Analysis of zz-www.sudokuoftheday.co.uk-20190117-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: 6.91..83.........47..3.6..13...5..7....8.....1...9.3....3..7..5..2..8.1.5..9....6 initial
Autosolve
position: 6.91.5837.31..9..47..3.6..13...5..7....8.....1...9.3...63.17..5..2568.1351.9....6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B4: 2,4 => SOL * DIS # B5: 2,4 => CTR => B5: 5,7,9 * DIS # E2: 7 => CTR => E2: 2,8 * DIS # E2: 2,7 => CTR => E2: 8 * DIS # D6: 2,7 => CTR => D6: 4,6 * DIS # C3: 4,8 => CTR => C3: 5 * DIS # G5: 5,6 => CTR => G5: 1 * DIS # H5: 5,6 => CTR => H5: 4 * PRF # G7: 4 => SOL * DIS # H7: 8 => CTR => H7: 2,9 * DIS # F4: 2,4 => CTR => F4: 1 * DIS # F5: 2,4 => CTR => F5: 1,3 * DIS # D6: 2,4 => CTR => D6: 6,7 * DIS # F9: 3 => CTR => F9: 2,4 * DIS # G5: 5 => CTR => G5: 1,6 * DIS # I4: 8 => CTR => I4: 2,9 * DIS # B5: 2,9 => CTR => B5: 4,5,7 * DIS # B6: 2,8 => CTR => B6: 4,5,7 * DIS # A7: 4,9 => CTR => A7: 8 * PRF # B8: 4,9 => SOL * PRF # G8: 7 => SOL * DIS # A5: 2 => CTR => A5: 4,9 * DIS # F9: 3 => CTR => F9: 2,4 * DIS # D6: 2,4 => CTR => D6: 6,7 * DIS # F9: 2,3 => CTR => F9: 4 * PRF # F9: 4 => SOL * DIS # E5: 2,3 => CTR => E5: 7 * CNT 27 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B4: 2,4 => SOL * STA B4: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.91..83.........47..3.6..13...5..7....8.....1...9.3....3..7..5..2..8.1.5..9....6 | initial |
| 6.91.5837.31..9..47..3.6..13...5..7....8.....1...9.3...63.17..5..2568.1351.9....6 | autosolve |
| 649125837231789564785346921328451679956873142174692358863217495492568713517934286 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 2,4 A2: 2,8 E1: 2,4 D2: 2,7 E3: 4,8 G2: 5,6 H2: 5,6 G3: 2,9 H3: 2,9 F6: 2,4 G4: 1,6 I5: 2,9 I6: 2,8 A8: 4,9 D7: 2,4 E9: 2,3 H9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F5: 1.. / F4 = 1 => 18 pairs (_) / F5 = 1 => 0 pairs (X) G4,G5: 1.. / G4 = 1 => 0 pairs (X) / G5 = 1 => 18 pairs (_) F4,G4: 1.. / F4 = 1 => 18 pairs (_) / G4 = 1 => 0 pairs (X) F5,G5: 1.. / F5 = 1 => 0 pairs (X) / G5 = 1 => 18 pairs (_) B1,A2: 2.. / B1 = 2 => 0 pairs (X) / A2 = 2 => 19 pairs (_) G3,H3: 2.. / G3 = 2 => 18 pairs (_) / H3 = 2 => 17 pairs (_) B1,E1: 2.. / B1 = 2 => 0 pairs (X) / E1 = 2 => 19 pairs (_) A2,A5: 2.. / A2 = 2 => 19 pairs (_) / A5 = 2 => 0 pairs (X) E5,F5: 3.. / E5 = 3 => 0 pairs (X) / F5 = 3 => 18 pairs (_) E9,F9: 3.. / E9 = 3 => 18 pairs (_) / F9 = 3 => 0 pairs (X) E5,E9: 3.. / E5 = 3 => 0 pairs (X) / E9 = 3 => 18 pairs (_) F5,F9: 3.. / F5 = 3 => 18 pairs (_) / F9 = 3 => 0 pairs (X) E1,E3: 4.. / E1 = 4 => 0 pairs (X) / E3 = 4 => 19 pairs (_) H5,H6: 4.. / H5 = 4 => 24 pairs (_) / H6 = 4 => 0 pairs (X) D7,F9: 4.. / D7 = 4 => 0 pairs (X) / F9 = 4 => 0 pairs (_) B1,E1: 4.. / B1 = 4 => 19 pairs (_) / E1 = 4 => 0 pairs (X) B3,C3: 5.. / B3 = 5 => 0 pairs (X) / C3 = 5 => 19 pairs (_) G2,H2: 5.. / G2 = 5 => 18 pairs (_) / H2 = 5 => 0 pairs (X) G2,G5: 5.. / G2 = 5 => 18 pairs (_) / G5 = 5 => 0 pairs (X) G2,H2: 6.. / G2 = 6 => 0 pairs (X) / H2 = 6 => 18 pairs (_) D4,D6: 6.. / D4 = 6 => 0 pairs (X) / D6 = 6 => 18 pairs (_) D2,E2: 7.. / D2 = 7 => 18 pairs (_) / E2 = 7 => 0 pairs (X) E5,D6: 7.. / E5 = 7 => 18 pairs (_) / D6 = 7 => 0 pairs (X) B8,C9: 7.. / B8 = 7 => 20 pairs (_) / C9 = 7 => 0 pairs (*) G8,G9: 7.. / G8 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) B8,G8: 7.. / B8 = 7 => 20 pairs (_) / G8 = 7 => 0 pairs (*) C9,G9: 7.. / C9 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) D2,D6: 7.. / D2 = 7 => 18 pairs (_) / D6 = 7 => 0 pairs (X) E2,E5: 7.. / E2 = 7 => 0 pairs (X) / E5 = 7 => 18 pairs (_) E2,E3: 8.. / E2 = 8 => 19 pairs (_) / E3 = 8 => 0 pairs (X) I4,I6: 8.. / I4 = 8 => 0 pairs (X) / I6 = 8 => 17 pairs (_) A7,C9: 8.. / A7 = 8 => 19 pairs (_) / C9 = 8 => 0 pairs (X) H7,H9: 8.. / H7 = 8 => 0 pairs (X) / H9 = 8 => 19 pairs (_) A2,E2: 8.. / A2 = 8 => 0 pairs (X) / E2 = 8 => 19 pairs (_) A7,H7: 8.. / A7 = 8 => 19 pairs (_) / H7 = 8 => 0 pairs (X) C9,H9: 8.. / C9 = 8 => 0 pairs (X) / H9 = 8 => 19 pairs (_) A2,A7: 8.. / A2 = 8 => 0 pairs (X) / A7 = 8 => 19 pairs (_) G3,H3: 9.. / G3 = 9 => 17 pairs (_) / H3 = 9 => 18 pairs (_) I4,I5: 9.. / I4 = 9 => 19 pairs (_) / I5 = 9 => 19 pairs (_) B4,I4: 9.. / B4 = 9 => 19 pairs (_) / I4 = 9 => 19 pairs (_) H3,H7: 9.. / H3 = 9 => 18 pairs (_) / H7 = 9 => 17 pairs (_) * DURATION: 0:00:57.847968 START: 03:00:34.162147 END: 03:01:32.010115 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,D2,D7,E1,E3,E9,F6,G2,G3,G4,H2,H3,H9,I5,I6) * 6.91.5837.31..9..47..3.6..13...5..7....8.....1...9.3...63.17..5..2568.1351.9....6 * PAIR B1: 2,4 COL B B4: 2,4,8,9 # reduction candidate for 2,4 B4: 2,4 => SOLVED * 649125837231789564785346921328451679956873142174692358863217495492568713517934286 B4: 8,9 # 18 pairs B5: 2,4,5,7,9 # reduction candidate for 2,4 B5: 2,4 => CTR * 6.91.5837.31..9..4785346..1398.5..72...8....915..92348863.17..59725684135149.3786 B5: 5,7,9 # 17 pairs B6: 2,4,5,7,8 # reduction candidate for 2,4 B6: 2,4 # 28 pairs * PAIR A2: 2,8 ROW 2 E2: 2,8,7 # reduction candidate for 2,8 E2: 7 => CTR * 6.91.5837831279..47..386..13...5..7.2..83...91..79.3...63417.854.2568.1351892...6 E2: 2,8 # 18 pairs * PAIR D2: 2,7 BLK 2 E2: 2,7,8 # reduction candidate for 2,7 E2: 2,7 => CTR * 629145837831.29..47..38629139..5..782..8731.9187.9.352.63217.85.72568.13518934726 E2: 8 # 19 pairs * PAIR D2: 2,7 COL D D6: 2,7,4,6 # reduction candidate for 2,7 D6: 2,7 => CTR * 629145837831279..47..386..13..65.17.2..831..91..79.3..9634172.5..2568.1351.923.86 D6: 4,6 # 18 pairs * PAIR E3: 4,8 ROW 3 B3: 4,8,5 # reduction candidate for 4,8 B3: 4,8 # 19 pairs C3: 4,8,5 # reduction candidate for 4,8 C3: 4,8 => CTR * 649125837231789..4758346..13.425167.9.687..4.1...943...63417..54.2568.1351.9..4.6 C3: 5 # 19 pairs * PAIR G2: 5,6 COL G G5: 5,6,1 # reduction candidate for 5,6 G5: 5,6 => CTR * 629145837831279..47..386..13..65.17.2..831..91..79.3..9634172.5..2568.1351.923.86 G5: 1 # 18 pairs * PAIR H2: 5,6 COL H H5: 5,6,4 # reduction candidate for 5,6 H5: 5,6 => CTR * 649125837231789..4785346..13.8.5..7....87315.1576923488632174.5..2568.1351.9...86 H5: 4 # 24 pairs H6: 5,6,4 # reduction candidate for 5,6 H6: 5,6 # 24 pairs * PAIR G3: 2,9 COL G G7: 2,9,4 # reduction candidate for 2,9 G7: 4 => SOLVED * 649125837231789564785346921328451679956873142174692358863217495492568713517934286 G7: 2,9 # 21 pairs * PAIR H3: 2,9 COL H H7: 2,9,8 # reduction candidate for 2,9 H7: 8 => CTR * 629145837831729..47..38629139..5..782..8731.9187.923...63217.85.72568.13518934726 H7: 2,9 # 19 pairs * PAIR F6: 2,4 BLK 5 D4: 2,4,6 # reduction candidate for 2,4 D4: 2,4 # 18 pairs F4: 2,4,1 # reduction candidate for 2,4 F4: 2,4 => CTR * 629145837831279..47..386..13..65.17.2..831..91..79.3..9634172.5..2568.1351.923.86 F4: 1 # 18 pairs F5: 2,4,1,3 # reduction candidate for 2,4 F5: 2,4 => CTR * 6.91.5837.31..9..47..3.6..13...5167...683.1..1...9.3...63.17..5..2568.1351.9....6 F5: 1,3 # 18 pairs D6: 2,4,6,7 # reduction candidate for 2,4 D6: 2,4 => CTR * 6.91.5837.317.9..47..3.6..13..65.17....87....1...9.3...63.17..5..2568.1351.9....6 D6: 6,7 # 18 pairs * PAIR F6: 2,4 ROW 6 B6: 2,4,5,7,8 # reduction candidate for 2,4 B6: 2,4 # 28 pairs B6: 5,7,8 # 17 pairs * PAIR F6: 2,4 COL F F9: 2,4,3 # reduction candidate for 2,4 F9: 3 => CTR * 629145837831279..47..386..13..65.17.2..831..91..79.3..9634172.5..2568.1351.923.86 F9: 2,4 # 18 pairs * PAIR G4: 1,6 BLK 6 G5: 1,6,5 # reduction candidate for 1,6 G5: 5 => CTR * 6291458378312796547..386..13..65.17.2..8315.91..79.3..9634172.5..2568.1351.923.86 G5: 1,6 # 18 pairs * PAIR I5: 2,9 BLK 6 I4: 2,9,8 # reduction candidate for 2,9 I4: 8 => CTR * 6.91.5837.31..9..47..3.6..1394.5..782..8...491...943.2.63417..547256891351.9....6 I4: 2,9 # 17 pairs * PAIR I5: 2,9 ROW 5 A5: 2,9,4 # reduction candidate for 2,9 A5: 2,9 # 21 pairs B5: 2,9,4,5,7 # reduction candidate for 2,9 B5: 2,9 => CTR * 6.91.5837231789..47..346..13...5..7.4..8731..1...9.34.863.17..59.2568.13514932..6 B5: 4,5,7 # 17 pairs * PAIR I6: 2,8 BLK 6 I4: 2,8,9 # reduction candidate for 2,8 I4: 9 # 19 pairs I4: 2,8 # 19 pairs * PAIR I6: 2,8 ROW 6 B6: 2,8,4,5,7 # reduction candidate for 2,8 B6: 2,8 => CTR * 6.91.5837.31..9..47..3.6..13...5..7..7.8...4.1..7943..863417..54925687135179..486 B6: 4,5,7 # 17 pairs * PAIR A8: 4,9 BLK 7 A7: 4,9,8 # reduction candidate for 4,9 A7: 4,9 => CTR * 629145837831.29..47..38629139..5..782..8731.9187.9.352.63217.85.72568.13518934726 A7: 8 # 19 pairs B8: 4,9,7 # reduction candidate for 4,9 B8: 4,9 => SOLVED * 649125837231789564785346921328451679956873142174692358863217495492568713517934286 B8: 7 # 20 pairs * PAIR A8: 4,9 ROW 8 G8: 4,9,7 # reduction candidate for 4,9 G8: 7 => SOLVED * 649125837231789564785346921328451679956873142174692358863217495492568713517934286 G8: 4,9 # 20 pairs * PAIR A8: 4,9 COL A A5: 4,9,2 # reduction candidate for 4,9 A5: 2 => CTR * 629145837831.29..47..38629139..521782..87...918..9.3.2.63.17.85..2568.135189..726 A5: 4,9 # 19 pairs * PAIR D7: 2,4 BLK 8 F9: 2,4,3 # reduction candidate for 2,4 F9: 3 => CTR * 629145837831279..47..386..13..65.17.2..831..91..79.3..9634172.5..2568.1351.923.86 F9: 2,4 # 18 pairs * PAIR D7: 2,4 ROW 7 G7: 2,4,9 # reduction candidate for 2,4 G7: 2,4 # 20 pairs G7: 9 # 19 pairs * PAIR D7: 2,4 COL D D4: 2,4,6 # reduction candidate for 2,4 D4: 2,4 # 18 pairs D6: 2,4,6,7 # reduction candidate for 2,4 D6: 2,4 => CTR * 6.91.5837.317.9..47..3.6..13..65.17....87....1...9.3...63.17..5..2568.1351.9....6 D6: 6,7 # 18 pairs * PAIR E9: 2,3 BLK 8 F9: 2,3,4 # reduction candidate for 2,3 F9: 2,3 => CTR * 6491258372317895647.5346..13.425167.95687314212.69435.863417..5..2568.1351.932.86 F9: 4 => SOLVED * 649125837231789564785346921328451679956873142174692358863217495492568713517934286 * PAIR E9: 2,3 COL E E5: 2,3,7 # reduction candidate for 2,3 E5: 2,3 => CTR * 6.9145837831279..47..386..13..65.17.2..831..91..79.3...63417.854.2568.1351892...6 E5: 7 # 18 pairs * PAIR H9: 2,8 BLK 9 H7: 2,8,9 # reduction candidate for 2,8 H7: 2,8 # 18 pairs H7: 9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190117-absurd-base-pr-000.dot * REASONING * PRF # B4: 2,4 => SOL * DIS # B5: 2,4 => CTR => B5: 5,7,9 * DIS # E2: 7 => CTR => E2: 2,8 * DIS # E2: 2,7 => CTR => E2: 8 * DIS # D6: 2,7 => CTR => D6: 4,6 * DIS # C3: 4,8 => CTR => C3: 5 * DIS # G5: 5,6 => CTR => G5: 1 * DIS # H5: 5,6 => CTR => H5: 4 * PRF # G7: 4 => SOL * DIS # H7: 8 => CTR => H7: 2,9 * DIS # F4: 2,4 => CTR => F4: 1 * DIS # F5: 2,4 => CTR => F5: 1,3 * DIS # D6: 2,4 => CTR => D6: 6,7 * DIS # F9: 3 => CTR => F9: 2,4 * DIS # G5: 5 => CTR => G5: 1,6 * DIS # I4: 8 => CTR => I4: 2,9 * DIS # B5: 2,9 => CTR => B5: 4,5,7 * DIS # B6: 2,8 => CTR => B6: 4,5,7 * DIS # A7: 4,9 => CTR => A7: 8 * PRF # B8: 4,9 => SOL * PRF # G8: 7 => SOL * DIS # A5: 2 => CTR => A5: 4,9 * DIS # F9: 3 => CTR => F9: 2,4 * DIS # D6: 2,4 => CTR => D6: 6,7 * DIS # F9: 2,3 => CTR => F9: 4 * PRF # F9: 4 => SOL * DIS # E5: 2,3 => CTR => E5: 7 * CNT 27 HDP CHAINS / 66 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,D2,D7,E1,E3,E9,F6,G2,G3,G4,H2,H3,H9,I5,I6) * 6.91.5837.31..9..47..3.6..13...5..7....8.....1...9.3...63.17..5..2568.1351.9....6 * PAIR B1: 2,4 COL B B4: 2,4,8,9 # reduction candidate for 2,4 B4: 2,4 => SOLVED * 649125837231789564785346921328451679956873142174692358863217495492568713517934286 * DURATION: 0:00:01.750997 START: 03:02:20.047918 END: 03:02:21.798915 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190117-absurd-base-pr-001.dot * REASONING * PRF # B4: 2,4 => SOL * STA B4: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190117, absurd
Solution
position: 649125837231789564785346921328451679956873142174692358863217495492568713517934286 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 # B4: 2,4 => SOL * INC # B4: 8,9 => UNS * DIS # B5: 2,4 => CTR => B5: 5,7,9 * INC # B5: 5,7,9 => UNS * INC # B6: 2,4 => UNS * INC # E2: 2,8 => UNS * DIS # E2: 7 => CTR => E2: 2,8 * DIS # E2: 2,7 => CTR => E2: 8 * INC # E2: 8 => UNS * DIS # D6: 2,7 => CTR => D6: 4,6 * INC # D6: 4,6 => UNS * INC # B3: 4,8 => UNS * DIS # C3: 4,8 => CTR => C3: 5 * INC # C3: 5 => UNS * DIS # G5: 5,6 => CTR => G5: 1 * INC # G5: 1 => UNS * DIS # H5: 5,6 => CTR => H5: 4 * INC # H5: 4 => UNS * INC # H6: 5,6 => UNS * INC # G7: 2,9 => UNS * PRF # G7: 4 => SOL * INC # H7: 2,9 => UNS * DIS # H7: 8 => CTR => H7: 2,9 * INC # D4: 2,4 => UNS * DIS # F4: 2,4 => CTR => F4: 1 * INC # F4: 1 => UNS * DIS # F5: 2,4 => CTR => F5: 1,3 * INC # F5: 1,3 => UNS * DIS # D6: 2,4 => CTR => D6: 6,7 * INC # D6: 6,7 => UNS * INC # B6: 2,4 => UNS * INC # B6: 5,7,8 => UNS * INC # F9: 2,4 => UNS * DIS # F9: 3 => CTR => F9: 2,4 * INC # G5: 1,6 => UNS * DIS # G5: 5 => CTR => G5: 1,6 * INC # I4: 2,9 => UNS * DIS # I4: 8 => CTR => I4: 2,9 * INC # A5: 2,9 => UNS * DIS # B5: 2,9 => CTR => B5: 4,5,7 * INC # B5: 4,5,7 => UNS * INC # I4: 2,8 => UNS * INC # I4: 9 => UNS * DIS # B6: 2,8 => CTR => B6: 4,5,7 * INC # B6: 4,5,7 => UNS * DIS # A7: 4,9 => CTR => A7: 8 * INC # A7: 8 => UNS * PRF # B8: 4,9 => SOL * INC # B8: 7 => UNS * INC # G8: 4,9 => UNS * PRF # G8: 7 => SOL * INC # A5: 4,9 => UNS * DIS # A5: 2 => CTR => A5: 4,9 * INC # F9: 2,4 => UNS * DIS # F9: 3 => CTR => F9: 2,4 * INC # G7: 2,4 => UNS * INC # G7: 9 => UNS * INC # D4: 2,4 => UNS * DIS # D6: 2,4 => CTR => D6: 6,7 * INC # D6: 6,7 => UNS * DIS # F9: 2,3 => CTR => F9: 4 * PRF # F9: 4 => SOL * DIS # E5: 2,3 => CTR => E5: 7 * INC # E5: 7 => UNS * INC # H7: 2,8 => UNS * INC # H7: 9 => UNS * CNT 66 HDP CHAINS / 66 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B4: 2,4 => SOL * STA B4: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED