Analysis of zz-www.sudokuoftheday.co.uk-20190216-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: .1....5......9..7.8......46.9..51..3.539...1.....2...5.417.......2..6.97....35... initial
Autosolve
position: .1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 3,4 => CTR => D2: 1,6 * DIS # A2: 6 => CTR => A2: 3,4 * DIS # F6: 3,4 => CTR => F6: 7,8 * DIS # B3: 2 => CTR => B3: 3,7 * DIS # G2: 2 => CTR => G2: 1,8 * DIS # G2: 8 => CTR => G2: 1,2 * PRF # E5: 4,6 => SOL * DIS # E5: 7 => CTR => E5: 4,6 * DIS # D6: 4,6 => CTR => D6: 3 * DIS # C4: 4,6 => CTR => C4: 7,8 * PRF # G4: 4,6 => SOL * DIS # D2: 1,3 => CTR => D2: 4,6 * DIS # G4: 4,8 => CTR => G4: 6,7 * DIS # G5: 4,8 => CTR => G5: 6,7 * DIS # F5: 7 => CTR => F5: 4,8 * PRF # G4: 6,8 => SOL * DIS # C6: 6,8 => CTR => C6: 4,7 * DIS # A2: 4 => CTR => A2: 3,6 * DIS # D2: 1,4 => CTR => D2: 3,6 * CNT 19 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 3,4 => CTR => D2: 1,6 * DIS D2: 1,6 # A2: 6 => CTR => A2: 3,4 * PRF D2: 1,6 + A2: 3,4 # B3: 3,7 => SOL * STA D2: 1,6 + A2: 3,4 + B3: 3,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1....5......9..7.8......46.9..51..3.539...1.....2...5.417.......2..6.97....35... | initial |
| .1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235... | autosolve |
| 416872539325694178879513246798451623253968714164327985641789352532146897987235461 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) F2: 3,4 E3: 1,7 F3: 3,7 I2: 1,8 G3: 1,2 D4: 4,6 I5: 4,8 H6: 6,8 A7: 3,6 B8: 3,8 D8: 1,4 E8: 1,4 G7: 3,6 G8: 3,8 G9: 1,4 H9: 6,8 I9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,E3: 1.. / D2 = 1 => 0 pairs (X) / E3 = 1 => 20 pairs (_) D8,E8: 1.. / D8 = 1 => 20 pairs (_) / E8 = 1 => 0 pairs (X) G9,I9: 1.. / G9 = 1 => 0 pairs (X) / I9 = 1 => 16 pairs (_) E3,G3: 1.. / E3 = 1 => 20 pairs (_) / G3 = 1 => 0 pairs (X) D2,D8: 1.. / D2 = 1 => 0 pairs (X) / D8 = 1 => 20 pairs (_) E3,E8: 1.. / E3 = 1 => 20 pairs (_) / E8 = 1 => 0 pairs (X) I2,I9: 1.. / I2 = 1 => 0 pairs (X) / I9 = 1 => 16 pairs (_) B2,B3: 2.. / B2 = 2 => 20 pairs (_) / B3 = 2 => 0 pairs (X) G2,G3: 2.. / G2 = 2 => 0 pairs (X) / G3 = 2 => 20 pairs (_) B2,G2: 2.. / B2 = 2 => 20 pairs (_) / G2 = 2 => 0 pairs (X) B3,G3: 2.. / B3 = 2 => 0 pairs (X) / G3 = 2 => 20 pairs (_) D6,F6: 3.. / D6 = 3 => 17 pairs (_) / F6 = 3 => 0 pairs (X) A7,B8: 3.. / A7 = 3 => 0 pairs (X) / B8 = 3 => 0 pairs (_) G7,G8: 3.. / G7 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) B3,F3: 3.. / B3 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) A7,G7: 3.. / A7 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) B8,G8: 3.. / B8 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) A2,A7: 3.. / A2 = 3 => 0 pairs (*) / A7 = 3 => 0 pairs (X) D2,D6: 3.. / D2 = 3 => 0 pairs (X) / D6 = 3 => 17 pairs (_) D8,E8: 4.. / D8 = 4 => 0 pairs (X) / E8 = 4 => 20 pairs (_) G9,I9: 4.. / G9 = 4 => 16 pairs (_) / I9 = 4 => 0 pairs (X) I5,I9: 4.. / I5 = 4 => 16 pairs (_) / I9 = 4 => 0 pairs (X) E1,D2: 6.. / E1 = 6 => 0 pairs (X) / D2 = 6 => 0 pairs (_) G7,H9: 6.. / G7 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) E5,G5: 6.. / E5 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) A7,G7: 6.. / A7 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) E1,E5: 6.. / E1 = 6 => 0 pairs (X) / E5 = 6 => 0 pairs (_) H6,H9: 6.. / H6 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) G4,G5: 7.. / G4 = 7 => 25 pairs (_) / G5 = 7 => 0 pairs (*) B9,C9: 7.. / B9 = 7 => 22 pairs (_) / C9 = 7 => 20 pairs (_) A1,A4: 7.. / A1 = 7 => 25 pairs (_) / A4 = 7 => 0 pairs (*) G2,I2: 8.. / G2 = 8 => 0 pairs (X) / I2 = 8 => 16 pairs (_) F5,F6: 8.. / F5 = 8 => 16 pairs (_) / F6 = 8 => 0 pairs (X) G8,H9: 8.. / G8 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) C4,G4: 8.. / C4 = 8 => 19 pairs (_) / G4 = 8 => 0 pairs (X) B8,G8: 8.. / B8 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) H6,H9: 8.. / H6 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) I2,I5: 8.. / I2 = 8 => 16 pairs (_) / I5 = 8 => 0 pairs (X) * DURATION: 0:00:50.873662 START: 03:46:20.261135 END: 03:47:11.134797 2019-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,D4,D8,E3,E8,F2,F3,G3,G7,G8,G9,H6,H9,I2,I5,I9) * .1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235... * PAIR F2: 3,4 BLK 2 D2: 3,4,1,6 # reduction candidate for 3,4 D2: 3,4 => CTR * .1.862539..5.9..7.8.9517246.9..51.2325397.61.1...2.985641789352532..6.979..235... D2: 1,6 # 18 pairs * PAIR F2: 3,4 ROW 2 A2: 3,4,6 # reduction candidate for 3,4 A2: 6 => CTR * .1.8625396.5.9..7.8.95...46.9..51.232539...1.1...2.965341789652582..6397967235.8. A2: 3,4 # 20 pairs * PAIR F2: 3,4 COL F F6: 3,4,7,8 # reduction candidate for 3,4 F6: 3,4 => CTR * .1.8.2539..5.9..788.95.7.46.9..51.232539786141...2.985641789352532..6897987235461 F6: 7,8 # 20 pairs * PAIR F3: 3,7 ROW 3 B3: 3,7,2 # reduction candidate for 3,7 B3: 2 => CTR * .1.8.2539..5194278829573146.9.651.2325394..1.1..32.9.5.41789.525.2.16.979..2354.1 B3: 3,7 # 20 pairs * PAIR F3: 3,7 COL F F6: 3,7,4,8 # reduction candidate for 3,7 F6: 4,8 # 26 pairs F6: 3,7 # 17 pairs * PAIR I2: 1,8 BLK 3 G2: 1,8,2 # reduction candidate for 1,8 G2: 2 => CTR * .1.842539..5.9.2788295.3146.9..51.232539...141..32.9.5.41789.525.2.16.979..2354.1 G2: 1,8 # 20 pairs * PAIR G3: 1,2 BLK 3 G2: 1,2,8 # reduction candidate for 1,2 G2: 8 => CTR * .16872539.256948718.951.246.98.51.232539...181...28965.41789652582146397967235184 G2: 1,2 # 16 pairs * PAIR D4: 4,6 BLK 5 E5: 4,6,7 # reduction candidate for 4,6 E5: 4,6 => SOLVED * 416872539325694178879513246798451623253968714164327985641789352532146897987235461 E5: 7 => CTR * .1.862539..5.9..7.8.95...46.9..51.2325397.61.1...2.985641789352532.46897987235.6. D6: 4,6,3 # reduction candidate for 4,6 D6: 4,6 => CTR * .1.8.2539..5394.7.839517246.9..51.232539786141...23985.41789.525.2..6.979..235... D6: 3 # 17 pairs * PAIR D4: 4,6 ROW 4 A4: 4,6,7 # reduction candidate for 4,6 A4: 4,6 # 25 pairs C4: 4,6,7,8 # reduction candidate for 4,6 C4: 4,6 => CTR * .1.8.2539..5.9..7.8.95...46.9..518232539.87141...27965.41789652582..6.979..235... C4: 7,8 # 18 pairs G4: 4,6,7,8 # reduction candidate for 4,6 G4: 4,6 => SOLVED * 416872539325694178879513246798451623253968714164327985641789352532146897987235461 G4: 7,8 # 20 pairs * PAIR D4: 4,6 COL D D2: 4,6,1,3 # reduction candidate for 4,6 D2: 1,3 => CTR * 714862539365194.7.8.95...46.9..51.232539..61.1...2.985641789352532..6897987235.6. D2: 4,6 # 21 pairs * PAIR I5: 4,8 BLK 6 G4: 4,8,6,7 # reduction candidate for 4,8 G4: 4,8 => CTR * .1.8.2539..5.9..7.8.95...46.9..51.232539..71.1...27965.417896525.2..63979..235.8. G4: 6,7 # 22 pairs G5: 4,8,6,7 # reduction candidate for 4,8 G5: 4,8 => CTR * 7168425394.5693.7.8.95...46.9..51723253967.1.1...28965.417896525.2..63979..235.8. G5: 6,7 # 18 pairs * PAIR I5: 4,8 ROW 5 F5: 4,8,7 # reduction candidate for 4,8 F5: 7 => CTR * .1.8.2539..5.94.7.8.95.3.46.98.51723253967.1.1743289653417896525.2..63979..235.8. F5: 4,8 # 20 pairs * PAIR H6: 6,8 BLK 6 G4: 6,8,4,7 # reduction candidate for 6,8 G4: 6,8 => SOLVED * 416872539325694178879513246798451623253968714164327985641789352532146897987235461 G4: 4,7 # 20 pairs G5: 6,8,4,7 # reduction candidate for 6,8 G5: 6,8 # 23 pairs * PAIR H6: 6,8 ROW 6 B6: 6,8,7 # reduction candidate for 6,8 B6: 6,8 # 19 pairs C6: 6,8,4,7 # reduction candidate for 6,8 C6: 6,8 => CTR * .1.862539365.942788295.3146.9865172325397.6141...2.985641789352532..6897987235461 C6: 4,7 # 18 pairs * PAIR A7: 3,6 COL A A2: 3,6,4 # reduction candidate for 3,6 A2: 4 => CTR * .1.8.25394.5.93.7.8395.7246.9..51.2325397.61.1..32.985.41789.525.2..6.979..235... A2: 3,6 # 21 pairs * PAIR D8: 1,4 COL D D2: 1,4,3,6 # reduction candidate for 1,4 D2: 1,4 => CTR * 714862539365.942788295.314649865172325394.61.1..32.985641789352532..6897987235.6. D2: 3,6 # 21 pairs * PAIR H9: 6,8 ROW 9 B9: 6,8,7 # reduction candidate for 6,8 B9: 6,8 # 20 pairs C9: 6,8,7 # reduction candidate for 6,8 C9: 6,8 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190216-absurd-base-pr-000.dot * REASONING * DIS # D2: 3,4 => CTR => D2: 1,6 * DIS # A2: 6 => CTR => A2: 3,4 * DIS # F6: 3,4 => CTR => F6: 7,8 * DIS # B3: 2 => CTR => B3: 3,7 * DIS # G2: 2 => CTR => G2: 1,8 * DIS # G2: 8 => CTR => G2: 1,2 * PRF # E5: 4,6 => SOL * DIS # E5: 7 => CTR => E5: 4,6 * DIS # D6: 4,6 => CTR => D6: 3 * DIS # C4: 4,6 => CTR => C4: 7,8 * PRF # G4: 4,6 => SOL * DIS # D2: 1,3 => CTR => D2: 4,6 * DIS # G4: 4,8 => CTR => G4: 6,7 * DIS # G5: 4,8 => CTR => G5: 6,7 * DIS # F5: 7 => CTR => F5: 4,8 * PRF # G4: 6,8 => SOL * DIS # C6: 6,8 => CTR => C6: 4,7 * DIS # A2: 4 => CTR => A2: 3,6 * DIS # D2: 1,4 => CTR => D2: 3,6 * CNT 19 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,D4,D8,E3,E8,F2,F3,G3,G7,G8,G9,H6,H9,I2,I5,I9) * .1.8.2539..5.9..7.8.95...46.9..51.232539...1.1...2.9.5.41789.525.2..6.979..235... * PAIR F2: 3,4 BLK 2 D2: 3,4,1,6 # reduction candidate for 3,4 D2: 3,4 => CTR * .1.862539..5.9..7.8.9517246.9..51.2325397.61.1...2.985641789352532..6.979..235... * PAIR F2: 3,4 ROW 2 A2: 3,4,6 # reduction candidate for 3,4 A2: 6 => CTR * .1.8.25396.5194.788.9573146.9.651.2325394..1.1..32.9.5.41789.525.2..6.979..235... * PAIR RESTART * PAIR F3: 3,7 ROW 3 B3: 3,7,2 # reduction candidate for 3,7 B3: 3,7 => SOLVED * 416872539325694178879513246798451623253968714164327985641789352532146897987235461 * DURATION: 0:00:04.014327 START: 03:47:38.621332 END: 03:47:42.635659 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190216-absurd-base-pr-001.dot * REASONING * DIS # D2: 3,4 => CTR => D2: 1,6 * DIS D2: 1,6 # A2: 6 => CTR => A2: 3,4 * PRF D2: 1,6 + A2: 3,4 # B3: 3,7 => SOL * STA D2: 1,6 + A2: 3,4 + B3: 3,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190216, absurd
Solution
position: 416872539325694178879513246798451623253968714164327985641789352532146897987235461 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 # D2: 3,4 => CTR => D2: 1,6 * INC # D2: 1,6 => UNS * INC # A2: 3,4 => UNS * DIS # A2: 6 => CTR => A2: 3,4 * DIS # F6: 3,4 => CTR => F6: 7,8 * INC # F6: 7,8 => UNS * INC # B3: 3,7 => UNS * DIS # B3: 2 => CTR => B3: 3,7 * INC # F6: 3,7 => UNS * INC # F6: 4,8 => UNS * INC # G2: 1,8 => UNS * DIS # G2: 2 => CTR => G2: 1,8 * INC # G2: 1,2 => UNS * DIS # G2: 8 => CTR => G2: 1,2 * PRF # E5: 4,6 => SOL * DIS # E5: 7 => CTR => E5: 4,6 * DIS # D6: 4,6 => CTR => D6: 3 * INC # D6: 3 => UNS * INC # A4: 4,6 => UNS * DIS # C4: 4,6 => CTR => C4: 7,8 * INC # C4: 7,8 => UNS * PRF # G4: 4,6 => SOL * INC # G4: 7,8 => UNS * INC # D2: 4,6 => UNS * DIS # D2: 1,3 => CTR => D2: 4,6 * DIS # G4: 4,8 => CTR => G4: 6,7 * INC # G4: 6,7 => UNS * DIS # G5: 4,8 => CTR => G5: 6,7 * INC # G5: 6,7 => UNS * INC # F5: 4,8 => UNS * DIS # F5: 7 => CTR => F5: 4,8 * PRF # G4: 6,8 => SOL * INC # G4: 4,7 => UNS * INC # G5: 6,8 => UNS * INC # B6: 6,8 => UNS * DIS # C6: 6,8 => CTR => C6: 4,7 * INC # C6: 4,7 => UNS * INC # A2: 3,6 => UNS * DIS # A2: 4 => CTR => A2: 3,6 * DIS # D2: 1,4 => CTR => D2: 3,6 * INC # D2: 3,6 => UNS * INC # B9: 6,8 => UNS * INC # C9: 6,8 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 3,4 => CTR => D2: 1,6 * INC D2: 1,6 # A2: 3,4 => UNS * DIS D2: 1,6 # A2: 6 => CTR => A2: 3,4 * PRF D2: 1,6 + A2: 3,4 # B3: 3,7 => SOL * STA D2: 1,6 + A2: 3,4 + B3: 3,7 * CNT 4 HDP CHAINS / 4 HYP OPENED