Analysis of zz-www.sudokuoftheday.co.uk-20060627-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: .....4.2......96181...6...37...4...1....7.86..869...4.5.1.....6..2....39.....71.. initial
Autosolve
position: .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A9: 6,8 => CTR => A9: 9 * DIS # D1: 3,5 => CTR => D1: 1,7,8 * DIS # D2: 3,5 => CTR => D2: 7 * DIS # B2: 4 => CTR => B2: 3,5 * DIS # I6: 2 => CTR => I6: 5,7 * DIS # D9: 6,8 => CTR => D9: 2,3,5 * DIS # I6: 2,5 => CTR => I6: 7 * DIS # D5: 2,5 => CTR => D5: 3 * DIS # I6: 2 => CTR => I6: 5,7 * DIS # D7: 3,8 => CTR => D7: 4 * DIS # E7: 3,8 => CTR => E7: 9 * DIS # D9: 3,8 => CTR => D9: 2,5,6 * PRF # E9: 3,8 => SOL * DIS # D9: 5,8 => CTR => D9: 2,3,6 * CNT 14 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A9: 6,8 => CTR => A9: 9 * DIS A9: 9 # E1: 3,5 => CTR => E1: 1,8 * DIS A9: 9 + E1: 1,8 # I6: 2 => CTR => I6: 5,7 * DIS A9: 9 + E1: 1,8 + I6: 5,7 # D8: 6,8 => CTR => D8: 1,4 * DIS A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 # D9: 6,8 => CTR => D9: 2 * PRF A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 # D1: 1,8 => SOL * STA A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 + D1: 1,8 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....4.2......96181...6...37...4...1....7.86..869...4.5.1.....6..2....39.....71.. | initial |
| .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4 | autosolve |
| 637814925254739618198562473725648391419375862386921547571493286842156739963287154 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 6,8 B3: 5,9 E2: 3,5 I1: 5,7 H3: 5,7 A5: 4,9 C5: 4,9 D4: 6,8 F4: 6,8 I5: 2,5 G6: 5,7 F7: 3,8 H7: 7,8 G8: 5,7 H9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E1: 1.. / D1 = 1 => 15 pairs (_) / E1 = 1 => 22 pairs (_) E6,F6: 1.. / E6 = 1 => 17 pairs (_) / F6 = 1 => 16 pairs (_) D1,D8: 1.. / D1 = 1 => 15 pairs (_) / D8 = 1 => 22 pairs (_) F6,F8: 1.. / F6 = 1 => 16 pairs (_) / F8 = 1 => 17 pairs (_) D3,F3: 2.. / D3 = 2 => 19 pairs (_) / F3 = 2 => 17 pairs (_) I5,I6: 2.. / I5 = 2 => 19 pairs (_) / I6 = 2 => 0 pairs (X) D9,E9: 2.. / D9 = 2 => 19 pairs (_) / E9 = 2 => 17 pairs (_) E6,E9: 2.. / E6 = 2 => 19 pairs (_) / E9 = 2 => 17 pairs (_) D5,F5: 3.. / D5 = 3 => 18 pairs (_) / F5 = 3 => 0 pairs (X) F5,F7: 3.. / F5 = 3 => 0 pairs (X) / F7 = 3 => 18 pairs (_) B2,C2: 4.. / B2 = 4 => 0 pairs (X) / C2 = 4 => 19 pairs (_) A5,C5: 4.. / A5 = 4 => 19 pairs (_) / C5 = 4 => 0 pairs (X) D7,D8: 4.. / D7 = 4 => 15 pairs (_) / D8 = 4 => 0 pairs (X) B7,D7: 4.. / B7 = 4 => 0 pairs (X) / D7 = 4 => 15 pairs (_) A5,A8: 4.. / A5 = 4 => 19 pairs (_) / A8 = 4 => 0 pairs (X) C2,C5: 4.. / C2 = 4 => 19 pairs (_) / C5 = 4 => 0 pairs (X) I1,H3: 5.. / I1 = 5 => 15 pairs (_) / H3 = 5 => 0 pairs (X) G8,H9: 5.. / G8 = 5 => 0 pairs (X) / H9 = 5 => 15 pairs (_) G6,G8: 5.. / G6 = 5 => 15 pairs (_) / G8 = 5 => 0 pairs (X) H3,H9: 5.. / H3 = 5 => 0 pairs (X) / H9 = 5 => 15 pairs (_) A1,B1: 6.. / A1 = 6 => 18 pairs (_) / B1 = 6 => 0 pairs (X) D4,F4: 6.. / D4 = 6 => 20 pairs (_) / F4 = 6 => 14 pairs (_) F4,F8: 6.. / F4 = 6 => 14 pairs (_) / F8 = 6 => 20 pairs (_) I1,H3: 7.. / I1 = 7 => 0 pairs (X) / H3 = 7 => 15 pairs (_) G6,I6: 7.. / G6 = 7 => 0 pairs (X) / I6 = 7 => 15 pairs (_) B7,B8: 7.. / B7 = 7 => 15 pairs (_) / B8 = 7 => 0 pairs (X) H7,G8: 7.. / H7 = 7 => 0 pairs (X) / G8 = 7 => 15 pairs (_) C2,D2: 7.. / C2 = 7 => 0 pairs (X) / D2 = 7 => 16 pairs (_) B7,H7: 7.. / B7 = 7 => 15 pairs (_) / H7 = 7 => 0 pairs (X) B8,G8: 7.. / B8 = 7 => 0 pairs (X) / G8 = 7 => 15 pairs (_) G6,G8: 7.. / G6 = 7 => 0 pairs (X) / G8 = 7 => 15 pairs (_) H3,H7: 7.. / H3 = 7 => 15 pairs (_) / H7 = 7 => 0 pairs (X) I1,I6: 7.. / I1 = 7 => 0 pairs (X) / I6 = 7 => 15 pairs (_) D4,F4: 8.. / D4 = 8 => 14 pairs (_) / F4 = 8 => 20 pairs (_) H7,H9: 8.. / H7 = 8 => 15 pairs (_) / H9 = 8 => 0 pairs (X) B3,C3: 9.. / B3 = 9 => 16 pairs (_) / C3 = 9 => 0 pairs (X) A5,C5: 9.. / A5 = 9 => 0 pairs (X) / C5 = 9 => 19 pairs (_) E7,E9: 9.. / E7 = 9 => 15 pairs (_) / E9 = 9 => 0 pairs (X) B7,E7: 9.. / B7 = 9 => 0 pairs (X) / E7 = 9 => 15 pairs (_) A5,A9: 9.. / A5 = 9 => 0 pairs (X) / A9 = 9 => 19 pairs (_) * DURATION: 0:00:51.195460 START: 00:08:00.114906 END: 00:08:51.310366 2019-05-01 * CP COUNT: (40) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B3,C5,D4,E2,F4,F7,G6,G8,H3,H7,H9,I1,I5) * .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4 * PAIR A1: 6,8 COL A A8: 6,8,4 # reduction candidate for 6,8 A8: 6,8 # 19 pairs A9: 6,8,9 # reduction candidate for 6,8 A9: 6,8 => CTR * 63871492524...9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154 A9: 9 # 19 pairs * PAIR E2: 3,5 BLK 2 D1: 3,5,1,7,8 # reduction candidate for 3,5 D1: 3,5 => CTR * ...514927254739618197.6.453725.4.39141937.86.3869.174.5714.32.6..21...39.....71.4 D1: 1,7,8 # 15 pairs E1: 3,5,1,8 # reduction candidate for 3,5 E1: 3,5 # 26 pairs D2: 3,5,7 # reduction candidate for 3,5 D2: 3,5 => CTR * 638714925247..9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154 D2: 7 # 16 pairs * PAIR E2: 3,5 ROW 2 B2: 3,5,4 # reduction candidate for 3,5 B2: 4 => CTR * 63871492524...9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154 B2: 3,5 # 19 pairs * PAIR E2: 3,5 COL E E9: 3,5,2,8,9 # reduction candidate for 3,5 E9: 3,5 # 22 pairs E9: 2,8,9 # 15 pairs * PAIR I1: 5,7 ROW 1 D1: 5,7,1,3,8 # reduction candidate for 5,7 D1: 5,7 # 30 pairs D1: 1,3,8 # 15 pairs * PAIR I1: 5,7 COL I I6: 5,7,2 # reduction candidate for 5,7 I6: 2 => CTR * .....49272....961819..6.453725.4.391.1..7.8653869.57425.1.9.27687241.539....27184 I6: 5,7 # 19 pairs * PAIR H3: 5,7 ROW 3 D3: 5,7,2,8 # reduction candidate for 5,7 D3: 5,7 # 26 pairs D3: 2,8 # 16 pairs * PAIR D4: 6,8 COL D D8: 6,8,1,4,5 # reduction candidate for 6,8 D8: 6,8 # 18 pairs D9: 6,8,2,3,5 # reduction candidate for 6,8 D9: 6,8 => CTR * ..71349252..759618159268473725846391914375862386912547571493286462581739...627154 D9: 2,3,5 # 17 pairs * PAIR F4: 6,8 COL F F8: 6,8,1,5 # reduction candidate for 6,8 F8: 6,8 # 21 pairs F8: 1,5 # 15 pairs * PAIR I5: 2,5 BLK 6 I6: 2,5,7 # reduction candidate for 2,5 I6: 2,5 => CTR * 6..1849272....9618198762453725648391419.7.86.3869..74.5.1.9.276872416539.....7184 I6: 7 # 15 pairs * PAIR I5: 2,5 ROW 5 D5: 2,5,3 # reduction candidate for 2,5 D5: 2,5 => CTR * .....492.2....96181...6.4.3725.4.391.1..7386.3869...4.5.1..82768724.6.39.....71.4 D5: 3 # 18 pairs F5: 2,5,3 # reduction candidate for 2,5 F5: 2,5 # 18 pairs * PAIR G6: 5,7 BLK 6 I6: 5,7,2 # reduction candidate for 5,7 I6: 2 => CTR * .....49272....961819..6.453725.4.391.1..7.8653869.57425.1.9.27687241.539....27184 I6: 5,7 # 19 pairs * PAIR F7: 3,8 BLK 8 D7: 3,8,4 # reduction candidate for 3,8 D7: 3,8 => CTR * 6.81.49272.47.9618197.6.453725648391419.7.86.3869.174.541893276872416539963..7184 D7: 4 # 15 pairs E7: 3,8,9 # reduction candidate for 3,8 E7: 3,8 => CTR * .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5914..276.72...539....97184 E7: 9 # 15 pairs D9: 3,8,2,5,6 # reduction candidate for 3,8 D9: 3,8 => CTR * .....49252....96181...6.473725.4.391.1..7.8623869.2547571493286..2..1739...827154 D9: 2,5,6 # 15 pairs E9: 3,8,2,5,9 # reduction candidate for 3,8 E9: 3,8 => SOLVED * 637814925254739618198562473725648391419375862386921547571493286842156739963287154 E9: 2,5,9 # 15 pairs * PAIR H9: 5,8 ROW 9 D9: 5,8,2,3,6 # reduction candidate for 5,8 D9: 5,8 => CTR * 637184925254739618198.6.473725648391419375862386912.47571493286842...739963827154 D9: 2,3,6 # 15 pairs E9: 5,8,2,3,9 # reduction candidate for 5,8 E9: 5,8 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060627-absurd-base-pr-000.dot * REASONING * DIS # A9: 6,8 => CTR => A9: 9 * DIS # D1: 3,5 => CTR => D1: 1,7,8 * DIS # D2: 3,5 => CTR => D2: 7 * DIS # B2: 4 => CTR => B2: 3,5 * DIS # I6: 2 => CTR => I6: 5,7 * DIS # D9: 6,8 => CTR => D9: 2,3,5 * DIS # I6: 2,5 => CTR => I6: 7 * DIS # D5: 2,5 => CTR => D5: 3 * DIS # I6: 2 => CTR => I6: 5,7 * DIS # D7: 3,8 => CTR => D7: 4 * DIS # E7: 3,8 => CTR => E7: 9 * DIS # D9: 3,8 => CTR => D9: 2,5,6 * PRF # E9: 3,8 => SOL * DIS # D9: 5,8 => CTR => D9: 2,3,6 * CNT 14 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B3,C5,D4,E2,F4,F7,G6,G8,H3,H7,H9,I1,I5) * .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4 * PAIR A1: 6,8 COL A A8: 6,8,4 # reduction candidate for 6,8 A8: 6,8 # 19 pairs A9: 6,8,9 # reduction candidate for 6,8 A9: 6,8 => CTR * 63871492524...9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154 * RESTART * PAIR RESTART * PAIR E2: 3,5 BLK 2 E1: 3,5,1,8 # reduction candidate for 3,5 E1: 3,5 => CTR * ...1.492.2.47.9618197.6.453725.4.391419.7.86.3869...4.5.1.9.2.6..2....399....71.4 * PAIR I1: 5,7 COL I I6: 5,7,2 # reduction candidate for 5,7 I6: 2 => CTR * .....4927254739618197.6.453725.4.391419.7.8653869..7425.1.9.276.724..5399...27184 * PAIR RESTART * PAIR D4: 6,8 COL D D8: 6,8,1,4 # reduction candidate for 6,8 D8: 6,8 => CTR * ...184925254739618198.6.473725.4.391419.7.8623869..547571493286842651.399....71.4 D9: 6,8,2 # reduction candidate for 6,8 D9: 6,8 => CTR * .631.492.25473961819.26.4.3725.4.391419.7.8623869.2.4.5.1.9.2.6..2..1.399..627154 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B7,B8,C1,C3,D3,D7,D8,E1,E8,E9,G6,G8,H3,H7,H9,I1,I6) * 63...492.25473961819..624.3725648391419375862386921.4.5.1.932.68.2..6.399632.71.4 * PAIR E1: 1,8 BLK 2 D1: 1,8,5 # reduction candidate for 1,8 D1: 1,8 => SOLVED * 637814925254739618198562473725648391419375862386921547571493286842156739963287154 * DURATION: 0:00:08.965392 START: 00:09:18.845945 END: 00:09:27.811337 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060627-absurd-base-pr-001.dot * REASONING * DIS # A9: 6,8 => CTR => A9: 9 * DIS A9: 9 # E1: 3,5 => CTR => E1: 1,8 * DIS A9: 9 + E1: 1,8 # I6: 2 => CTR => I6: 5,7 * DIS A9: 9 + E1: 1,8 + I6: 5,7 # D8: 6,8 => CTR => D8: 1,4 * DIS A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 # D9: 6,8 => CTR => D9: 2 * PRF A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 # D1: 1,8 => SOL * STA A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 + D1: 1,8 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060627, absurd
Solution
position: 637814925254739618198562473725648391419375862386921547571493286842156739963287154 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 # A8: 6,8 => UNS * DIS # A9: 6,8 => CTR => A9: 9 * INC # A9: 9 => UNS * DIS # D1: 3,5 => CTR => D1: 1,7,8 * INC # D1: 1,7,8 => UNS * INC # E1: 3,5 => UNS * DIS # D2: 3,5 => CTR => D2: 7 * INC # D2: 7 => UNS * INC # B2: 3,5 => UNS * DIS # B2: 4 => CTR => B2: 3,5 * INC # E9: 3,5 => UNS * INC # E9: 2,8,9 => UNS * INC # D1: 5,7 => UNS * INC # D1: 1,3,8 => UNS * INC # I6: 5,7 => UNS * DIS # I6: 2 => CTR => I6: 5,7 * INC # D3: 5,7 => UNS * INC # D3: 2,8 => UNS * INC # D8: 6,8 => UNS * DIS # D9: 6,8 => CTR => D9: 2,3,5 * INC # D9: 2,3,5 => UNS * INC # F8: 6,8 => UNS * INC # F8: 1,5 => UNS * DIS # I6: 2,5 => CTR => I6: 7 * INC # I6: 7 => UNS * DIS # D5: 2,5 => CTR => D5: 3 * INC # D5: 3 => UNS * INC # F5: 2,5 => UNS * INC # I6: 5,7 => UNS * DIS # I6: 2 => CTR => I6: 5,7 * DIS # D7: 3,8 => CTR => D7: 4 * INC # D7: 4 => UNS * DIS # E7: 3,8 => CTR => E7: 9 * INC # E7: 9 => UNS * DIS # D9: 3,8 => CTR => D9: 2,5,6 * INC # D9: 2,5,6 => UNS * PRF # E9: 3,8 => SOL * INC # E9: 2,5,9 => UNS * DIS # D9: 5,8 => CTR => D9: 2,3,6 * INC # D9: 2,3,6 => UNS * INC # E9: 5,8 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A8: 6,8 => UNS * DIS # A9: 6,8 => CTR => A9: 9 * DIS A9: 9 # E1: 3,5 => CTR => E1: 1,8 * INC A9: 9 + E1: 1,8 # I6: 5,7 => UNS * DIS A9: 9 + E1: 1,8 # I6: 2 => CTR => I6: 5,7 * DIS A9: 9 + E1: 1,8 + I6: 5,7 # D8: 6,8 => CTR => D8: 1,4 * DIS A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 # D9: 6,8 => CTR => D9: 2 * PRF A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 # D1: 1,8 => SOL * STA A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 + D1: 1,8 * CNT 8 HDP CHAINS / 8 HYP OPENED