Analysis of zz-www.sudokuoftheday.co.uk-20190214-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: .....5.7..67..2.3...1.....46...3....3.9.14.567..8..39.....6.7.514.....6.....5..4. initial
Autosolve
position: .....5.7..67..2.3...1.....461.5394.73.9714.56754826391...468715145....6.876.51.4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I1: 8,9 => SOL * DIS # I1: 2 => CTR => I1: 8,9 * DIS # E2: 4 => CTR => E2: 8,9 * PRF # I1: 9 => SOL * DIS # C1: 3 => CTR => C1: 2,8 * DIS # B1: 2,8 => CTR => B1: 3,9 * DIS # G8: 9 => CTR => G8: 2,8 * DIS # B7: 3 => CTR => B7: 2,9 * DIS # A3: 2,9 => CTR => A3: 5 * DIS # C1: 2,3 => CTR => C1: 8 * PRF # C1: 8 => SOL * PRF # E3: 8 => SOL * DIS # G8: 2,9 => CTR => G8: 8 * PRF # G8: 8 => SOL * DIS # D9: 3 => CTR => D9: 2,9 * PRF # I8: 2,3 => SOL * DIS # I8: 8 => CTR => I8: 2,3 * DIS # D9: 9 => CTR => D9: 2,3 * CNT 18 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I1: 8,9 => SOL * STA I1: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....5.7..67..2.3...1.....46...3....3.9.14.567..8..39.....6.7.514.....6.....5..4. | initial |
| .....5.7..67..2.3...1.....461.5394.73.9714.56754826391...468715145....6.876.51.4. | autosolve |
| 238645179467192538591387624612539487389714256754826391923468715145973862876251943 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) D1: 1,6 D2: 1,9 F3: 3,7 G1: 1,6 G2: 1,5 I2: 8,9 G3: 5,6 H3: 2,8 C4: 2,8 B5: 2,8 H4: 2,8 G5: 2,8 A7: 2,9 C7: 2,3 E8: 7,9 F8: 3,7 G9: 2,9 I9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D2: 1.. / D1 = 1 => 0 pairs (X) / D2 = 1 => 15 pairs (_) G1,G2: 1.. / G1 = 1 => 15 pairs (_) / G2 = 1 => 0 pairs (X) D1,G1: 1.. / D1 = 1 => 0 pairs (X) / G1 = 1 => 15 pairs (_) D2,G2: 1.. / D2 = 1 => 15 pairs (_) / G2 = 1 => 0 pairs (X) I1,H3: 2.. / I1 = 2 => 0 pairs (X) / H3 = 2 => 0 pairs (_) C4,B5: 2.. / C4 = 2 => 0 pairs (*) / B5 = 2 => 0 pairs (X) H4,G5: 2.. / H4 = 2 => 0 pairs (X) / G5 = 2 => 0 pairs (_) D8,D9: 2.. / D8 = 2 => 21 pairs (_) / D9 = 2 => 19 pairs (_) C4,H4: 2.. / C4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) B5,G5: 2.. / B5 = 2 => 0 pairs (X) / G5 = 2 => 0 pairs (_) H3,H4: 2.. / H3 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 19 pairs (_) / C1 = 3 => 0 pairs (X) D3,F3: 3.. / D3 = 3 => 14 pairs (_) / F3 = 3 => 20 pairs (_) B7,C7: 3.. / B7 = 3 => 0 pairs (X) / C7 = 3 => 19 pairs (_) I8,I9: 3.. / I8 = 3 => 0 pairs (X) / I9 = 3 => 19 pairs (_) D9,I9: 3.. / D9 = 3 => 0 pairs (X) / I9 = 3 => 19 pairs (_) B1,B7: 3.. / B1 = 3 => 19 pairs (_) / B7 = 3 => 0 pairs (X) C1,C7: 3.. / C1 = 3 => 0 pairs (X) / C7 = 3 => 19 pairs (_) F3,F8: 3.. / F3 = 3 => 20 pairs (_) / F8 = 3 => 14 pairs (_) A1,A2: 4.. / A1 = 4 => 0 pairs (X) / A2 = 4 => 16 pairs (_) E1,E2: 4.. / E1 = 4 => 16 pairs (_) / E2 = 4 => 0 pairs (X) A1,E1: 4.. / A1 = 4 => 0 pairs (X) / E1 = 4 => 16 pairs (_) A2,E2: 4.. / A2 = 4 => 16 pairs (_) / E2 = 4 => 0 pairs (X) A2,A3: 5.. / A2 = 5 => 0 pairs (X) / A3 = 5 => 15 pairs (_) G2,G3: 5.. / G2 = 5 => 15 pairs (_) / G3 = 5 => 0 pairs (X) A2,G2: 5.. / A2 = 5 => 0 pairs (X) / G2 = 5 => 15 pairs (_) A3,G3: 5.. / A3 = 5 => 15 pairs (_) / G3 = 5 => 0 pairs (X) D1,D3: 6.. / D1 = 6 => 15 pairs (_) / D3 = 6 => 0 pairs (X) G1,G3: 6.. / G1 = 6 => 0 pairs (X) / G3 = 6 => 15 pairs (_) D1,G1: 6.. / D1 = 6 => 15 pairs (_) / G1 = 6 => 0 pairs (X) D3,G3: 6.. / D3 = 6 => 0 pairs (X) / G3 = 6 => 15 pairs (_) E3,F3: 7.. / E3 = 7 => 20 pairs (_) / F3 = 7 => 14 pairs (_) E8,F8: 7.. / E8 = 7 => 14 pairs (_) / F8 = 7 => 20 pairs (_) E3,E8: 7.. / E3 = 7 => 20 pairs (_) / E8 = 7 => 14 pairs (_) F3,F8: 7.. / F3 = 7 => 14 pairs (_) / F8 = 7 => 20 pairs (_) C4,B5: 8.. / C4 = 8 => 0 pairs (X) / B5 = 8 => 0 pairs (_) H4,G5: 8.. / H4 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) G8,I8: 8.. / G8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) E2,I2: 8.. / E2 = 8 => 19 pairs (_) / I2 = 8 => 0 pairs (*) C4,H4: 8.. / C4 = 8 => 0 pairs (X) / H4 = 8 => 0 pairs (_) B5,G5: 8.. / B5 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) C1,C4: 8.. / C1 = 8 => 0 pairs (*) / C4 = 8 => 0 pairs (X) G5,G8: 8.. / G5 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) H3,H4: 8.. / H3 = 8 => 0 pairs (X) / H4 = 8 => 0 pairs (_) I1,I2: 9.. / I1 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) A7,B7: 9.. / A7 = 9 => 23 pairs (_) / B7 = 9 => 23 pairs (_) G8,G9: 9.. / G8 = 9 => 0 pairs (X) / G9 = 9 => 19 pairs (_) D9,G9: 9.. / D9 = 9 => 0 pairs (X) / G9 = 9 => 19 pairs (_) * DURATION: 0:01:05.368627 START: 03:43:17.745647 END: 03:44:23.114274 2019-05-01 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,C4,C7,D1,D2,E8,F3,F8,G1,G2,G3,G5,G9,H3,H4,I2,I9) * .....5.7..67..2.3...1.....461.5394.73.9714.56754826391...468715145....6.876.51.4. * PAIR I2: 8,9 BLK 3 I1: 8,9,2 # reduction candidate for 8,9 I1: 8,9 => SOLVED * 238645179467192538591387624612539487389714256754826391923468715145973862876251943 I1: 2 => CTR * .83..5.72.67182539..1....84618539427329714856754826391..2468715145....68876.51.43 * PAIR I2: 8,9 ROW 2 E2: 8,9,4 # reduction candidate for 8,9 E2: 4 => CTR * 4....5.7..67.42.38..1....24612539487389714256754826391..3468715145...86.876.5194. E2: 8,9 # 16 pairs * PAIR H3: 2,8 BLK 3 I1: 2,8,9 # reduction candidate for 2,8 I1: 9 => SOLVED * 238645179467192538591387624612539487389714256754826391923468715145973862876251943 I1: 2,8 # 19 pairs * PAIR H3: 2,8 ROW 3 B3: 2,8,9 # reduction candidate for 2,8 B3: 9 # 27 pairs B3: 2,8 # 25 pairs * PAIR C4: 2,8 COL C C1: 2,8,3 # reduction candidate for 2,8 C1: 3 => CTR * ..3..5.72.67.82.392.1...584618539427329714856754826391932468715145....68876.51.43 C1: 2,8 # 19 pairs * PAIR B5: 2,8 COL B B1: 2,8,3,9 # reduction candidate for 2,8 B1: 2,8 => CTR * .83..5.72.67.82.39291.....4618539427329714856754826391.32468715145....68876.51.43 B1: 3,9 # 19 pairs B3: 2,8,9 # reduction candidate for 2,8 B3: 2,8 # 25 pairs * PAIR G5: 2,8 COL G G8: 2,8,9 # reduction candidate for 2,8 G8: 9 => CTR * .....5.72.67182539521.....461.5394.73.9714856754826391...468715145...968876951243 G8: 2,8 # 19 pairs * PAIR A7: 2,9 BLK 7 B7: 2,9,3 # reduction candidate for 2,9 B7: 3 => CTR * ..3..5.72.67.82.392.1...584618539427329714856754826391932468715145....68876.51.43 B7: 2,9 # 19 pairs * PAIR A7: 2,9 COL A A1: 2,9,4 # reduction candidate for 2,9 A1: 2,9 # 16 pairs A3: 2,9,5 # reduction candidate for 2,9 A3: 2,9 => CTR * .....5.7.567.42138..1...524612539487389714256754826391..3468715145...86.876.5194. A3: 5 # 15 pairs * PAIR C7: 2,3 BLK 7 B7: 2,3,9 # reduction candidate for 2,3 B7: 9 # 23 pairs B7: 2,3 # 23 pairs * PAIR C7: 2,3 COL C C1: 2,3,8 # reduction candidate for 2,3 C1: 2,3 => CTR * .....5.72.67.82.392.1...5846185394273297148567548263919..468715145....68876.51.43 C1: 8 => SOLVED * 238645179467192538591387624612539487389714256754826391923468715145973862876251943 * PAIR E8: 7,9 COL E E3: 7,9,8 # reduction candidate for 7,9 E3: 8 => SOLVED * 238645179467192538591387624612539487389714256754826391923468715145973862876251943 E3: 7,9 # 21 pairs * PAIR G9: 2,9 BLK 9 G8: 2,9,8 # reduction candidate for 2,9 G8: 2,9 => CTR * .83.45.72467182539..1....84618539427329714856754826391..2468715145....68876.51.43 G8: 8 => SOLVED * 238645179467192538591387624612539487389714256754826391923468715145973862876251943 * PAIR G9: 2,9 ROW 9 D9: 2,9,3 # reduction candidate for 2,9 D9: 3 => CTR * .....5.7..67..2.3...1.73.24612539487389714256754826391..3468715145297863876351942 D9: 2,9 # 19 pairs * PAIR I9: 2,3 BLK 9 I8: 2,3,8 # reduction candidate for 2,3 I8: 2,3 => SOLVED * 238645179467192538591387624612539487389714256754826391923468715145973862876251943 I8: 8 => CTR * .83.45.72467182539..1....84618539427329714856754826391..2468715145....68876.51.43 * PAIR I9: 2,3 ROW 9 D9: 2,3,9 # reduction candidate for 2,3 D9: 9 => CTR * .....5.72.6718253952139768461.5394.73.9714.56754826391...4687151452.3.68876951243 D9: 2,3 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190214-absurd-base-pr-000.dot * REASONING * PRF # I1: 8,9 => SOL * DIS # I1: 2 => CTR => I1: 8,9 * DIS # E2: 4 => CTR => E2: 8,9 * PRF # I1: 9 => SOL * DIS # C1: 3 => CTR => C1: 2,8 * DIS # B1: 2,8 => CTR => B1: 3,9 * DIS # G8: 9 => CTR => G8: 2,8 * DIS # B7: 3 => CTR => B7: 2,9 * DIS # A3: 2,9 => CTR => A3: 5 * DIS # C1: 2,3 => CTR => C1: 8 * PRF # C1: 8 => SOL * PRF # E3: 8 => SOL * DIS # G8: 2,9 => CTR => G8: 8 * PRF # G8: 8 => SOL * DIS # D9: 3 => CTR => D9: 2,9 * PRF # I8: 2,3 => SOL * DIS # I8: 8 => CTR => I8: 2,3 * DIS # D9: 9 => CTR => D9: 2,3 * CNT 18 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,C4,C7,D1,D2,E8,F3,F8,G1,G2,G3,G5,G9,H3,H4,I2,I9) * .....5.7..67..2.3...1.....461.5394.73.9714.56754826391...468715145....6.876.51.4. * PAIR I2: 8,9 BLK 3 I1: 8,9,2 # reduction candidate for 8,9 I1: 8,9 => SOLVED * 238645179467192538591387624612539487389714256754826391923468715145973862876251943 * DURATION: 0:00:01.825808 START: 03:44:49.747423 END: 03:44:51.573231 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190214-absurd-base-pr-001.dot * REASONING * PRF # I1: 8,9 => SOL * STA I1: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190214, absurd
Solution
position: 238645179467192538591387624612539487389714256754826391923468715145973862876251943 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 # I1: 8,9 => SOL * DIS # I1: 2 => CTR => I1: 8,9 * INC # E2: 8,9 => UNS * DIS # E2: 4 => CTR => E2: 8,9 * INC # I1: 2,8 => UNS * PRF # I1: 9 => SOL * INC # B3: 2,8 => UNS * INC # B3: 9 => UNS * INC # C1: 2,8 => UNS * DIS # C1: 3 => CTR => C1: 2,8 * DIS # B1: 2,8 => CTR => B1: 3,9 * INC # B1: 3,9 => UNS * INC # B3: 2,8 => UNS * INC # G8: 2,8 => UNS * DIS # G8: 9 => CTR => G8: 2,8 * INC # B7: 2,9 => UNS * DIS # B7: 3 => CTR => B7: 2,9 * INC # A1: 2,9 => UNS * DIS # A3: 2,9 => CTR => A3: 5 * INC # A3: 5 => UNS * INC # B7: 2,3 => UNS * INC # B7: 9 => UNS * DIS # C1: 2,3 => CTR => C1: 8 * PRF # C1: 8 => SOL * INC # E3: 7,9 => UNS * PRF # E3: 8 => SOL * DIS # G8: 2,9 => CTR => G8: 8 * PRF # G8: 8 => SOL * INC # D9: 2,9 => UNS * DIS # D9: 3 => CTR => D9: 2,9 * PRF # I8: 2,3 => SOL * DIS # I8: 8 => CTR => I8: 2,3 * INC # D9: 2,3 => UNS * DIS # D9: 9 => CTR => D9: 2,3 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I1: 8,9 => SOL * STA I1: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED