,E6: 8.. / D6 = 8 => 0 pairs (X) / E6 = 8 => 13 pairs (_) D1,F2: 9.. / D1 = 9 => 0 pairs (X) / F2 = 9 => 20 pairs (_) I5,I6: 9.. / I5 = 9 => 0 pairs (X) / I6 = 9 => 16 pairs (_) * DURATION: 0:00:36.699062 START: 23:35:31.036053 END: 23:36:07.735115 2019-04-30 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D3,E3,E6,E7,F5,G1,G9,H4,H7,I2,I3) * ....57..2..51..87..74..8.9..4.291......76.........46..72....4.3.8..72951......... * PAIR D3: 3,6 BLK 2 D1: 3,6,4,9 # reduction candidate for 3,6 D1: 3,6 => SOLVED * 968357142235149876174628395546291738892763514317584629729815463683472951451936287 D1: 4,9 # 13 pairs F2: 3,6,9 # reduction candidate for 3,6 F2: 3,6 => CTR * ...957.42295143876.74628.95.4.291......765..4..7..462972.5..4.3.8..72951......2.7 F2: 9 # 20 pairs * PAIR D3: 3,6 ROW 3 A3: 3,6,1,2 # reduction candidate for 3,6 A3: 3,6 # 16 pairs A3: 1,2 # 13 pairs * PAIR D3: 3,6 COL D D8: 3,6,4 # reduction candidate for 3,6 D8: 3,6 # 15 pairs D9: 3,6,4,8,9 # reduction candidate for 3,6 D9: 3,6 => CTR * .6.957.42295143876.74628.95.4.291...9..765..45.783462972.5..4.3.8.47295145.3..2.7 D9: 4,8,9 # 12 pairs * PAIR E3: 2,3 BLK 2 E2: 2,3,4 # reduction candidate for 2,3 E2: 2,3 => CTR * ...457..2..51.9874.746.8.95.4.291......76..4......46..72....4.3486372951....46... E2: 4 => SOLVED * 968357142235149876174628395546291738892763514317584629729815463683472951451936287 * PAIR E3: 2,3 ROW 3 A3: 2,3,1,6 # reduction candidate for 2,3 A3: 2,3 # 19 pairs A3: 1,6 # 13 pairs * PAIR G1: 1,3 BLK 3 H1: 1,3,4,6 # reduction candidate for 1,3 H1: 1,3 => CTR * ...457..2..51.9874.746.8.95.4.291......76..4......46..72....4.3486372951....46... H1: 4,6 # 17 pairs G3: 1,3,5 # reduction candidate for 1,3 G3: 1,3 # 17 pairs * PAIR G1: 1,3 ROW 1 A1: 1,3,6,8,9 # reduction candidate for 1,3 A1: 1,3 # 19 pairs B1: 1,3,6,9 # reduction candidate for 1,3 B1: 1,3 # 18 pairs C1: 1,3,6,8,9 # reduction candidate for 1,3 C1: 1,3 => CTR * 8..457.62.651.9874.746.8.95647291538..876.2499.2..461772..16483486372951......726 C1: 6,8,9 # 12 pairs * PAIR G1: 1,3 COL G G5: 1,3,2,5 # reduction candidate for 1,3 G5: 1,3 => CTR * ....57..2..51..874174328596.4.2917....276......7..462.72....4.3.8..72951......2.7 G5: 2,5 # 13 pairs * PAIR I2: 4,6 BLK 3 H1: 4,6,1,3 # reduction candidate for 4,6 H1: 1,3 => CTR * ...457..2..51.9874.746.8.95.4.291......76..4......46..72....4.3486372951....46... H1: 4,6 # 17 pairs * PAIR F5: 3,5 BLK 5 D6: 3,5,8 # reduction candidate for 3,5 D6: 8 => CTR * ....57..22.514.876.74.28.95.4.2915.....765..4...8346.972.5..4.3.8..72951......728 D6: 3,5 # 13 pairs * PAIR F5: 3,5 ROW 5 A5: 3,5,1,8,9 # reduction candidate for 3,5 A5: 3,5 # 21 pairs B5: 3,5,1,9 # reduction candidate for 3,5 B5: 3,5 # 14 pairs G5: 3,5,1,2 # reduction candidate for 3,5 G5: 3,5 => SOLVED * 968357142235149876174628395546291738892763514317584629729815463683472951451936287 G5: 1,2 # 13 pairs * PAIR E6: 3,8 BLK 5 D6: 3,8,5 # reduction candidate for 3,8 D6: 5 # 14 pairs D6: 3,8 # 14 pairs * PAIR E6: 3,8 COL E E9: 3,8,1,4 # reduction candidate for 3,8 E9: 3,8 => SOLVED * 968357142235149876174628395546291738892763514317584629729815463683472951451936287 E9: 1,4 # 13 pairs * PAIR H4: 3,8 BLK 6 H5: 3,8,1,2,4 # reduction candidate for 3,8 H5: 3,8 => CTR * ....57.42..514.876.74.28.95.4.291......76...4.....461972....4.3.8..72951.......2. H5: 1,2,4 # 12 pairs * PAIR H4: 3,8 ROW 4 A4: 3,8,5,6 # reduction candidate for 3,8 A4: 3,8 => CTR * ..8457312..51..874.74..8596846291735..276.148..7..462972....4.3.83.72951....4.2.7 A4: 5,6 # 13 pairs C4: 3,8,6,7 # reduction candidate for 3,8 C4: 3,8 => CTR * 8..457312..51..874.74..8596648291735..276.148..7..462972....4.3.8..72951....4.2.7 C4: 6,7 # 13 pairs * PAIR C8: 3,6 BLK 7 A8: 3,6,4 # reduction candidate for 3,6 A8: 3,6 => SOLVED * 968357142235149876174628395546291738892763514317584629729815463683472951451936287 A8: 4 # 15 pairs A9: 3,6,1,4,5,9 # reduction candidate for 3,6 A9: 3,6 # 19 pairs B9: 3,6,1,5,9 # reduction candidate for 3,6 B9: 3,6 # 19 pairs C9: 3,6,1,9 # reduction candidate for 3,6 C9: 3,6 # 22 pairs * PAIR C8: 3,6 ROW 8 D8: 3,6,4 # reduction candidate for 3,6 D8: 4 => SOLVED * 968357142235149876174628395546291738892763514317584629729815463683472951451936287 D8: 3,6 # 15 pairs * PAIR C8: 3,6 COL C C1: 3,6,1,8,9 # reduction candidate for 3,6 C1: 3,6 # 23 pairs C4: 3,6,7,8 # reduction candidate for 3,6 C4: 3,6 # 21 pairs * PAIR E7: 1,8 BLK 8 E9: 1,8,3,4 # reduction candidate for 1,8 E9: 1,8 => CTR * ....57.422.514.876.74.28.95.4.291......765..4..783462972.5..4.3.8..72951......2.7 E9: 3,4 # 13 pairs * PAIR H7: 6,8 BLK 9 H9: 6,8,2 # reduction candidate for 6,8 H9: 6,8 # 17 pairs I9: 6,8,7 # reduction candidate for 6,8 I9: 6,8 => CTR * ...457..2..51.9874.746.8.95647291538...76.249..2..461772..1.483486372951...84672. I9: 7 # 17 pairs * PAIR H7: 6,8 ROW 7 D7: 6,8,5,9 # reduction candidate for 6,8 D7: 6,8 # 14 pairs D7: 5,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060603-absurd-base-pr-000.dot * REASONING * PRF # D1: 3,6 => SOL * DIS # F2: 3,6 => CTR => F2: 9 * DIS # D9: 3,6 => CTR => D9: 4,8,9 * DIS # E2: 2,3 => CTR => E2: 4 * PRF # E2: 4 => SOL * DIS # H1: 1,3 => CTR => H1: 4,6 * DIS # C1: 1,3 => CTR => C1: 6,8,9 * DIS # G5: 1,3 => CTR => G5: 2,5 * DIS # H1: 1,3 => CTR => H1: 4,6 * DIS # D6: 8 => CTR => D6: 3,5 * PRF # G5: 3,5 => SOL * PRF # E9: 3,8 => SOL * DIS # H5: 3,8 => CTR => H5: 1,2,4 * DIS # A4: 3,8 => CTR => A4: 5,6 * DIS # C4: 3,8 => CTR => C4: 6,7 * PRF # A8: 3,6 => SOL * PRF # D8: 4 => SOL * DIS # E9: 1,8 => CTR => E9: 3,4 * DIS # I9: 6,8 => CTR => I9: 7 * CNT 19 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D3,E3,E6,E7,F5,G1,G9,H4,H7,I2,I3) * ....57..2..51..87..74..8.9..4.291......76.........46..72....4.3.8..72951......... * PAIR D3: 3,6 BLK 2 D1: 3,6,4,9 # reduction candidate for 3,6 D1: 3,6 => SOLVED * 968357142235149876174628395546291738892763514317584629729815463683472951451936287 * DURATION: 0:00:01.907685 START: 23:36:38.119198 END: 23:36:40.026883 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060603-absurd-base-pr-001.dot * REASONING * PRF # D1: 3,6 => SOL * STA D1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060603, absurd
Solution
position: 968357142235149876174628395546291738892763514317584629729815463683472951451936287 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:
* PRF # D1: 3,6 => SOL * INC # D1: 4,9 => UNS * DIS # F2: 3,6 => CTR => F2: 9 * INC # F2: 9 => UNS * INC # A3: 3,6 => UNS * INC # A3: 1,2 => UNS * INC # D8: 3,6 => UNS * DIS # D9: 3,6 => CTR => D9: 4,8,9 * INC # D9: 4,8,9 => UNS * DIS # E2: 2,3 => CTR => E2: 4 * PRF # E2: 4 => SOL * INC # A3: 2,3 => UNS * INC # A3: 1,6 => UNS * DIS # H1: 1,3 => CTR => H1: 4,6 * INC # H1: 4,6 => UNS * INC # G3: 1,3 => UNS * INC # A1: 1,3 => UNS * INC # B1: 1,3 => UNS * DIS # C1: 1,3 => CTR => C1: 6,8,9 * INC # C1: 6,8,9 => UNS * DIS # G5: 1,3 => CTR => G5: 2,5 * INC # G5: 2,5 => UNS * INC # H1: 4,6 => UNS * DIS # H1: 1,3 => CTR => H1: 4,6 * INC # D6: 3,5 => UNS * DIS # D6: 8 => CTR => D6: 3,5 * INC # A5: 3,5 => UNS * INC # B5: 3,5 => UNS * PRF # G5: 3,5 => SOL * INC # G5: 1,2 => UNS * INC # D6: 3,8 => UNS * INC # D6: 5 => UNS * PRF # E9: 3,8 => SOL * INC # E9: 1,4 => UNS * DIS # H5: 3,8 => CTR => H5: 1,2,4 * INC # H5: 1,2,4 => UNS * DIS # A4: 3,8 => CTR => A4: 5,6 * INC # A4: 5,6 => UNS * DIS # C4: 3,8 => CTR => C4: 6,7 * INC # C4: 6,7 => UNS * PRF # A8: 3,6 => SOL * INC # A8: 4 => UNS * INC # A9: 3,6 => UNS * INC # B9: 3,6 => UNS * INC # C9: 3,6 => UNS * INC # D8: 3,6 => UNS * PRF # D8: 4 => SOL * INC # C1: 3,6 => UNS * INC # C4: 3,6 => UNS * DIS # E9: 1,8 => CTR => E9: 3,4 * INC # E9: 3,4 => UNS * INC # H9: 6,8 => UNS * DIS # I9: 6,8 => CTR => I9: 7 * INC # I9: 7 => UNS * INC # D7: 6,8 => UNS * INC # D7: 5,9 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D1: 3,6 => SOL * STA D1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED