Analysis of zz-www.sudokuoftheday.co.uk-20060522-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: .......7..97.18......7.54.9.516.....7..1.....2...89...3..9....6..2.....7..6.379.4 initial
Autosolve
position: ....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 3,8 => CTR => C1: 4,5 * DIS # F1: 3,4 => CTR => F1: 2,6 * DIS # D6: 3,4 => CTR => D6: 5 * PRF # B8: 1,8 => SOL * DIS # B1: 1,8 => CTR => B1: 2,3,4 * CNT 5 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 3,8 => CTR => C1: 4,5 * DIS C1: 4,5 # F1: 3,4 => CTR => F1: 2,6 * PRF C1: 4,5 + F1: 2,6 # B5: 3,4 => SOL * STA C1: 4,5 + F1: 2,6 + B5: 3,4 * CNT 3 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......7..97.18......7.54.9.516.....7..1.....2...89...3..9....6..2.....7..6.379.4 | initial |
| ....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4 | autosolve |
| 635492178497318562128765439851674293749123685263589741374951826912846357586237914 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C3: 3,8 E3: 2,6 A4: 4,8 C6: 3,4 B9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H6,I6: 1.. / H6 = 1 => 15 pairs (_) / I6 = 1 => 5 pairs (_) F7,F8: 1.. / F7 = 1 => 6 pairs (_) / F8 = 1 => 0 pairs (X) I1,I6: 1.. / I1 = 1 => 15 pairs (_) / I6 = 1 => 5 pairs (_) B1,B3: 2.. / B1 = 2 => 6 pairs (_) / B3 = 2 => 6 pairs (_) D9,H9: 2.. / D9 = 2 => 13 pairs (_) / H9 = 2 => 0 pairs (X) G8,H8: 3.. / G8 = 3 => 6 pairs (_) / H8 = 3 => 5 pairs (_) H5,H6: 4.. / H5 = 4 => 10 pairs (_) / H6 = 4 => 13 pairs (_) C7,B8: 4.. / C7 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) A2,D2: 4.. / A2 = 4 => 17 pairs (_) / D2 = 4 => 9 pairs (_) A4,F4: 4.. / A4 = 4 => 0 pairs (X) / F4 = 4 => 16 pairs (_) E5,D6: 5.. / E5 = 5 => 0 pairs (X) / D6 = 5 => 9 pairs (_) C7,A9: 5.. / C7 = 5 => 13 pairs (_) / A9 = 5 => 8 pairs (_) C1,C7: 5.. / C1 = 5 => 8 pairs (_) / C7 = 5 => 13 pairs (_) F1,E3: 6.. / F1 = 6 => 0 pairs (X) / E3 = 6 => 6 pairs (_) B5,B6: 6.. / B5 = 6 => 19 pairs (_) / B6 = 6 => 5 pairs (_) E8,F8: 6.. / E8 = 6 => 0 pairs (X) / F8 = 6 => 6 pairs (_) B6,H6: 6.. / B6 = 6 => 5 pairs (_) / H6 = 6 => 19 pairs (_) E3,E8: 6.. / E3 = 6 => 6 pairs (_) / E8 = 6 => 0 pairs (X) F1,F8: 6.. / F1 = 6 => 0 pairs (X) / F8 = 6 => 6 pairs (_) A4,B5: 8.. / A4 = 8 => 16 pairs (_) / B5 = 8 => 0 pairs (X) D8,D9: 8.. / D8 = 8 => 7 pairs (_) / D9 = 8 => 0 pairs (X) * DURATION: 0:00:19.695618 START: 23:19:54.067328 END: 23:20:13.762946 2019-04-30 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C3,C6,E3) * ....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4 * PAIR C3: 3,8 BLK 1 B1: 3,8,1,2,4 # reduction candidate for 3,8 B1: 3,8 # 9 pairs C1: 3,8,4,5 # reduction candidate for 3,8 C1: 3,8 => CTR * ....9..7..97.18...6..7254.9851674.9.7.9152.4.2.43897..375941..6942.....7186.379.4 C1: 4,5 # 6 pairs B3: 3,8,1,2 # reduction candidate for 3,8 B3: 3,8 # 10 pairs * PAIR C3: 3,8 ROW 3 H3: 3,8,1,2,6 # reduction candidate for 3,8 H3: 3,8 # 8 pairs H3: 1,2,6 # 6 pairs * PAIR E3: 2,6 BLK 2 F1: 2,6,3,4 # reduction candidate for 2,6 F1: 3,4 => CTR * ..5.9..7..97.18....28765439851674.9.7.9152...2.3.897..374921..69.2..6..7516837924 F1: 2,6 # 13 pairs * PAIR E3: 2,6 ROW 3 H3: 2,6,1,3,8 # reduction candidate for 2,6 H3: 2,6 # 13 pairs H3: 1,3,8 # 5 pairs * PAIR A4: 4,8 BLK 4 B5: 4,8,3,6 # reduction candidate for 4,8 B5: 3,6 # 17 pairs B5: 4,8 # 12 pairs * PAIR A4: 4,8 COL A A1: 4,8,1,5,6 # reduction candidate for 4,8 A1: 4,8 # 12 pairs A1: 1,5,6 # 5 pairs * PAIR C6: 3,4 BLK 4 B5: 3,4,6,8 # reduction candidate for 3,4 B5: 3,4 # 17 pairs B6: 3,4,6 # reduction candidate for 3,4 B6: 3,4 # 19 pairs * PAIR C6: 3,4 ROW 6 D6: 3,4,5 # reduction candidate for 3,4 D6: 3,4 => CTR * ..5.9..7..97.18....28765439851674.9.7.9152...2.3.897..374921..69.2.46..7516837924 D6: 5 # 9 pairs H6: 3,4,1,5,6 # reduction candidate for 3,4 H6: 3,4 # 9 pairs * PAIR C6: 3,4 COL C C1: 3,4,5,8 # reduction candidate for 3,4 C1: 3,4 # 13 pairs C1: 5,8 # 6 pairs * PAIR B9: 1,8 BLK 7 B8: 1,8,4 # reduction candidate for 1,8 B8: 1,8 => SOLVED * 635492178497318562128765439851674293749123685263589741374951826912846357586237914 B8: 4 # 10 pairs A9: 1,8,5 # reduction candidate for 1,8 A9: 1,8 # 13 pairs * PAIR B9: 1,8 ROW 9 H9: 1,8,2,5 # reduction candidate for 1,8 H9: 1,8 # 16 pairs H9: 2,5 # 7 pairs * PAIR B9: 1,8 COL B B1: 1,8,2,3,4 # reduction candidate for 1,8 B1: 1,8 => CTR * .85.92173.97.18...12.7654.9851674.9.769123.4.23458976137.941..6942856..7516237984 B1: 2,3,4 # 5 pairs B3: 1,8,2,3 # reduction candidate for 1,8 B3: 1,8 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060522-absurd-base-pr-000.dot * REASONING * DIS # C1: 3,8 => CTR => C1: 4,5 * DIS # F1: 3,4 => CTR => F1: 2,6 * DIS # D6: 3,4 => CTR => D6: 5 * PRF # B8: 1,8 => SOL * DIS # B1: 1,8 => CTR => B1: 2,3,4 * CNT 5 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C3,C6,E3) * ....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4 * PAIR C3: 3,8 BLK 1 B1: 3,8,1,2,4 # reduction candidate for 3,8 B1: 3,8 # 9 pairs C1: 3,8,4,5 # reduction candidate for 3,8 C1: 3,8 => CTR * ....9..7..97.18...6..7254.9851674.9.7.9152.4.2.43897..375941..6942.....7186.379.4 B3: 3,8,1,2 # reduction candidate for 3,8 B3: 3,8 # 10 pairs * PAIR C3: 3,8 ROW 3 H3: 3,8,1,2,6 # reduction candidate for 3,8 H3: 3,8 # 9 pairs H3: 1,2,6 # 6 pairs * PAIR RESTART * PAIR C3: 3,8 BLK 1 B1: 3,8,1,2,4 # reduction candidate for 3,8 B1: 3,8 # 9 pairs B3: 3,8,1,2 # reduction candidate for 3,8 B3: 3,8 # 10 pairs * PAIR C3: 3,8 ROW 3 H3: 3,8,1,2,6 # reduction candidate for 3,8 H3: 3,8 # 9 pairs H3: 1,2,6 # 6 pairs * PAIR E3: 2,6 BLK 2 F1: 2,6,3,4 # reduction candidate for 2,6 F1: 3,4 => CTR * ..5.9..7..97.18....28765439851674.9.7.9152...2.3.897..374921..69.2..6..7516837924 * PAIR A4: 4,8 BLK 4 B5: 4,8,3,6 # reduction candidate for 4,8 B5: 4,8 # 20 pairs B5: 3,6 # 19 pairs * PAIR A4: 4,8 COL A A1: 4,8,1,5,6 # reduction candidate for 4,8 A1: 4,8 # 16 pairs A1: 1,5,6 # 14 pairs * PAIR C6: 3,4 BLK 4 B5: 3,4,6,8 # reduction candidate for 3,4 B5: 3,4 => SOLVED * 635492178497318562128765439851674293749123685263589741374951826912846357586237914 * DURATION: 0:00:09.910080 START: 23:20:29.006059 END: 23:20:38.916139 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060522-absurd-base-pr-001.dot * REASONING * DIS # C1: 3,8 => CTR => C1: 4,5 * DIS C1: 4,5 # F1: 3,4 => CTR => F1: 2,6 * PRF C1: 4,5 + F1: 2,6 # B5: 3,4 => SOL * STA C1: 4,5 + F1: 2,6 + B5: 3,4 * CNT 3 HDP CHAINS / 16 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060522, absurd
Solution
position: 635492178497318562128765439851674293749123685263589741374951826912846357586237914 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: 3,8 => UNS * DIS # C1: 3,8 => CTR => C1: 4,5 * INC # C1: 4,5 => UNS * INC # B3: 3,8 => UNS * INC # H3: 3,8 => UNS * INC # H3: 1,2,6 => UNS * INC # F1: 2,6 => UNS * DIS # F1: 3,4 => CTR => F1: 2,6 * INC # H3: 2,6 => UNS * INC # H3: 1,3,8 => UNS * INC # B5: 4,8 => UNS * INC # B5: 3,6 => UNS * INC # A1: 4,8 => UNS * INC # A1: 1,5,6 => UNS * INC # B5: 3,4 => UNS * INC # B6: 3,4 => UNS * DIS # D6: 3,4 => CTR => D6: 5 * INC # D6: 5 => UNS * INC # H6: 3,4 => UNS * INC # C1: 3,4 => UNS * INC # C1: 5,8 => UNS * PRF # B8: 1,8 => SOL * INC # B8: 4 => UNS * INC # A9: 1,8 => UNS * INC # H9: 1,8 => UNS * INC # H9: 2,5 => UNS * DIS # B1: 1,8 => CTR => B1: 2,3,4 * INC # B1: 2,3,4 => UNS * INC # B3: 1,8 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,8 => UNS * DIS # C1: 3,8 => CTR => C1: 4,5 * INC C1: 4,5 # B3: 3,8 => UNS * INC C1: 4,5 # H3: 3,8 => UNS * INC C1: 4,5 # H3: 1,2,6 => UNS * INC C1: 4,5 # B1: 3,8 => UNS * INC C1: 4,5 # B3: 3,8 => UNS * INC C1: 4,5 # H3: 3,8 => UNS * INC C1: 4,5 # H3: 1,2,6 => UNS * INC C1: 4,5 # F1: 2,6 => UNS * DIS C1: 4,5 # F1: 3,4 => CTR => F1: 2,6 * INC C1: 4,5 + F1: 2,6 # B5: 4,8 => UNS * INC C1: 4,5 + F1: 2,6 # B5: 3,6 => UNS * INC C1: 4,5 + F1: 2,6 # A1: 4,8 => UNS * INC C1: 4,5 + F1: 2,6 # A1: 1,5,6 => UNS * PRF C1: 4,5 + F1: 2,6 # B5: 3,4 => SOL * STA C1: 4,5 + F1: 2,6 + B5: 3,4 * CNT 16 HDP CHAINS / 16 HYP OPENED