Analysis of zz-www.sudokuoftheday.co.uk-20060428-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: 5...9.2....2..54.....4.2.19..5..6.78.8.14.6..........43.726........7....8.6.5.... initial
Autosolve
position: 5...982..932.1548...8432519..5.26.78.8.14.6.....58...43.726.8.....87....8.6.5.7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B7: 1,4 => SOL * DIS # B9: 1,4 => CTR => B9: 2,9 * PRF # C8: 9 => SOL * PRF # B4: 9 => SOL * PRF # C6: 1 => SOL * PRF # G4: 1 => SOL * PRF # B7: 1,4 => SOL * DIS # B9: 1,4 => CTR => B9: 2,9 * PRF # F8: 1,4 => SOL * PRF # F9: 3,9 => SOL * PRF # F8: 1,4 => SOL * PRF # G6: 3,9 => SOL * CNT 12 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B7: 1,4 => SOL * STA B7: 1,4 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5...9.2....2..54.....4.2.19..5..6.78.8.14.6..........43.726........7....8.6.5.... | initial |
| 5...982..932.1548...8432519..5.26.78.8.14.6.....58...43.726.8.....87....8.6.5.7.. | autosolve |
| 514798263932615487678432519495326178783149652261587934347261895159874326826953741 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 1,4 C1: 1,4 A3: 6,7 B3: 6,7 D1: 6,7 D2: 6,7 H1: 3,6 I2: 6,7 A4: 1,4 A5: 2,7 C5: 3,9 B6: 6,7 D4: 3,9 A8: 1,4 B8: 2,5 D9: 3,9 I7: 1,5 G8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 18 pairs (_) / C1 = 1 => 21 pairs (_) G4,G6: 1.. / G4 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) I7,I9: 1.. / I7 = 1 => 19 pairs (_) / I9 = 1 => 20 pairs (_) C6,G6: 1.. / C6 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) A4,A8: 1.. / A4 = 1 => 21 pairs (_) / A8 = 1 => 18 pairs (_) A5,A6: 2.. / A5 = 2 => 21 pairs (_) / A6 = 2 => 18 pairs (_) B8,B9: 2.. / B8 = 2 => 21 pairs (_) / B9 = 2 => 20 pairs (_) A6,H6: 2.. / A6 = 2 => 18 pairs (_) / H6 = 2 => 21 pairs (_) H1,I1: 3.. / H1 = 3 => 20 pairs (_) / I1 = 3 => 17 pairs (_) C5,C6: 3.. / C5 = 3 => 20 pairs (_) / C6 = 3 => 28 pairs (_) D4,G4: 3.. / D4 = 3 => 20 pairs (_) / G4 = 3 => 0 pairs (X) F8,G8: 3.. / F8 = 3 => 0 pairs (X) / G8 = 3 => 0 pairs (_) D4,D9: 3.. / D4 = 3 => 20 pairs (_) / D9 = 3 => 0 pairs (X) B1,C1: 4.. / B1 = 4 => 21 pairs (_) / C1 = 4 => 18 pairs (_) A4,B4: 4.. / A4 = 4 => 18 pairs (_) / B4 = 4 => 21 pairs (_) H7,H9: 4.. / H7 = 4 => 19 pairs (_) / H9 = 4 => 19 pairs (_) A4,A8: 4.. / A4 = 4 => 18 pairs (_) / A8 = 4 => 21 pairs (_) C1,C8: 4.. / C1 = 4 => 18 pairs (_) / C8 = 4 => 21 pairs (_) H5,I5: 5.. / H5 = 5 => 21 pairs (_) / I5 = 5 => 21 pairs (_) B7,B8: 5.. / B7 = 5 => 21 pairs (_) / B8 = 5 => 20 pairs (_) A3,B3: 6.. / A3 = 6 => 16 pairs (_) / B3 = 6 => 17 pairs (_) D1,D2: 6.. / D1 = 6 => 16 pairs (_) / D2 = 6 => 16 pairs (_) A6,B6: 6.. / A6 = 6 => 17 pairs (_) / B6 = 6 => 16 pairs (_) H8,I8: 6.. / H8 = 6 => 20 pairs (_) / I8 = 6 => 17 pairs (_) D2,I2: 6.. / D2 = 6 => 16 pairs (_) / I2 = 6 => 16 pairs (_) A3,A6: 6.. / A3 = 6 => 16 pairs (_) / A6 = 6 => 17 pairs (_) B3,B6: 6.. / B3 = 6 => 17 pairs (_) / B6 = 6 => 16 pairs (_) H1,H8: 6.. / H1 = 6 => 17 pairs (_) / H8 = 6 => 20 pairs (_) A3,B3: 7.. / A3 = 7 => 17 pairs (_) / B3 = 7 => 16 pairs (_) D1,D2: 7.. / D1 = 7 => 16 pairs (_) / D2 = 7 => 16 pairs (_) I1,I2: 7.. / I1 = 7 => 16 pairs (_) / I2 = 7 => 16 pairs (_) F5,F6: 7.. / F5 = 7 => 21 pairs (_) / F6 = 7 => 18 pairs (_) D1,I1: 7.. / D1 = 7 => 16 pairs (_) / I1 = 7 => 16 pairs (_) D2,I2: 7.. / D2 = 7 => 16 pairs (_) / I2 = 7 => 16 pairs (_) A5,F5: 7.. / A5 = 7 => 18 pairs (_) / F5 = 7 => 21 pairs (_) B3,B6: 7.. / B3 = 7 => 16 pairs (_) / B6 = 7 => 17 pairs (_) D4,D9: 9.. / D4 = 9 => 0 pairs (X) / D9 = 9 => 20 pairs (_) * DURATION: 0:00:47.353251 START: 22:43:24.178379 END: 22:44:11.531630 2019-04-30 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A5,A8,B1,B3,B6,B8,C1,C5,D1,D2,D4,D9,G8,H1,I2,I7) * 5...982..932.1548...8432519..5.26.78.8.14.6.....58...43.726.8.....87....8.6.5.7.. * PAIR B1: 1,4 COL B B4: 1,4,9 # reduction candidate for 1,4 B4: 1,4 # 27 pairs B7: 1,4,5,9 # reduction candidate for 1,4 B7: 1,4 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 B7: 5,9 # 19 pairs B9: 1,4,2,9 # reduction candidate for 1,4 B9: 1,4 => CTR * 5.4.982..932.1548...8432519.95326178.8314.6.5..158.93435726.8.11298743..8.6.5.7.2 B9: 2,9 # 19 pairs * PAIR C1: 1,4 COL C C8: 1,4,9 # reduction candidate for 1,4 C8: 9 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 C8: 1,4 # 27 pairs * PAIR A3: 6,7 COL A A6: 6,7,2 # reduction candidate for 6,7 A6: 6,7 # 21 pairs A6: 2 # 18 pairs * PAIR D1: 6,7 ROW 1 I1: 6,7,3 # reduction candidate for 6,7 I1: 6,7 # 20 pairs I1: 3 # 17 pairs * PAIR H1: 3,6 BLK 3 I1: 3,6,7 # reduction candidate for 3,6 I1: 7 # 16 pairs I1: 3,6 # 16 pairs * PAIR I2: 6,7 BLK 3 I1: 6,7,3 # reduction candidate for 6,7 I1: 6,7 # 20 pairs I1: 3 # 17 pairs * PAIR A4: 1,4 BLK 4 B4: 1,4,9 # reduction candidate for 1,4 B4: 9 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 B4: 1,4 # 27 pairs * PAIR A5: 2,7 BLK 4 A6: 2,7,6 # reduction candidate for 2,7 A6: 6 # 17 pairs A6: 2,7 # 16 pairs * PAIR C5: 3,9 BLK 4 C6: 3,9,1 # reduction candidate for 3,9 C6: 1 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 C6: 3,9 # 27 pairs * PAIR C5: 3,9 ROW 5 F5: 3,9,7 # reduction candidate for 3,9 F5: 3,9 # 18 pairs H5: 3,9,2,5 # reduction candidate for 3,9 H5: 3,9 # 23 pairs * PAIR B6: 6,7 BLK 4 A6: 6,7,2 # reduction candidate for 6,7 A6: 6,7 # 21 pairs A6: 2 # 18 pairs * PAIR D4: 3,9 BLK 5 F5: 3,9,7 # reduction candidate for 3,9 F5: 3,9 # 18 pairs F6: 3,9,7 # reduction candidate for 3,9 F6: 3,9 # 21 pairs * PAIR D4: 3,9 ROW 4 G4: 3,9,1 # reduction candidate for 3,9 G4: 1 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 G4: 3,9 # 27 pairs * PAIR A8: 1,4 BLK 7 B7: 1,4,5,9 # reduction candidate for 1,4 B7: 1,4 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 B7: 5,9 # 19 pairs C8: 1,4,9 # reduction candidate for 1,4 C8: 1,4 # 27 pairs B9: 1,4,2,9 # reduction candidate for 1,4 B9: 1,4 => CTR * 5.4.982..932.1548...8432519.95326178.8314.6.5..158.93435726.8.11298743..8.6.5.7.2 B9: 2,9 # 19 pairs * PAIR A8: 1,4 ROW 8 F8: 1,4,3,9 # reduction candidate for 1,4 F8: 1,4 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 F8: 3,9 # 27 pairs * PAIR B8: 2,5 ROW 8 H8: 2,5,6 # reduction candidate for 2,5 H8: 2,5 # 17 pairs I8: 2,5,6 # reduction candidate for 2,5 I8: 2,5 # 20 pairs * PAIR D9: 3,9 BLK 8 F8: 3,9,1,4 # reduction candidate for 3,9 F8: 3,9 # 27 pairs F9: 3,9,1,4 # reduction candidate for 3,9 F9: 3,9 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 F9: 1,4 # 19 pairs * PAIR D9: 3,9 ROW 9 H9: 3,9,2,4 # reduction candidate for 3,9 H9: 3,9 # 22 pairs H9: 2,4 # 19 pairs * PAIR I7: 1,5 ROW 7 B7: 1,5,4,9 # reduction candidate for 1,5 B7: 4,9 # 21 pairs B7: 1,5 # 21 pairs * PAIR G8: 3,9 BLK 9 H9: 3,9,2,4 # reduction candidate for 3,9 H9: 3,9 # 22 pairs H9: 2,4 # 19 pairs * PAIR G8: 3,9 ROW 8 F8: 3,9,1,4 # reduction candidate for 3,9 F8: 1,4 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 F8: 3,9 # 27 pairs * PAIR G8: 3,9 COL G G4: 3,9,1 # reduction candidate for 3,9 G4: 3,9 # 27 pairs G6: 3,9,1 # reduction candidate for 3,9 G6: 3,9 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 G6: 1 # 27 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060428-absurd-base-pr-000.dot * REASONING * PRF # B7: 1,4 => SOL * DIS # B9: 1,4 => CTR => B9: 2,9 * PRF # C8: 9 => SOL * PRF # B4: 9 => SOL * PRF # C6: 1 => SOL * PRF # G4: 1 => SOL * PRF # B7: 1,4 => SOL * DIS # B9: 1,4 => CTR => B9: 2,9 * PRF # F8: 1,4 => SOL * PRF # F9: 3,9 => SOL * PRF # F8: 1,4 => SOL * PRF # G6: 3,9 => SOL * CNT 12 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A5,A8,B1,B3,B6,B8,C1,C5,D1,D2,D4,D9,G8,H1,I2,I7) * 5...982..932.1548...8432519..5.26.78.8.14.6.....58...43.726.8.....87....8.6.5.7.. * PAIR B1: 1,4 COL B B4: 1,4,9 # reduction candidate for 1,4 B4: 1,4 # 27 pairs B7: 1,4,5,9 # reduction candidate for 1,4 B7: 1,4 => SOLVED * 514798263932615487678432519495326178783149652261587934347261895159874326826953741 * DURATION: 0:00:02.459085 START: 22:44:51.876663 END: 22:44:54.335748 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060428-absurd-base-pr-001.dot * REASONING * PRF # B7: 1,4 => SOL * STA B7: 1,4 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060428, absurd
Solution
position: 514798263932615487678432519495326178783149652261587934347261895159874326826953741 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 # B4: 1,4 => UNS * PRF # B7: 1,4 => SOL * INC # B7: 5,9 => UNS * DIS # B9: 1,4 => CTR => B9: 2,9 * INC # B9: 2,9 => UNS * INC # C8: 1,4 => UNS * PRF # C8: 9 => SOL * INC # A6: 6,7 => UNS * INC # A6: 2 => UNS * INC # I1: 6,7 => UNS * INC # I1: 3 => UNS * INC # I1: 3,6 => UNS * INC # I1: 7 => UNS * INC # I1: 6,7 => UNS * INC # I1: 3 => UNS * INC # B4: 1,4 => UNS * PRF # B4: 9 => SOL * INC # A6: 2,7 => UNS * INC # A6: 6 => UNS * INC # C6: 3,9 => UNS * PRF # C6: 1 => SOL * INC # F5: 3,9 => UNS * INC # H5: 3,9 => UNS * INC # A6: 6,7 => UNS * INC # A6: 2 => UNS * INC # F5: 3,9 => UNS * INC # F6: 3,9 => UNS * INC # G4: 3,9 => UNS * PRF # G4: 1 => SOL * PRF # B7: 1,4 => SOL * INC # B7: 5,9 => UNS * INC # C8: 1,4 => UNS * DIS # B9: 1,4 => CTR => B9: 2,9 * INC # B9: 2,9 => UNS * PRF # F8: 1,4 => SOL * INC # F8: 3,9 => UNS * INC # H8: 2,5 => UNS * INC # I8: 2,5 => UNS * INC # F8: 3,9 => UNS * PRF # F9: 3,9 => SOL * INC # F9: 1,4 => UNS * INC # H9: 3,9 => UNS * INC # H9: 2,4 => UNS * INC # B7: 1,5 => UNS * INC # B7: 4,9 => UNS * INC # H9: 3,9 => UNS * INC # H9: 2,4 => UNS * INC # F8: 3,9 => UNS * PRF # F8: 1,4 => SOL * INC # G4: 3,9 => UNS * PRF # G6: 3,9 => SOL * INC # G6: 1 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 1,4 => UNS * PRF # B7: 1,4 => SOL * STA B7: 1,4 * CNT 2 HDP CHAINS / 2 HYP OPENED