Analysis of zz-www.sudokuoftheday.co.uk-20060530-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...5...9..5.89.3176..........8.4....7...3.....8175...5.7..21.439.....27.......5. initial
Autosolve
position: 8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G1: 6,7 => SOL * PRF # G1: 6,7 => SOL * PRF # G1: 6,7 => SOL * DIS # H5: 4,8 => CTR => H5: 1,9 * DIS # G5: 4,9 => CTR => G5: 2,5,8 * DIS # H5: 4,9 => CTR => H5: 1,8 * DIS # C9: 1,4 => CTR => C9: 2,6 * DIS # E9: 9 => CTR => E9: 1,4 * DIS # G9: 3,8 => CTR => G9: 9 * PRF # G9: 9 => SOL * CNT 10 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G1: 6,7 => SOL * STA G1: 6,7 * CNT 1 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8...5...9..5.89.3176..........8.4....7...3.....8175...5.7..21.439.....27.......5. | initial |
| 8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5. | autosolve |
| 813257649245689731769431285951824376472963518638175492587392164394516827126748953 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 1,3 C1: 1,3 A2: 2,4 B2: 2,4 D1: 2,4 F1: 6,7 D2: 6,7 G2: 6,7 H3: 4,8 H6: 4,9 C8: 1,4 E8: 1,4 F8: 6,8 F9: 7,8 H7: 6,9 G8: 6,8 I9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 17 pairs (_) / C1 = 1 => 25 pairs (_) H4,H5: 1.. / H4 = 1 => 0 pairs (X) / H5 = 1 => 21 pairs (_) E8,E9: 1.. / E8 = 1 => 17 pairs (_) / E9 = 1 => 18 pairs (_) C8,E8: 1.. / C8 = 1 => 18 pairs (_) / E8 = 1 => 17 pairs (_) B1,B9: 1.. / B1 = 1 => 17 pairs (_) / B9 = 1 => 25 pairs (_) A2,B2: 2.. / A2 = 2 => 17 pairs (_) / B2 = 2 => 19 pairs (_) D1,G1: 2.. / D1 = 2 => 22 pairs (_) / G1 = 2 => 22 pairs (_) B1,C1: 3.. / B1 = 3 => 25 pairs (_) / C1 = 3 => 17 pairs (_) D3,E3: 3.. / D3 = 3 => 20 pairs (_) / E3 = 3 => 22 pairs (_) C4,B6: 3.. / C4 = 3 => 25 pairs (_) / B6 = 3 => 17 pairs (_) D7,E7: 3.. / D7 = 3 => 22 pairs (_) / E7 = 3 => 20 pairs (_) G9,I9: 3.. / G9 = 3 => 0 pairs (X) / I9 = 3 => 21 pairs (_) B1,B6: 3.. / B1 = 3 => 25 pairs (_) / B6 = 3 => 17 pairs (_) C1,C4: 3.. / C1 = 3 => 17 pairs (_) / C4 = 3 => 25 pairs (_) D3,D7: 3.. / D3 = 3 => 20 pairs (_) / D7 = 3 => 22 pairs (_) E3,E7: 3.. / E3 = 3 => 22 pairs (_) / E7 = 3 => 20 pairs (_) A2,B2: 4.. / A2 = 4 => 19 pairs (_) / B2 = 4 => 17 pairs (_) C8,E8: 4.. / C8 = 4 => 17 pairs (_) / E8 = 4 => 18 pairs (_) G3,I3: 5.. / G3 = 5 => 18 pairs (_) / I3 = 5 => 17 pairs (_) G5,I5: 5.. / G5 = 5 => 17 pairs (_) / I5 = 5 => 18 pairs (_) G3,G5: 5.. / G3 = 5 => 18 pairs (_) / G5 = 5 => 17 pairs (_) I3,I5: 5.. / I3 = 5 => 17 pairs (_) / I5 = 5 => 18 pairs (_) F1,D2: 6.. / F1 = 6 => 0 pairs (X) / D2 = 6 => 0 pairs (_) A9,C9: 6.. / A9 = 6 => 18 pairs (_) / C9 = 6 => 19 pairs (_) H7,G8: 6.. / H7 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) D2,G2: 6.. / D2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) A6,I6: 6.. / A6 = 6 => 23 pairs (_) / I6 = 6 => 18 pairs (_) F8,G8: 6.. / F8 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) F1,F8: 6.. / F1 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) H1,H7: 6.. / H1 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) F1,D2: 7.. / F1 = 7 => 0 pairs (*) / D2 = 7 => 0 pairs (X) G4,H4: 7.. / G4 = 7 => 0 pairs (X) / H4 = 7 => 21 pairs (_) D9,F9: 7.. / D9 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) D2,G2: 7.. / D2 = 7 => 0 pairs (X) / G2 = 7 => 0 pairs (_) D2,D9: 7.. / D2 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) F1,F9: 7.. / F1 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) H1,H4: 7.. / H1 = 7 => 0 pairs (X) / H4 = 7 => 21 pairs (_) F8,F9: 8.. / F8 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) F8,G8: 8.. / F8 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) H3,H5: 8.. / H3 = 8 => 19 pairs (_) / H5 = 8 => 0 pairs (X) H7,G9: 9.. / H7 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) * DURATION: 0:00:50.892980 START: 23:30:13.832289 END: 23:31:04.725269 2019-04-30 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B2,C1,C8,D1,D2,E8,F1,F8,F9,G2,G8,H3,H6,H7,I9) * 8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5. * PAIR C1: 1,3 COL C C4: 1,3,2,6 # reduction candidate for 1,3 C4: 1,3 # 23 pairs C4: 2,6 # 18 pairs * PAIR A2: 2,4 COL A A5: 2,4,1,6,9 # reduction candidate for 2,4 A5: 2,4 # 20 pairs A6: 2,4,6,9 # reduction candidate for 2,4 A6: 2,4 # 21 pairs A9: 2,4,1,6 # reduction candidate for 2,4 A9: 2,4 # 23 pairs * PAIR B2: 2,4 COL B B6: 2,4,3 # reduction candidate for 2,4 B6: 2,4 # 25 pairs B9: 2,4,1 # reduction candidate for 2,4 B9: 2,4 # 17 pairs * PAIR D1: 2,4 BLK 2 D3: 2,4,3 # reduction candidate for 2,4 D3: 2,4 # 22 pairs E3: 2,4,3 # reduction candidate for 2,4 E3: 2,4 # 20 pairs * PAIR D1: 2,4 ROW 1 G1: 2,4,6,7 # reduction candidate for 2,4 G1: 6,7 => SOLVED * 813257649245689731769431285951824376472963518638175492587392164394516827126748953 G1: 2,4 # 19 pairs * PAIR F1: 6,7 ROW 1 G1: 6,7,2,4 # reduction candidate for 6,7 G1: 6,7 => SOLVED * 813257649245689731769431285951824376472963518638175492587392164394516827126748953 G1: 2,4 # 19 pairs H1: 6,7,4 # reduction candidate for 6,7 H1: 6,7 # 19 pairs * PAIR G2: 6,7 BLK 3 G1: 6,7,2,4 # reduction candidate for 6,7 G1: 6,7 => SOLVED * 813257649245689731769431285951824376472963518638175492587392164394516827126748953 G1: 2,4 # 19 pairs H1: 6,7,4 # reduction candidate for 6,7 H1: 6,7 # 19 pairs * PAIR H3: 4,8 BLK 3 G3: 4,8,2,5 # reduction candidate for 4,8 G3: 4,8 # 22 pairs G3: 2,5 # 18 pairs * PAIR H3: 4,8 COL H H5: 4,8,1,9 # reduction candidate for 4,8 H5: 4,8 => CTR * 8...5..79..5789631769..1....5.8.471..7...3.....8175...587..216439.5.6.27.......5. H5: 1,9 # 21 pairs * PAIR H6: 4,9 BLK 6 G5: 4,9,2,5,8 # reduction candidate for 4,9 G5: 4,9 => CTR * 8...5...9..5.89.31769..1548.5.8.4.1..7...3.85..8175.9.587..216439.5.6827.......5. G5: 2,5,8 # 17 pairs H5: 4,9,1,8 # reduction candidate for 4,9 H5: 4,9 => CTR * 8...5..79..5789631769..1.8..5.8.471..7...3.....8175...587..216439.5.6.27.......5. H5: 1,8 # 18 pairs G6: 4,9,2,3 # reduction candidate for 4,9 G6: 4,9 # 22 pairs * PAIR H6: 4,9 ROW 6 A6: 4,9,2,6 # reduction candidate for 4,9 A6: 4,9 # 23 pairs A6: 2,6 # 19 pairs * PAIR C8: 1,4 BLK 7 A9: 1,4,2,6 # reduction candidate for 1,4 A9: 1,4 # 17 pairs B9: 1,4,2 # reduction candidate for 1,4 B9: 1,4 # 20 pairs C9: 1,4,2,6 # reduction candidate for 1,4 C9: 1,4 => CTR * 81325...9245.89.31769..1582.5.8.4..3.7...38.5.381752.6587..219439.5.862762...7358 C9: 2,6 # 18 pairs * PAIR C8: 1,4 COL C C5: 1,4,2,6 # reduction candidate for 1,4 C5: 2,6 # 22 pairs C5: 1,4 # 20 pairs * PAIR E8: 1,4 BLK 8 E9: 1,4,9 # reduction candidate for 1,4 E9: 9 => CTR * 8..256..9..5789631769341.8..5.8.4....7...3.....8175...587..21.439.51..27...497.5. E9: 1,4 # 20 pairs * PAIR H7: 6,9 ROW 7 D7: 6,9,3 # reduction candidate for 6,9 D7: 6,9 # 20 pairs E7: 6,9,3 # reduction candidate for 6,9 E7: 6,9 # 22 pairs * PAIR I9: 3,8 BLK 9 G9: 3,8,9 # reduction candidate for 3,8 G9: 3,8 => CTR * 8...56..9..5789.31769..1....5.8.4....7...3.....8175...587..219439.5..627.......5. G9: 9 => SOLVED * 813257649245689731769431285951824376472963518638175492587392164394516827126748953 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060530-absurd-base-pr-000.dot * REASONING * PRF # G1: 6,7 => SOL * PRF # G1: 6,7 => SOL * PRF # G1: 6,7 => SOL * DIS # H5: 4,8 => CTR => H5: 1,9 * DIS # G5: 4,9 => CTR => G5: 2,5,8 * DIS # H5: 4,9 => CTR => H5: 1,8 * DIS # C9: 1,4 => CTR => C9: 2,6 * DIS # E9: 9 => CTR => E9: 1,4 * DIS # G9: 3,8 => CTR => G9: 9 * PRF # G9: 9 => SOL * CNT 10 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B2,C1,C8,D1,D2,E8,F1,F8,F9,G2,G8,H3,H6,H7,I9) * 8...5...9..5.89.31769..1....5.8.4....7...3.....8175...587..21.439.5...27.......5. * PAIR C1: 1,3 COL C C4: 1,3,2,6 # reduction candidate for 1,3 C4: 1,3 # 23 pairs C4: 2,6 # 18 pairs * PAIR A2: 2,4 COL A A5: 2,4,1,6,9 # reduction candidate for 2,4 A5: 2,4 # 20 pairs A6: 2,4,6,9 # reduction candidate for 2,4 A6: 2,4 # 21 pairs A9: 2,4,1,6 # reduction candidate for 2,4 A9: 2,4 # 23 pairs * PAIR B2: 2,4 COL B B6: 2,4,3 # reduction candidate for 2,4 B6: 2,4 # 25 pairs B9: 2,4,1 # reduction candidate for 2,4 B9: 2,4 # 17 pairs * PAIR D1: 2,4 BLK 2 D3: 2,4,3 # reduction candidate for 2,4 D3: 2,4 # 22 pairs E3: 2,4,3 # reduction candidate for 2,4 E3: 2,4 # 20 pairs * PAIR D1: 2,4 ROW 1 G1: 2,4,6,7 # reduction candidate for 2,4 G1: 6,7 => SOLVED * 813257649245689731769431285951824376472963518638175492587392164394516827126748953 * DURATION: 0:00:08.141050 START: 23:31:31.807905 END: 23:31:39.948955 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060530-absurd-base-pr-001.dot * REASONING * PRF # G1: 6,7 => SOL * STA G1: 6,7 * CNT 1 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060530, absurd
Solution
position: 813257649245689731769431285951824376472963518638175492587392164394516827126748953 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:
* INC # C4: 1,3 => UNS * INC # C4: 2,6 => UNS * INC # A5: 2,4 => UNS * INC # A6: 2,4 => UNS * INC # A9: 2,4 => UNS * INC # B6: 2,4 => UNS * INC # B9: 2,4 => UNS * INC # D3: 2,4 => UNS * INC # E3: 2,4 => UNS * INC # G1: 2,4 => UNS * PRF # G1: 6,7 => SOL * PRF # G1: 6,7 => SOL * INC # G1: 2,4 => UNS * INC # H1: 6,7 => UNS * PRF # G1: 6,7 => SOL * INC # G1: 2,4 => UNS * INC # H1: 6,7 => UNS * INC # G3: 4,8 => UNS * INC # G3: 2,5 => UNS * DIS # H5: 4,8 => CTR => H5: 1,9 * INC # H5: 1,9 => UNS * DIS # G5: 4,9 => CTR => G5: 2,5,8 * INC # G5: 2,5,8 => UNS * DIS # H5: 4,9 => CTR => H5: 1,8 * INC # H5: 1,8 => UNS * INC # G6: 4,9 => UNS * INC # A6: 4,9 => UNS * INC # A6: 2,6 => UNS * INC # A9: 1,4 => UNS * INC # B9: 1,4 => UNS * DIS # C9: 1,4 => CTR => C9: 2,6 * INC # C9: 2,6 => UNS * INC # C5: 1,4 => UNS * INC # C5: 2,6 => UNS * INC # E9: 1,4 => UNS * DIS # E9: 9 => CTR => E9: 1,4 * INC # D7: 6,9 => UNS * INC # E7: 6,9 => UNS * DIS # G9: 3,8 => CTR => G9: 9 * PRF # G9: 9 => SOL * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 1,3 => UNS * INC # C4: 2,6 => UNS * INC # A5: 2,4 => UNS * INC # A6: 2,4 => UNS * INC # A9: 2,4 => UNS * INC # B6: 2,4 => UNS * INC # B9: 2,4 => UNS * INC # D3: 2,4 => UNS * INC # E3: 2,4 => UNS * INC # G1: 2,4 => UNS * PRF # G1: 6,7 => SOL * STA G1: 6,7 * CNT 11 HDP CHAINS / 11 HYP OPENED