Analysis of zz-www.sudokuoftheday.co.uk-20190217-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: .78.5..3...3..92......1.6..3.9.....6..1...5..8....1947...89.4...85.6............2 initial
Autosolve
position: .78.5.13...3..92......1.6..3.9...8167.19..5238....1947...89.465.85.6..91...1.5.82 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 4,5 => CTR => A2: 1,6 * DIS # A3: 2,9 => CTR => A3: 4,5 * DIS # A3: 2,4 => CTR => A3: 5,9 * DIS # D3: 2,4 => CTR => D3: 3,7 * DIS # F3: 2,4 => CTR => F3: 3,7,8 * DIS # I3: 8 => CTR => I3: 4,9 * PRF # I3: 9 => SOL * DIS # E2: 7 => CTR => E2: 4,8 * DIS # F5: 8 => CTR => F5: 4,6 * DIS # E4: 4,7 => CTR => E4: 2 * DIS # F3: 4,7 => CTR => F3: 2,3,8 * DIS # E2: 7 => CTR => E2: 4,8 * DIS # B7: 1,2 => CTR => B7: 3 * DIS # F7: 3 => CTR => F7: 2,7 * DIS # A3: 2,4 => CTR => A3: 5,9 * DIS # E9: 4 => CTR => E9: 3,7 * CNT 16 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 4,5 => CTR => A2: 1,6 * DIS A2: 1,6 # A1: 4 => CTR => A1: 2,9 * PRF A2: 1,6 + A1: 2,9 # E2: 4,8 => SOL * STA A2: 1,6 + A1: 2,9 + E2: 4,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .78.5..3...3..92......1.6..3.9.....6..1...5..8....1947...89.4...85.6............2 | initial |
| .78.5.13...3..92......1.6..3.9...8167.19..5238....1947...89.465.85.6..91...1.5.82 | autosolve |
| 978256134613749258524318679349527816761984523852631947137892465285463791496175382 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B2: 1,6 B3: 2,9 C3: 2,4 I1: 4,9 H2: 5,7 I2: 4,8 H3: 5,7 B5: 4,6 C6: 2,6 F4: 4,7 E5: 4,8 E6: 2,3 A7: 1,2 C7: 2,7 A8: 2,4 G8: 3,7 G9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 0 pairs (X) / B2 = 1 => 17 pairs (_) A7,B7: 1.. / A7 = 1 => 17 pairs (_) / B7 = 1 => 0 pairs (X) A2,A7: 1.. / A2 = 1 => 0 pairs (X) / A7 = 1 => 17 pairs (_) B2,B7: 1.. / B2 = 1 => 17 pairs (_) / B7 = 1 => 0 pairs (X) E4,E6: 2.. / E4 = 2 => 19 pairs (_) / E6 = 2 => 0 pairs (X) B4,E4: 2.. / B4 = 2 => 0 pairs (X) / E4 = 2 => 19 pairs (_) D3,F3: 3.. / D3 = 3 => 19 pairs (_) / F3 = 3 => 0 pairs (X) D6,E6: 3.. / D6 = 3 => 0 pairs (X) / E6 = 3 => 19 pairs (_) B7,B9: 3.. / B7 = 3 => 18 pairs (_) / B9 = 3 => 0 pairs (X) G8,G9: 3.. / G8 = 3 => 17 pairs (_) / G9 = 3 => 18 pairs (_) B7,F7: 3.. / B7 = 3 => 18 pairs (_) / F7 = 3 => 0 pairs (X) E6,E9: 3.. / E6 = 3 => 19 pairs (_) / E9 = 3 => 0 pairs (X) B4,B5: 4.. / B4 = 4 => 18 pairs (_) / B5 = 4 => 19 pairs (_) C3,C9: 4.. / C3 = 4 => 18 pairs (_) / C9 = 4 => 0 pairs (X) A2,A3: 5.. / A2 = 5 => 0 pairs (X) / A3 = 5 => 15 pairs (_) H2,H3: 5.. / H2 = 5 => 15 pairs (_) / H3 = 5 => 0 pairs (X) B4,B6: 5.. / B4 = 5 => 19 pairs (_) / B6 = 5 => 19 pairs (_) D4,D6: 5.. / D4 = 5 => 19 pairs (_) / D6 = 5 => 19 pairs (_) A2,H2: 5.. / A2 = 5 => 0 pairs (X) / H2 = 5 => 15 pairs (_) A3,H3: 5.. / A3 = 5 => 15 pairs (_) / H3 = 5 => 0 pairs (X) B4,D4: 5.. / B4 = 5 => 19 pairs (_) / D4 = 5 => 19 pairs (_) B6,D6: 5.. / B6 = 5 => 19 pairs (_) / D6 = 5 => 19 pairs (_) F5,D6: 6.. / F5 = 6 => 19 pairs (_) / D6 = 6 => 18 pairs (_) B5,F5: 6.. / B5 = 6 => 18 pairs (_) / F5 = 6 => 19 pairs (_) C6,C9: 6.. / C6 = 6 => 0 pairs (X) / C9 = 6 => 21 pairs (_) F1,F5: 6.. / F1 = 6 => 18 pairs (_) / F5 = 6 => 19 pairs (_) H2,H3: 7.. / H2 = 7 => 0 pairs (X) / H3 = 7 => 15 pairs (_) C7,C9: 7.. / C7 = 7 => 18 pairs (_) / C9 = 7 => 0 pairs (X) G8,G9: 7.. / G8 = 7 => 18 pairs (_) / G9 = 7 => 17 pairs (_) C7,F7: 7.. / C7 = 7 => 18 pairs (_) / F7 = 7 => 0 pairs (X) E2,F3: 8.. / E2 = 8 => 0 pairs (X) / F3 = 8 => 20 pairs (_) I2,I3: 8.. / I2 = 8 => 20 pairs (_) / I3 = 8 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 20 pairs (_) / F5 = 8 => 0 pairs (X) E2,I2: 8.. / E2 = 8 => 0 pairs (X) / I2 = 8 => 20 pairs (_) F3,I3: 8.. / F3 = 8 => 20 pairs (_) / I3 = 8 => 0 pairs (X) E2,E5: 8.. / E2 = 8 => 0 pairs (X) / E5 = 8 => 20 pairs (_) F3,F5: 8.. / F3 = 8 => 20 pairs (_) / F5 = 8 => 0 pairs (X) I1,I3: 9.. / I1 = 9 => 17 pairs (_) / I3 = 9 => 0 pairs (*) A9,B9: 9.. / A9 = 9 => 16 pairs (_) / B9 = 9 => 20 pairs (_) A1,I1: 9.. / A1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) B3,B9: 9.. / B3 = 9 => 16 pairs (_) / B9 = 9 => 20 pairs (_) * DURATION: 0:00:49.567665 START: 03:47:51.513927 END: 03:48:41.081592 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B2,B3,B5,C3,C6,C7,E5,E6,F4,G8,G9,H2,H3,I1,I2) * .78.5.13...3..92......1.6..3.9...8167.19..5238....1947...89.465.85.6..91...1.5.82 * PAIR B2: 1,6 BLK 1 A2: 1,6,4,5 # reduction candidate for 1,6 A2: 4,5 => CTR * 678.5.1394136792585923186743.9.478167419865238....19471..89.465.85.6..91..41.5.82 A2: 1,6 # 17 pairs * PAIR B3: 2,9 BLK 1 A1: 2,9,4,6 # reduction candidate for 2,9 A1: 2,9 # 20 pairs A3: 2,9,4,5 # reduction candidate for 2,9 A3: 2,9 => CTR * 678.5.1395136.927...4.1865.3.9...8167.19.65238....19471..89.465.85.6..91...1.5.82 A3: 4,5 # 18 pairs * PAIR C3: 2,4 BLK 1 A1: 2,4,6,9 # reduction candidate for 2,4 A1: 2,4 # 16 pairs A3: 2,4,5,9 # reduction candidate for 2,4 A3: 2,4 => CTR * 678.5.1395136.927..9..186543.9...8167.19.65238....19471..89.465.85.6..91...1.5.82 A3: 5,9 # 18 pairs * PAIR C3: 2,4 ROW 3 D3: 2,4,3,7 # reduction candidate for 2,4 D3: 2,4 => CTR * .78.5613961378925459..136783.9...8167.19.85238..631947.3.89.465.8536.791..6175382 D3: 3,7 # 18 pairs F3: 2,4,3,7,8 # reduction candidate for 2,4 F3: 2,4 => CTR * .78.5613961378925459.31.6783.9...8167.19485238..631947...89.465.85.6..91..6175382 F3: 3,7,8 # 17 pairs * PAIR I1: 4,9 BLK 3 I3: 4,9,8 # reduction candidate for 4,9 I3: 8 => CTR * .78.56139613789254594.1.6783.95278167619485238526319471..89.465.85.6..91..61.5.82 I3: 4,9 # 20 pairs * PAIR I1: 4,9 ROW 1 A1: 4,9,2,6 # reduction candidate for 4,9 A1: 4,9 # 23 pairs A1: 2,6 # 20 pairs * PAIR I2: 4,8 BLK 3 I3: 4,8,9 # reduction candidate for 4,8 I3: 9 => SOLVED * 978256134613749258524318679349527816761984523852631947137892465285463791496175382 I3: 4,8 # 17 pairs * PAIR I2: 4,8 ROW 2 E2: 4,8,7 # reduction candidate for 4,8 E2: 7 => CTR * 978.5.134..34792585243186793.9.2.8167.198.5238.2.319472..89.465485.6..91.9.145382 E2: 4,8 # 22 pairs * PAIR B5: 4,6 ROW 5 F5: 4,6,8 # reduction candidate for 4,6 F5: 8 => CTR * .78.5613.613.892545.4.1.678349527816761948523852631947137892465285.64791496175382 F5: 4,6 # 20 pairs * PAIR C6: 2,6 BLK 4 B6: 2,6,5 # reduction candidate for 2,6 B6: 5 # 19 pairs B6: 2,6 # 19 pairs * PAIR F4: 4,7 BLK 5 D4: 4,7,5 # reduction candidate for 4,7 D4: 4,7 # 19 pairs E4: 4,7,2 # reduction candidate for 4,7 E4: 4,7 => CTR * .78.5.13...3..92......1.6..3295..816741986523856321947...89.465.85.6..91...135782 E4: 2 # 19 pairs * PAIR F4: 4,7 COL F F3: 4,7,2,3,8 # reduction candidate for 4,7 F3: 4,7 => CTR * .78.5613961378925459.31.6.83.9...8167.19485238..631947...89.465.85.6..91..6175382 F3: 2,3,8 # 17 pairs F8: 4,7,2,3 # reduction candidate for 4,7 F8: 4,7 # 21 pairs * PAIR E5: 4,8 BLK 5 F5: 4,8,6 # reduction candidate for 4,8 F5: 6 # 19 pairs F5: 4,8 # 18 pairs * PAIR E5: 4,8 COL E E2: 4,8,7 # reduction candidate for 4,8 E2: 7 => CTR * 978.5.134..34792585243186793.9.2.8167.198.5238.2.319472..89.465485.6..91.9.145382 E2: 4,8 # 22 pairs * PAIR A7: 1,2 BLK 7 B7: 1,2,3 # reduction candidate for 1,2 B7: 1,2 => CTR * .78.5.139..3..92...9431.6.83.9.2.8167.198.5238...31947..7893465.85.6.391936145782 B7: 3 # 18 pairs * PAIR C7: 2,7 ROW 7 F7: 2,7,3 # reduction candidate for 2,7 F7: 3 => CTR * .78.5.139..3..92...9431.6.83.9.2.8167.198.5238...31947..7893465.85.6.391936145782 F7: 2,7 # 18 pairs * PAIR A8: 2,4 ROW 8 D8: 2,4,3,7 # reduction candidate for 2,4 D8: 2,4 # 19 pairs F8: 2,4,3,7 # reduction candidate for 2,4 F8: 2,4 # 20 pairs * PAIR A8: 2,4 COL A A1: 2,4,6,9 # reduction candidate for 2,4 A1: 2,4 # 16 pairs A3: 2,4,5,9 # reduction candidate for 2,4 A3: 2,4 => CTR * 678.5.1395136.927..9..186543.9...8167.19.65238....19471..89.465.85.6..91...1.5.82 A3: 5,9 # 18 pairs * PAIR G8: 3,7 ROW 8 D8: 3,7,2,4 # reduction candidate for 3,7 D8: 3,7 # 20 pairs F8: 3,7,2,4 # reduction candidate for 3,7 F8: 3,7 # 19 pairs * PAIR G9: 3,7 ROW 9 E9: 3,7,4 # reduction candidate for 3,7 E9: 4 => CTR * 978.5.134..34792585243186793.9.2.8167.198.5238.2.319472..89.465485.6..91.9.145382 E9: 3,7 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190217-absurd-base-pr-000.dot * REASONING * DIS # A2: 4,5 => CTR => A2: 1,6 * DIS # A3: 2,9 => CTR => A3: 4,5 * DIS # A3: 2,4 => CTR => A3: 5,9 * DIS # D3: 2,4 => CTR => D3: 3,7 * DIS # F3: 2,4 => CTR => F3: 3,7,8 * DIS # I3: 8 => CTR => I3: 4,9 * PRF # I3: 9 => SOL * DIS # E2: 7 => CTR => E2: 4,8 * DIS # F5: 8 => CTR => F5: 4,6 * DIS # E4: 4,7 => CTR => E4: 2 * DIS # F3: 4,7 => CTR => F3: 2,3,8 * DIS # E2: 7 => CTR => E2: 4,8 * DIS # B7: 1,2 => CTR => B7: 3 * DIS # F7: 3 => CTR => F7: 2,7 * DIS # A3: 2,4 => CTR => A3: 5,9 * DIS # E9: 4 => CTR => E9: 3,7 * CNT 16 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B2,B3,B5,C3,C6,C7,E5,E6,F4,G8,G9,H2,H3,I1,I2) * .78.5.13...3..92......1.6..3.9...8167.19..5238....1947...89.465.85.6..91...1.5.82 * PAIR B2: 1,6 BLK 1 A2: 1,6,4,5 # reduction candidate for 1,6 A2: 4,5 => CTR * 678.5.1394136792585923186743.9.478167419865238....19471..89.465.85.6..91..41.5.82 * PAIR B3: 2,9 BLK 1 A1: 2,9,4 # reduction candidate for 2,9 A1: 4 => CTR * 478.5.139..3..925.592.1.67.3.9...8167.19..5238.6..1947..789.465285.6..919641.5.82 * PAIR I2: 4,8 ROW 2 E2: 4,8,7 # reduction candidate for 4,8 E2: 4,8 => SOLVED * 978256134613749258524318679349527816761984523852631947137892465285463791496175382 * DURATION: 0:00:04.288976 START: 03:49:10.554819 END: 03:49:14.843795 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190217-absurd-base-pr-001.dot * REASONING * DIS # A2: 4,5 => CTR => A2: 1,6 * DIS A2: 1,6 # A1: 4 => CTR => A1: 2,9 * PRF A2: 1,6 + A1: 2,9 # E2: 4,8 => SOL * STA A2: 1,6 + A1: 2,9 + E2: 4,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190217, absurd
Solution
position: 978256134613749258524318679349527816761984523852631947137892465285463791496175382 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 # A2: 1,6 => UNS * DIS # A2: 4,5 => CTR => A2: 1,6 * INC # A1: 2,9 => UNS * DIS # A3: 2,9 => CTR => A3: 4,5 * INC # A3: 4,5 => UNS * INC # A1: 2,4 => UNS * DIS # A3: 2,4 => CTR => A3: 5,9 * INC # A3: 5,9 => UNS * DIS # D3: 2,4 => CTR => D3: 3,7 * INC # D3: 3,7 => UNS * DIS # F3: 2,4 => CTR => F3: 3,7,8 * INC # F3: 3,7,8 => UNS * INC # I3: 4,9 => UNS * DIS # I3: 8 => CTR => I3: 4,9 * INC # A1: 4,9 => UNS * INC # A1: 2,6 => UNS * INC # I3: 4,8 => UNS * PRF # I3: 9 => SOL * INC # E2: 4,8 => UNS * DIS # E2: 7 => CTR => E2: 4,8 * INC # F5: 4,6 => UNS * DIS # F5: 8 => CTR => F5: 4,6 * INC # B6: 2,6 => UNS * INC # B6: 5 => UNS * INC # D4: 4,7 => UNS * DIS # E4: 4,7 => CTR => E4: 2 * INC # E4: 2 => UNS * DIS # F3: 4,7 => CTR => F3: 2,3,8 * INC # F3: 2,3,8 => UNS * INC # F8: 4,7 => UNS * INC # F5: 4,8 => UNS * INC # F5: 6 => UNS * INC # E2: 4,8 => UNS * DIS # E2: 7 => CTR => E2: 4,8 * DIS # B7: 1,2 => CTR => B7: 3 * INC # B7: 3 => UNS * INC # F7: 2,7 => UNS * DIS # F7: 3 => CTR => F7: 2,7 * INC # D8: 2,4 => UNS * INC # F8: 2,4 => UNS * INC # A1: 2,4 => UNS * DIS # A3: 2,4 => CTR => A3: 5,9 * INC # A3: 5,9 => UNS * INC # D8: 3,7 => UNS * INC # F8: 3,7 => UNS * INC # E9: 3,7 => UNS * DIS # E9: 4 => CTR => E9: 3,7 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 1,6 => UNS * DIS # A2: 4,5 => CTR => A2: 1,6 * INC A2: 1,6 # A1: 2,9 => UNS * DIS A2: 1,6 # A1: 4 => CTR => A1: 2,9 * PRF A2: 1,6 + A1: 2,9 # E2: 4,8 => SOL * STA A2: 1,6 + A1: 2,9 + E2: 4,8 * CNT 5 HDP CHAINS / 5 HYP OPENED