Analysis of zz-www.sudokuoftheday.co.uk-20060728-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: ........2..5167.......528....8..3...9.....5.....695...1.9.2.4.7..6.7.1...37..1.68 initial
Autosolve
position: ....3..52..5167.......528....8.13...9...845.....695.8.1.9.26437..637.1.5.37.41.68 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C6: 1,4 => SOL * DIS # A8: 2,8 => CTR => A8: 4 * DIS # B8: 4 => CTR => B8: 2,8 * DIS # A3: 3,4 => CTR => A3: 6,7 * DIS # C6: 3,4 => CTR => C6: 1,2 * DIS # D1: 8 => CTR => D1: 4,9 * DIS # B3: 6,7 => CTR => B3: 4,9 * DIS # B1: 6,7 => CTR => B1: 1,4,9 * DIS # G4: 2,9 => CTR => G4: 6,7 * DIS # I2: 3 => CTR => I2: 4,9 * DIS # H4: 2,7 => CTR => H4: 4,9 * DIS # H5: 2 => CTR => H5: 1,7 * DIS # I5: 1,6 => CTR => I5: 3 * PRF # G4: 2,7 => SOL * DIS # H4: 2,7 => CTR => H4: 4,9 * DIS # H5: 2,7 => CTR => H5: 1 * DIS # G4: 2,9 => CTR => G4: 6,7 * CNT 17 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C6: 1,4 => SOL * STA C6: 1,4 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ........2..5167.......528....8..3...9.....5.....695...1.9.2.4.7..6.7.1...37..1.68 | initial |
| ....3..52..5167.......528....8.13...9...845.....695.8.1.9.26437..637.1.5.37.41.68 | autosolve |
| 714938652825167349693452871548213796962784513371695284159826437486379125237541968 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C1: 1,4 A2: 2,8 B2: 2,8 C3: 3,4 F1: 8,9 D3: 4,9 G1: 6,7 G2: 3,9 H2: 4,9 H3: 1,7 I3: 1,6 D4: 2,7 D5: 2,7 B7: 5,8 A9: 2,5 D7: 5,8 F8: 8,9 D9: 5,9 H8: 2,9 G9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 26 pairs (_) / C1 = 1 => 20 pairs (_) H3,I3: 1.. / H3 = 1 => 0 pairs (X) / I3 = 1 => 22 pairs (_) H3,H5: 1.. / H3 = 1 => 0 pairs (X) / H5 = 1 => 22 pairs (_) A2,B2: 2.. / A2 = 2 => 0 pairs (X) / B2 = 2 => 20 pairs (_) C5,C6: 2.. / C5 = 2 => 0 pairs (*) / C6 = 2 => 0 pairs (X) D4,D5: 2.. / D4 = 2 => 20 pairs (_) / D5 = 2 => 23 pairs (_) H8,G9: 2.. / H8 = 2 => 16 pairs (_) / G9 = 2 => 0 pairs (X) C6,G6: 2.. / C6 = 2 => 24 pairs (_) / G6 = 2 => 0 pairs (*) A9,G9: 2.. / A9 = 2 => 16 pairs (_) / G9 = 2 => 0 pairs (X) B2,B8: 2.. / B2 = 2 => 20 pairs (_) / B8 = 2 => 0 pairs (X) A3,C3: 3.. / A3 = 3 => 0 pairs (X) / C3 = 3 => 22 pairs (_) G2,I2: 3.. / G2 = 3 => 21 pairs (_) / I2 = 3 => 0 pairs (X) C5,I5: 3.. / C5 = 3 => 0 pairs (X) / I5 = 3 => 23 pairs (_) A3,A6: 3.. / A3 = 3 => 0 pairs (X) / A6 = 3 => 22 pairs (_) G2,G6: 3.. / G2 = 3 => 21 pairs (_) / G6 = 3 => 0 pairs (X) D1,D3: 4.. / D1 = 4 => 15 pairs (_) / D3 = 4 => 23 pairs (_) H2,I2: 4.. / H2 = 4 => 20 pairs (_) / I2 = 4 => 15 pairs (_) A8,B8: 4.. / A8 = 4 => 16 pairs (_) / B8 = 4 => 0 pairs (X) H2,H4: 4.. / H2 = 4 => 20 pairs (_) / H4 = 4 => 15 pairs (_) A4,B4: 5.. / A4 = 5 => 16 pairs (_) / B4 = 5 => 0 pairs (X) B7,A9: 5.. / B7 = 5 => 16 pairs (_) / A9 = 5 => 0 pairs (X) D7,D9: 5.. / D7 = 5 => 0 pairs (X) / D9 = 5 => 16 pairs (_) B7,D7: 5.. / B7 = 5 => 16 pairs (_) / D7 = 5 => 0 pairs (X) A9,D9: 5.. / A9 = 5 => 0 pairs (X) / D9 = 5 => 16 pairs (_) A4,A9: 5.. / A4 = 5 => 16 pairs (_) / A9 = 5 => 0 pairs (X) B4,B7: 5.. / B4 = 5 => 0 pairs (X) / B7 = 5 => 16 pairs (_) G1,I3: 6.. / G1 = 6 => 22 pairs (_) / I3 = 6 => 0 pairs (X) B5,I5: 6.. / B5 = 6 => 21 pairs (_) / I5 = 6 => 0 pairs (X) G1,G4: 6.. / G1 = 6 => 22 pairs (_) / G4 = 6 => 0 pairs (X) G1,H3: 7.. / G1 = 7 => 0 pairs (X) / H3 = 7 => 22 pairs (_) D4,D5: 7.. / D4 = 7 => 23 pairs (_) / D5 = 7 => 20 pairs (_) A2,B2: 8.. / A2 = 8 => 20 pairs (_) / B2 = 8 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 16 pairs (_) D7,F8: 8.. / D7 = 8 => 16 pairs (_) / F8 = 8 => 0 pairs (X) B7,D7: 8.. / B7 = 8 => 0 pairs (X) / D7 = 8 => 16 pairs (_) A2,A8: 8.. / A2 = 8 => 20 pairs (_) / A8 = 8 => 0 pairs (X) D1,D7: 8.. / D1 = 8 => 0 pairs (X) / D7 = 8 => 16 pairs (_) F1,F8: 8.. / F1 = 8 => 16 pairs (_) / F8 = 8 => 0 pairs (X) B1,B3: 9.. / B1 = 9 => 15 pairs (_) / B3 = 9 => 23 pairs (_) F8,D9: 9.. / F8 = 9 => 16 pairs (_) / D9 = 9 => 0 pairs (X) H8,G9: 9.. / H8 = 9 => 0 pairs (X) / G9 = 9 => 16 pairs (_) B3,D3: 9.. / B3 = 9 => 23 pairs (_) / D3 = 9 => 15 pairs (_) F8,H8: 9.. / F8 = 9 => 16 pairs (_) / H8 = 9 => 0 pairs (X) D9,G9: 9.. / D9 = 9 => 0 pairs (X) / G9 = 9 => 16 pairs (_) F1,F8: 9.. / F1 = 9 => 0 pairs (X) / F8 = 9 => 16 pairs (_) I2,I4: 9.. / I2 = 9 => 20 pairs (_) / I4 = 9 => 21 pairs (_) * DURATION: 0:01:03.432251 START: 01:21:32.592040 END: 01:22:36.024291 2019-05-01 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B7,C1,C3,D3,D4,D5,D7,D9,F1,F8,G1,G2,G9,H2,H3,H8,I3) * ....3..52..5167.......528....8.13...9...845.....695.8.1.9.26437..637.1.5.37.41.68 * PAIR C1: 1,4 BLK 1 B1: 1,4,6,7,9 # reduction candidate for 1,4 B1: 1,4 # 26 pairs B1: 6,7,9 # 20 pairs * PAIR C1: 1,4 COL C C6: 1,4,2,3 # reduction candidate for 1,4 C6: 1,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486379125237541968 C6: 2,3 # 23 pairs * PAIR A2: 2,8 COL A A8: 2,8,4 # reduction candidate for 2,8 A8: 2,8 => CTR * ..4839.52825167.4..934528...58.13...9.1.845.3372695.8.189526437246378195537941268 A8: 4 # 16 pairs * PAIR B2: 2,8 COL B B8: 2,8,4 # reduction candidate for 2,8 B8: 4 => CTR * ..4839.52825167.4..934528...58.13...9.1.845.3372695.8.189526437246378195537941268 B8: 2,8 # 16 pairs * PAIR C3: 3,4 BLK 1 A3: 3,4,6,7 # reduction candidate for 3,4 A3: 3,4 => CTR * 6914387528251673..3749528165.8.136..96..8457171.69528.159826437486379125237541968 A3: 6,7 # 24 pairs * PAIR C3: 3,4 COL C C6: 3,4,1,2 # reduction candidate for 3,4 C6: 3,4 => CTR * ..1.3..52825167349..4952871548213796962784513.1.6952841.9.26437..637.125237541968 C6: 1,2 # 23 pairs * PAIR F1: 8,9 BLK 2 D1: 8,9,4 # reduction candidate for 8,9 D1: 8,9 # 23 pairs D1: 4 # 15 pairs * PAIR D3: 4,9 BLK 2 D1: 4,9,8 # reduction candidate for 4,9 D1: 8 => CTR * ...839.52825167.4..934528...58.13...9...845.33.269578.189526437246378195537941268 D1: 4,9 # 16 pairs * PAIR D3: 4,9 ROW 3 B3: 4,9,6,7 # reduction candidate for 4,9 B3: 6,7 => CTR * 6914387528251673..3749528165.821367.9...845..7..69528.159826437486379125237541968 B3: 4,9 # 24 pairs * PAIR G1: 6,7 ROW 1 A1: 6,7,4 # reduction candidate for 6,7 A1: 6,7 # 21 pairs B1: 6,7,1,4,9 # reduction candidate for 6,7 B1: 6,7 => CTR * ..1.3..52..5167....9.4528....8.13...9...845....469528.1.9.26437.4637.125237541968 B1: 1,4,9 # 21 pairs * PAIR G1: 6,7 COL G G4: 6,7,2,9 # reduction candidate for 6,7 G4: 2,9 => CTR * ..1.3.652..51673....4952871..8.13...9.32845164126957831.9.26437.46379125237541968 G4: 6,7 # 23 pairs * PAIR G2: 3,9 BLK 3 I2: 3,9,4 # reduction candidate for 3,9 I2: 3,9 # 20 pairs I2: 4 # 15 pairs * PAIR H2: 4,9 BLK 3 I2: 4,9,3 # reduction candidate for 4,9 I2: 3 => CTR * ....3..52..5167.43....528....8.13..99.3.845....26953841.9.26437..637.195.37941268 I2: 4,9 # 21 pairs * PAIR H2: 4,9 COL H H4: 4,9,2,7 # reduction candidate for 4,9 H4: 2,7 => CTR * ..4839.52825167.4..934528...58.13...9.1.845.33.2695781189526437246378195537941268 H4: 4,9 # 16 pairs * PAIR H3: 1,7 COL H H5: 1,7,2 # reduction candidate for 1,7 H5: 2 => CTR * 6...39752..51679433...52816..8.1367996.78452...26953841.9.26437..637.195.37941268 H5: 1,7 # 21 pairs * PAIR I3: 1,6 COL I I5: 1,6,3 # reduction candidate for 1,6 I5: 1,6 => CTR * .91438.528251673..3.49528..5.8.132..9.32845....26957831598264374.6379125237541968 I5: 3 # 23 pairs * PAIR D4: 2,7 ROW 4 G4: 2,7,6,9 # reduction candidate for 2,7 G4: 2,7 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486379125237541968 G4: 6,9 # 21 pairs H4: 2,7,4,9 # reduction candidate for 2,7 H4: 2,7 => CTR * ..4839.52825167.4..934528...58.13...9.1.845.33.2695781189526437246378195537941268 H4: 4,9 # 16 pairs * PAIR D5: 2,7 ROW 5 H5: 2,7,1 # reduction candidate for 2,7 H5: 2,7 => CTR * 6...39752..51679433...52816..8.136.996..845....26953841.9.26437..637.195.37941268 H5: 1 # 22 pairs * PAIR H8: 2,9 COL H H4: 2,9,4,7 # reduction candidate for 2,9 H4: 2,9 # 22 pairs H4: 4,7 # 21 pairs * PAIR G9: 2,9 COL G G4: 2,9,6,7 # reduction candidate for 2,9 G4: 2,9 => CTR * ..1.3.652..51673....4952871..8.13...9.32845164126957831.9.26437.46379125237541968 G4: 6,7 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060728-absurd-base-pr-000.dot * REASONING * PRF # C6: 1,4 => SOL * DIS # A8: 2,8 => CTR => A8: 4 * DIS # B8: 4 => CTR => B8: 2,8 * DIS # A3: 3,4 => CTR => A3: 6,7 * DIS # C6: 3,4 => CTR => C6: 1,2 * DIS # D1: 8 => CTR => D1: 4,9 * DIS # B3: 6,7 => CTR => B3: 4,9 * DIS # B1: 6,7 => CTR => B1: 1,4,9 * DIS # G4: 2,9 => CTR => G4: 6,7 * DIS # I2: 3 => CTR => I2: 4,9 * DIS # H4: 2,7 => CTR => H4: 4,9 * DIS # H5: 2 => CTR => H5: 1,7 * DIS # I5: 1,6 => CTR => I5: 3 * PRF # G4: 2,7 => SOL * DIS # H4: 2,7 => CTR => H4: 4,9 * DIS # H5: 2,7 => CTR => H5: 1 * DIS # G4: 2,9 => CTR => G4: 6,7 * CNT 17 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B7,C1,C3,D3,D4,D5,D7,D9,F1,F8,G1,G2,G9,H2,H3,H8,I3) * ....3..52..5167.......528....8.13...9...845.....695.8.1.9.26437..637.1.5.37.41.68 * PAIR C1: 1,4 BLK 1 B1: 1,4,6,7,9 # reduction candidate for 1,4 B1: 1,4 # 26 pairs B1: 6,7,9 # 20 pairs * PAIR C1: 1,4 COL C C6: 1,4,2,3 # reduction candidate for 1,4 C6: 1,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486379125237541968 * DURATION: 0:00:03.058845 START: 01:23:08.418248 END: 01:23:11.477093 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060728-absurd-base-pr-001.dot * REASONING * PRF # C6: 1,4 => SOL * STA C6: 1,4 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060728, absurd
Solution
position: 714938652825167349693452871548213796962784513371695284159826437486379125237541968 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 # B1: 1,4 => UNS * INC # B1: 6,7,9 => UNS * PRF # C6: 1,4 => SOL * INC # C6: 2,3 => UNS * DIS # A8: 2,8 => CTR => A8: 4 * INC # A8: 4 => UNS * INC # B8: 2,8 => UNS * DIS # B8: 4 => CTR => B8: 2,8 * DIS # A3: 3,4 => CTR => A3: 6,7 * INC # A3: 6,7 => UNS * DIS # C6: 3,4 => CTR => C6: 1,2 * INC # C6: 1,2 => UNS * INC # D1: 8,9 => UNS * INC # D1: 4 => UNS * INC # D1: 4,9 => UNS * DIS # D1: 8 => CTR => D1: 4,9 * INC # B3: 4,9 => UNS * DIS # B3: 6,7 => CTR => B3: 4,9 * INC # A1: 6,7 => UNS * DIS # B1: 6,7 => CTR => B1: 1,4,9 * INC # B1: 1,4,9 => UNS * INC # G4: 6,7 => UNS * DIS # G4: 2,9 => CTR => G4: 6,7 * INC # I2: 3,9 => UNS * INC # I2: 4 => UNS * INC # I2: 4,9 => UNS * DIS # I2: 3 => CTR => I2: 4,9 * INC # H4: 4,9 => UNS * DIS # H4: 2,7 => CTR => H4: 4,9 * INC # H5: 1,7 => UNS * DIS # H5: 2 => CTR => H5: 1,7 * DIS # I5: 1,6 => CTR => I5: 3 * INC # I5: 3 => UNS * PRF # G4: 2,7 => SOL * INC # G4: 6,9 => UNS * DIS # H4: 2,7 => CTR => H4: 4,9 * INC # H4: 4,9 => UNS * DIS # H5: 2,7 => CTR => H5: 1 * INC # H5: 1 => UNS * INC # H4: 2,9 => UNS * INC # H4: 4,7 => UNS * DIS # G4: 2,9 => CTR => G4: 6,7 * INC # G4: 6,7 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 1,4 => UNS * INC # B1: 6,7,9 => UNS * PRF # C6: 1,4 => SOL * STA C6: 1,4 * CNT 3 HDP CHAINS / 3 HYP OPENED