Analysis of zz-www.sudokuoftheday.co.uk-20060823-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: ..8.42...5.....41...35...8......9.6..6....74...2...3.9...4...7......1.....435.69. initial
Autosolve
position: ..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 1,7 => SOL * PRF # D1: 6 => SOL * DIS # B6: 1,7 => CTR => B6: 8 * DIS # A3: 1 => CTR => A3: 4,9 * DIS # D2: 6,7 => CTR => D2: 8,9 * DIS # E2: 6,7 => CTR => E2: 8,9 * DIS # D2: 6,7 => CTR => D2: 8,9 * DIS # E2: 6,7 => CTR => E2: 8,9 * DIS # A4: 1,8 => CTR => A4: 3,4,7 * DIS # E4: 1,8 => CTR => E4: 3,7 * DIS # B9: 1 => CTR => B9: 7,8 * DIS # G7: 1 => CTR => G7: 5,8 * PRF # B9: 7 => SOL * CNT 13 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 1,7 => SOL * STA A1: 1,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..8.42...5.....41...35...8......9.6..6....74...2...3.9...4...7......1.....435.69. | initial |
| ..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69. | autosolve |
| 718642935526893417943517286457239168369185742182764359891426573635971824274358691 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 1,7 B3: 4,9 E3: 1,9 F3: 6,7 I2: 6,7 I3: 6,7 C5: 1,9 G4: 1,8 B7: 5,9 B8: 3,5 F7: 6,8 F9: 7,8 G8: 5,8 I9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E3: 1.. / D1 = 1 => 0 pairs (X) / E3 = 1 => 19 pairs (_) G7,I9: 1.. / G7 = 1 => 0 pairs (X) / I9 = 1 => 17 pairs (_) A3,E3: 1.. / A3 = 1 => 0 pairs (X) / E3 = 1 => 19 pairs (_) B9,I9: 1.. / B9 = 1 => 0 pairs (X) / I9 = 1 => 17 pairs (_) G4,G7: 1.. / G4 = 1 => 17 pairs (_) / G7 = 1 => 0 pairs (X) D4,D5: 2.. / D4 = 2 => 18 pairs (_) / D5 = 2 => 15 pairs (_) I4,I5: 2.. / I4 = 2 => 15 pairs (_) / I5 = 2 => 18 pairs (_) D4,I4: 2.. / D4 = 2 => 18 pairs (_) / I4 = 2 => 15 pairs (_) D5,I5: 2.. / D5 = 2 => 15 pairs (_) / I5 = 2 => 18 pairs (_) E4,E5: 3.. / E4 = 3 => 19 pairs (_) / E5 = 3 => 18 pairs (_) A8,B8: 3.. / A8 = 3 => 15 pairs (_) / B8 = 3 => 14 pairs (_) A5,E5: 3.. / A5 = 3 => 19 pairs (_) / E5 = 3 => 18 pairs (_) B4,B8: 3.. / B4 = 3 => 15 pairs (_) / B8 = 3 => 14 pairs (_) A3,B3: 4.. / A3 = 4 => 21 pairs (_) / B3 = 4 => 14 pairs (_) A4,B4: 4.. / A4 = 4 => 14 pairs (_) / B4 = 4 => 21 pairs (_) A3,A4: 4.. / A3 = 4 => 21 pairs (_) / A4 = 4 => 14 pairs (_) B3,B4: 4.. / B3 = 4 => 14 pairs (_) / B4 = 4 => 21 pairs (_) B4,C4: 5.. / B4 = 5 => 16 pairs (_) / C4 = 5 => 17 pairs (_) G7,G8: 5.. / G7 = 5 => 16 pairs (_) / G8 = 5 => 17 pairs (_) A1,C2: 6.. / A1 = 6 => 16 pairs (_) / C2 = 6 => 0 pairs (*) I2,I3: 6.. / I2 = 6 => 27 pairs (_) / I3 = 6 => 0 pairs (*) D6,E6: 6.. / D6 = 6 => 17 pairs (_) / E6 = 6 => 15 pairs (_) A1,D1: 6.. / A1 = 6 => 16 pairs (_) / D1 = 6 => 0 pairs (*) F3,I3: 6.. / F3 = 6 => 27 pairs (_) / I3 = 6 => 0 pairs (*) F3,F7: 6.. / F3 = 6 => 27 pairs (_) / F7 = 6 => 0 pairs (*) I2,I3: 7.. / I2 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) F3,I3: 7.. / F3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) B9,F9: 7.. / B9 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) F3,F9: 7.. / F3 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) D2,E2: 8.. / D2 = 8 => 16 pairs (_) / E2 = 8 => 15 pairs (_) F7,F9: 8.. / F7 = 8 => 27 pairs (_) / F9 = 8 => 0 pairs (*) A8,G8: 8.. / A8 = 8 => 17 pairs (_) / G8 = 8 => 16 pairs (_) B6,B9: 8.. / B6 = 8 => 16 pairs (_) / B9 = 8 => 0 pairs (X) A5,C5: 9.. / A5 = 9 => 26 pairs (_) / C5 = 9 => 18 pairs (_) D8,E8: 9.. / D8 = 9 => 15 pairs (_) / E8 = 9 => 23 pairs (_) B3,B7: 9.. / B3 = 9 => 21 pairs (_) / B7 = 9 => 14 pairs (_) D2,D8: 9.. / D2 = 9 => 23 pairs (_) / D8 = 9 => 15 pairs (_) * DURATION: 0:00:47.010227 START: 02:00:39.902807 END: 02:01:26.913034 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,B7,B8,C5,E3,F3,F7,F9,G4,G8,I2,I3,I9) * ..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69. * PAIR B1: 1,7 BLK 1 A1: 1,7,6 # reduction candidate for 1,7 A1: 1,7 => SOLVED * 718642935526893417943517286457239168369185742182764359891426573635971824274358691 A1: 6 # 16 pairs * PAIR B1: 1,7 ROW 1 D1: 1,7,6 # reduction candidate for 1,7 D1: 6 => SOLVED * 718642935526893417943517286457239168369185742182764359891426573635971824274358691 D1: 1,7 # 16 pairs * PAIR B1: 1,7 COL B B6: 1,7,8 # reduction candidate for 1,7 B6: 1,7 => CTR * 6.8.4293552...3416.435.62874....916..61..574..72..4359196428573735..1824284357691 B6: 8 # 16 pairs B9: 1,7,8 # reduction candidate for 1,7 B9: 1,7 # 16 pairs * PAIR B3: 4,9 BLK 1 A3: 4,9,1 # reduction candidate for 4,9 A3: 1 => CTR * .78142935529..341.14359.28.4....9.6.961.3574..82.14359.9.42.17335.9.1.242.435.69. A3: 4,9 # 19 pairs * PAIR E3: 1,9 ROW 3 A3: 1,9,4 # reduction candidate for 1,9 A3: 4 # 21 pairs A3: 1,9 # 14 pairs * PAIR F3: 6,7 BLK 2 D1: 6,7,1 # reduction candidate for 6,7 D1: 6,7 # 19 pairs D2: 6,7,8,9 # reduction candidate for 6,7 D2: 6,7 => CTR * ..8142935529.8341.14359.28.4....9.6.961.3574...2.14359.9.42.17335.9.1.242.435.69. D2: 8,9 # 15 pairs E2: 6,7,8,9 # reduction candidate for 6,7 E2: 6,7 => CTR * ..81429355298.341.14359.28.4....9.6.961235748..2614359.9.42.173...9.1.242.435.69. E2: 8,9 # 15 pairs * PAIR I2: 6,7 ROW 2 C2: 6,7,9 # reduction candidate for 6,7 C2: 6,7 # 19 pairs D2: 6,7,8,9 # reduction candidate for 6,7 D2: 6,7 => CTR * ..8142935529.8341.14359.28.4....9.6.961.3574...2.14359.9.42.17335.9.1.242.435.69. D2: 8,9 # 15 pairs E2: 6,7,8,9 # reduction candidate for 6,7 E2: 6,7 => CTR * ..81429355298.341.14359.28.4....9.6.961235748..2614359.9.42.173...9.1.242.435.69. E2: 8,9 # 15 pairs * PAIR C5: 1,9 BLK 4 A5: 1,9,3,8 # reduction candidate for 1,9 A5: 1,9 # 26 pairs A5: 3,8 # 22 pairs * PAIR C5: 1,9 COL C C7: 1,9,5,6 # reduction candidate for 1,9 C7: 5,6 # 24 pairs C7: 1,9 # 21 pairs * PAIR G4: 1,8 BLK 6 I4: 1,8,2 # reduction candidate for 1,8 I4: 1,8 # 18 pairs I5: 1,8,2 # reduction candidate for 1,8 I5: 1,8 # 15 pairs * PAIR G4: 1,8 ROW 4 A4: 1,8,3,4,7 # reduction candidate for 1,8 A4: 1,8 => CTR * ..8.4293552...341.49351.28..45.39.6.369.8574...2..4359951426873836..1524274358691 A4: 3,4,7 # 14 pairs D4: 1,8,2,7 # reduction candidate for 1,8 D4: 1,8 # 18 pairs E4: 1,8,3,7 # reduction candidate for 1,8 E4: 1,8 => CTR * 6781429355298734161435962874357.9.6296.23574...2..4359..6428.73..7..1.242.435769. E4: 3,7 # 15 pairs * PAIR G4: 1,8 COL G G7: 1,8,5 # reduction candidate for 1,8 G7: 1,8 # 17 pairs G7: 5 # 16 pairs * PAIR B7: 5,9 BLK 7 C7: 5,9,1,6 # reduction candidate for 5,9 C7: 5,9 # 29 pairs C7: 1,6 # 15 pairs * PAIR B8: 3,5 COL B B4: 3,5,4 # reduction candidate for 3,5 B4: 4 # 21 pairs B4: 3,5 # 14 pairs * PAIR F7: 6,8 ROW 7 A7: 6,8,1,9 # reduction candidate for 6,8 A7: 6,8 # 16 pairs A7: 1,9 # 15 pairs * PAIR F9: 7,8 ROW 9 B9: 7,8,1 # reduction candidate for 7,8 B9: 1 => CTR * 678142935529..341614359628745...986..6...574..82..4359...428173837..1524214357698 B9: 7,8 # 17 pairs * PAIR G8: 5,8 BLK 9 G7: 5,8,1 # reduction candidate for 5,8 G7: 1 => CTR * 678142935529..341614359628745...986..6...574..82..4359...428173837..1524214357698 G7: 5,8 # 17 pairs * PAIR I9: 1,8 BLK 9 G7: 1,8,5 # reduction candidate for 1,8 G7: 1,8 # 17 pairs G7: 5 # 16 pairs * PAIR I9: 1,8 ROW 9 B9: 1,8,7 # reduction candidate for 1,8 B9: 7 => SOLVED * 718642935526893417943517286457239168369185742182764359891426573635971824274358691 B9: 1,8 # 27 pairs * PAIR I9: 1,8 COL I I4: 1,8,2 # reduction candidate for 1,8 I4: 1,8 # 18 pairs I5: 1,8,2 # reduction candidate for 1,8 I5: 1,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060823-absurd-base-pr-000.dot * REASONING * PRF # A1: 1,7 => SOL * PRF # D1: 6 => SOL * DIS # B6: 1,7 => CTR => B6: 8 * DIS # A3: 1 => CTR => A3: 4,9 * DIS # D2: 6,7 => CTR => D2: 8,9 * DIS # E2: 6,7 => CTR => E2: 8,9 * DIS # D2: 6,7 => CTR => D2: 8,9 * DIS # E2: 6,7 => CTR => E2: 8,9 * DIS # A4: 1,8 => CTR => A4: 3,4,7 * DIS # E4: 1,8 => CTR => E4: 3,7 * DIS # B9: 1 => CTR => B9: 7,8 * DIS # G7: 1 => CTR => G7: 5,8 * PRF # B9: 7 => SOL * CNT 13 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,B7,B8,C5,E3,F3,F7,F9,G4,G8,I2,I3,I9) * ..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69. * PAIR B1: 1,7 BLK 1 A1: 1,7,6 # reduction candidate for 1,7 A1: 1,7 => SOLVED * 718642935526893417943517286457239168369185742182764359891426573635971824274358691 * DURATION: 0:00:01.705468 START: 02:02:00.863084 END: 02:02:02.568552 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060823-absurd-base-pr-001.dot * REASONING * PRF # A1: 1,7 => SOL * STA A1: 1,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060823, absurd
Solution
position: 718642935526893417943517286457239168369185742182764359891426573635971824274358691 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 # A1: 1,7 => SOL * INC # A1: 6 => UNS * INC # D1: 1,7 => UNS * PRF # D1: 6 => SOL * DIS # B6: 1,7 => CTR => B6: 8 * INC # B6: 8 => UNS * INC # B9: 1,7 => UNS * INC # A3: 4,9 => UNS * DIS # A3: 1 => CTR => A3: 4,9 * INC # A3: 1,9 => UNS * INC # A3: 4 => UNS * INC # D1: 6,7 => UNS * DIS # D2: 6,7 => CTR => D2: 8,9 * INC # D2: 8,9 => UNS * DIS # E2: 6,7 => CTR => E2: 8,9 * INC # E2: 8,9 => UNS * INC # C2: 6,7 => UNS * DIS # D2: 6,7 => CTR => D2: 8,9 * INC # D2: 8,9 => UNS * DIS # E2: 6,7 => CTR => E2: 8,9 * INC # E2: 8,9 => UNS * INC # A5: 1,9 => UNS * INC # A5: 3,8 => UNS * INC # C7: 1,9 => UNS * INC # C7: 5,6 => UNS * INC # I4: 1,8 => UNS * INC # I5: 1,8 => UNS * DIS # A4: 1,8 => CTR => A4: 3,4,7 * INC # A4: 3,4,7 => UNS * INC # D4: 1,8 => UNS * DIS # E4: 1,8 => CTR => E4: 3,7 * INC # E4: 3,7 => UNS * INC # G7: 1,8 => UNS * INC # G7: 5 => UNS * INC # C7: 5,9 => UNS * INC # C7: 1,6 => UNS * INC # B4: 3,5 => UNS * INC # B4: 4 => UNS * INC # A7: 6,8 => UNS * INC # A7: 1,9 => UNS * INC # B9: 7,8 => UNS * DIS # B9: 1 => CTR => B9: 7,8 * INC # G7: 5,8 => UNS * DIS # G7: 1 => CTR => G7: 5,8 * INC # G7: 1,8 => UNS * INC # G7: 5 => UNS * INC # B9: 1,8 => UNS * PRF # B9: 7 => SOL * INC # I4: 1,8 => UNS * INC # I5: 1,8 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 1,7 => SOL * STA A1: 1,7 * CNT 1 HDP CHAINS / 1 HYP OPENED