Analysis of zz-www.sudokuoftheday.co.uk-20060709-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...........26194.9..65..9.3.8......19.4.2....5..1.......3..6......28..7....4.. initial
Autosolve
position: ..2..9.4...7..26194.9..65.29.328176.7.19.4.2..2.5.719.....239.639...528.27..984.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1 => CTR => B3: 3,8 * DIS # D2: 4 => CTR => D2: 3,8 * DIS # E1: 1,7 => CTR => E1: 5 * PRF # D3: 1,7 => SOL * DIS # E8: 4 => CTR => E8: 1,7 * DIS # I1: 3,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * DIS # I1: 8 => CTR => I1: 3,7 * PRF # D3: 3,7 => SOL * DIS # B5: 6,8 => CTR => B5: 5 * DIS # I6: 3 => CTR => I6: 4,8 * DIS # C7: 4,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * DIS # I6: 3,8 => CTR => I6: 4 * DIS # B7: 4 => CTR => B7: 1,8 * DIS # D8: 1,7 => CTR => D8: 4,6 * DIS # D8: 4,7 => CTR => D8: 1,6 * DIS # D8: 4,7 => CTR => D8: 1,6 * DIS # D8: 1,7 => CTR => D8: 4,6 * CNT 19 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 1 => CTR => B3: 3,8 * PRF B3: 3,8 # D3: 1,7 => SOL * STA B3: 3,8 + D3: 1,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2...........26194.9..65..9.3.8......19.4.2....5..1.......3..6......28..7....4.. | initial |
| ..2..9.4...7..26194.9..65.29.328176.7.19.4.2..2.5.719.....239.639...528.27..984.. | autosolve |
| 162359847537842619489716532943281765751964328628537194815423976394675281276198453 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) A2: 5,8 B2: 3,8 E2: 4,5 E3: 1,7 G1: 3,8 H3: 3,7 B4: 4,5 A6: 6,8 C6: 4,8 E5: 3,6 E6: 3,6 I4: 4,5 G5: 3,8 A7: 1,8 C8: 4,6 C9: 5,6 D7: 4,7 D9: 1,6 H7: 5,7 I8: 1,7 H9: 3,5 I9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,B7: 1.. / A7 = 1 => 23 pairs (_) / B7 = 1 => 20 pairs (_) I8,I9: 1.. / I8 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) D9,I9: 1.. / D9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) A1,A7: 1.. / A1 = 1 => 20 pairs (_) / A7 = 1 => 23 pairs (_) E5,E6: 3.. / E5 = 3 => 0 pairs (X) / E6 = 3 => 22 pairs (_) H9,I9: 3.. / H9 = 3 => 0 pairs (X) / I9 = 3 => 0 pairs (_) B2,D2: 3.. / B2 = 3 => 24 pairs (_) / D2 = 3 => 27 pairs (_) E6,I6: 3.. / E6 = 3 => 22 pairs (_) / I6 = 3 => 0 pairs (X) G1,G5: 3.. / G1 = 3 => 0 pairs (X) / G5 = 3 => 22 pairs (_) H3,H9: 3.. / H3 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) D2,E2: 4.. / D2 = 4 => 0 pairs (X) / E2 = 4 => 27 pairs (_) B4,C6: 4.. / B4 = 4 => 20 pairs (_) / C6 = 4 => 0 pairs (X) I4,I6: 4.. / I4 = 4 => 0 pairs (X) / I6 = 4 => 20 pairs (_) B4,I4: 4.. / B4 = 4 => 20 pairs (_) / I4 = 4 => 0 pairs (X) C6,I6: 4.. / C6 = 4 => 0 pairs (X) / I6 = 4 => 20 pairs (_) B4,B7: 4.. / B4 = 4 => 20 pairs (_) / B7 = 4 => 0 pairs (X) E2,E8: 4.. / E2 = 4 => 27 pairs (_) / E8 = 4 => 0 pairs (X) A1,A2: 5.. / A1 = 5 => 0 pairs (X) / A2 = 5 => 27 pairs (_) E1,E2: 5.. / E1 = 5 => 27 pairs (_) / E2 = 5 => 0 pairs (X) B4,B5: 5.. / B4 = 5 => 0 pairs (X) / B5 = 5 => 20 pairs (_) I4,I5: 5.. / I4 = 5 => 20 pairs (_) / I5 = 5 => 0 pairs (X) C7,C9: 5.. / C7 = 5 => 0 pairs (*) / C9 = 5 => 0 pairs (X) H7,H9: 5.. / H7 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) A1,E1: 5.. / A1 = 5 => 0 pairs (X) / E1 = 5 => 27 pairs (_) A2,E2: 5.. / A2 = 5 => 27 pairs (_) / E2 = 5 => 0 pairs (X) B4,I4: 5.. / B4 = 5 => 0 pairs (X) / I4 = 5 => 20 pairs (_) B5,I5: 5.. / B5 = 5 => 20 pairs (_) / I5 = 5 => 0 pairs (X) C7,H7: 5.. / C7 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) C9,H9: 5.. / C9 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) A1,B1: 6.. / A1 = 6 => 0 pairs (X) / B1 = 6 => 22 pairs (_) B5,A6: 6.. / B5 = 6 => 0 pairs (X) / A6 = 6 => 22 pairs (_) E5,E6: 6.. / E5 = 6 => 22 pairs (_) / E6 = 6 => 0 pairs (X) C8,C9: 6.. / C8 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) D8,D9: 6.. / D8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) B5,E5: 6.. / B5 = 6 => 0 pairs (X) / E5 = 6 => 22 pairs (_) A6,E6: 6.. / A6 = 6 => 22 pairs (_) / E6 = 6 => 0 pairs (X) C8,D8: 6.. / C8 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) C9,D9: 6.. / C9 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) A1,A6: 6.. / A1 = 6 => 0 pairs (X) / A6 = 6 => 22 pairs (_) B1,B5: 6.. / B1 = 6 => 22 pairs (_) / B5 = 6 => 0 pairs (X) I1,H3: 7.. / I1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) H7,I8: 7.. / H7 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) D7,H7: 7.. / D7 = 7 => 0 pairs (X) / H7 = 7 => 0 pairs (_) H3,H7: 7.. / H3 = 7 => 0 pairs (X) / H7 = 7 => 0 pairs (_) I1,I8: 7.. / I1 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) D2,D3: 8.. / D2 = 8 => 27 pairs (_) / D3 = 8 => 24 pairs (_) G1,I1: 8.. / G1 = 8 => 22 pairs (_) / I1 = 8 => 0 pairs (X) B3,D3: 8.. / B3 = 8 => 27 pairs (_) / D3 = 8 => 24 pairs (_) C6,C7: 8.. / C6 = 8 => 20 pairs (_) / C7 = 8 => 0 pairs (X) G1,G5: 8.. / G1 = 8 => 22 pairs (_) / G5 = 8 => 0 pairs (X) * DURATION: 0:01:13.007682 START: 00:33:14.058813 END: 00:34:27.066495 2019-05-01 * CP COUNT: (50) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,B2,B4,C6,C8,C9,D7,D9,E2,E3,E5,E6,G1,G5,H3,H7,H9,I4,I8,I9) * ..2..9.4...7..26194.9..65.29.328176.7.19.4.2..2.5.719.....239.639...528.27..984.. * PAIR B2: 3,8 BLK 1 B3: 3,8,1 # reduction candidate for 3,8 B3: 1 => CTR * ..2..9.4...7..26194198765329.328176.7.19.432..2.53719.1...2397639.7.528127..984.. B3: 3,8 # 30 pairs * PAIR B2: 3,8 ROW 2 D2: 3,8,4 # reduction candidate for 3,8 D2: 4 => CTR * ..2..9.4..374526194.98.65329.328176.7.19.432..2.53719....72395639...528.27..984.. D2: 3,8 # 27 pairs * PAIR E3: 1,7 BLK 2 D1: 1,7,3 # reduction candidate for 1,7 D1: 1,7 # 29 pairs E1: 1,7,5 # reduction candidate for 1,7 E1: 1,7 => CTR * 562..9.4.8374526194198765329.328176.7.196432.62.53719.1..72395639...528.27..984.. E1: 5 # 27 pairs D3: 1,7,3,8 # reduction candidate for 1,7 D3: 1,7 => SOLVED * 162359847537842619489716532943281765751964328628537194815423976394675281276198453 D3: 3,8 # 23 pairs * PAIR E3: 1,7 COL E E8: 1,7,4 # reduction candidate for 1,7 E8: 4 => CTR * 5623.9.4...74526194.98.65.29.328176.7.19.4.2..2.5.719....723956396145287275698431 E8: 1,7 # 27 pairs * PAIR G1: 3,8 BLK 3 I1: 3,8,7 # reduction candidate for 3,8 I1: 3,8 => CTR * 5.2.79.4...7.526194.9.165729.328176.7.19.4.2..2.5.719....723956396145287275698431 I1: 7 => SOLVED * 162359847537842619489716532943281765751964328628537194815423976394675281276198453 * PAIR H3: 3,7 BLK 3 I1: 3,7,8 # reduction candidate for 3,7 I1: 8 => CTR * ..2.79348..7.526194.9.165729.328176.7.19.482..2.5.719....72395639...5287275698431 I1: 3,7 # 22 pairs * PAIR H3: 3,7 ROW 3 D3: 3,7,1,8 # reduction candidate for 3,7 D3: 3,7 => SOLVED * 162359847537842619489716532943281765751964328628537194815423976394675281276198453 D3: 1,8 # 23 pairs * PAIR A6: 6,8 BLK 4 B5: 6,8,5 # reduction candidate for 6,8 B5: 6,8 => CTR * 5.2.79.4...7.526194.9.165729532817647.19.4.25.245.719.148723956396145287275698431 B5: 5 # 20 pairs * PAIR C6: 4,8 ROW 6 I6: 4,8,3 # reduction candidate for 4,8 I6: 3 => CTR * ..2.79348..7.526194.9.165.29.32817647.19.4.25.245.7193.48723956396..5287275698431 I6: 4,8 # 22 pairs * PAIR C6: 4,8 COL C C7: 4,8,5 # reduction candidate for 4,8 C7: 4,8 => CTR * 5.2.79.4...7.526194.9.165729.328176.7.19.4.2..2.5.719....723956396145287275698431 C7: 5 => SOLVED * 162359847537842619489716532943281765751964328628537194815423976394675281276198453 * PAIR G5: 3,8 BLK 6 I5: 3,8,5 # reduction candidate for 3,8 I5: 3,8 # 20 pairs I6: 3,8,4 # reduction candidate for 3,8 I6: 3,8 => CTR * 5.2.79.4...7.526194.9.165729532817647.19.4.25.245.719.148723956396145287275698431 I6: 4 # 20 pairs * PAIR A7: 1,8 BLK 7 B7: 1,8,4 # reduction candidate for 1,8 B7: 4 => CTR * 5.2.79.4...7.526194.9.165729532817647.19.4.25.245.719.148723956396145287275698431 B7: 1,8 # 20 pairs * PAIR C8: 4,6 ROW 8 D8: 4,6,1,7 # reduction candidate for 4,6 D8: 1,7 => CTR * 5623.9.4...74526194.98.65729.328176.7.19.4.2..2.5.719....723956396145287275698431 D8: 4,6 # 27 pairs * PAIR D7: 4,7 BLK 8 D8: 4,7,1,6 # reduction candidate for 4,7 D8: 4,7 => CTR * ..2..9.4...7..26194.9..65729.328176.7.19.4.2..2.5.719....72395639641528.275698431 D8: 1,6 # 27 pairs E8: 4,7,1 # reduction candidate for 4,7 E8: 4,7 # 27 pairs * PAIR D9: 1,6 BLK 8 D8: 1,6,4,7 # reduction candidate for 1,6 D8: 4,7 => CTR * ..2..9.4...7..26194.9..65729.328176.7.19.4.2..2.5.719....72395639641528.275698431 D8: 1,6 # 27 pairs * PAIR I8: 1,7 ROW 8 D8: 1,7,4,6 # reduction candidate for 1,7 D8: 1,7 => CTR * 5623.9.4...74526194.98.65729.328176.7.19.4.2..2.5.719....723956396145287275698431 D8: 4,6 # 27 pairs E8: 1,7,4 # reduction candidate for 1,7 E8: 1,7 # 27 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060709-absurd-base-pr-000.dot * REASONING * DIS # B3: 1 => CTR => B3: 3,8 * DIS # D2: 4 => CTR => D2: 3,8 * DIS # E1: 1,7 => CTR => E1: 5 * PRF # D3: 1,7 => SOL * DIS # E8: 4 => CTR => E8: 1,7 * DIS # I1: 3,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * DIS # I1: 8 => CTR => I1: 3,7 * PRF # D3: 3,7 => SOL * DIS # B5: 6,8 => CTR => B5: 5 * DIS # I6: 3 => CTR => I6: 4,8 * DIS # C7: 4,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * DIS # I6: 3,8 => CTR => I6: 4 * DIS # B7: 4 => CTR => B7: 1,8 * DIS # D8: 1,7 => CTR => D8: 4,6 * DIS # D8: 4,7 => CTR => D8: 1,6 * DIS # D8: 4,7 => CTR => D8: 1,6 * DIS # D8: 1,7 => CTR => D8: 4,6 * CNT 19 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,B2,B4,C6,C8,C9,D7,D9,E2,E3,E5,E6,G1,G5,H3,H7,H9,I4,I8,I9) * ..2..9.4...7..26194.9..65.29.328176.7.19.4.2..2.5.719.....239.639...528.27..984.. * PAIR B2: 3,8 BLK 1 B3: 3,8,1 # reduction candidate for 3,8 B3: 1 => CTR * ..2..9.4...7..26194198765329.328176.7.19.432..2.53719.1...2397639.7.528127..984.. * PAIR E3: 1,7 BLK 2 D3: 1,7,3,8 # reduction candidate for 1,7 D3: 1,7 => SOLVED * 162359847537842619489716532943281765751964328628537194815423976394675281276198453 * DURATION: 0:00:03.594331 START: 00:34:58.612593 END: 00:35:02.206924 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060709-absurd-base-pr-001.dot * REASONING * DIS # B3: 1 => CTR => B3: 3,8 * PRF B3: 3,8 # D3: 1,7 => SOL * STA B3: 3,8 + D3: 1,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060709, absurd
Solution
position: 162359847537842619489716532943281765751964328628537194815423976394675281276198453 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 # B3: 3,8 => UNS * DIS # B3: 1 => CTR => B3: 3,8 * INC # D2: 3,8 => UNS * DIS # D2: 4 => CTR => D2: 3,8 * INC # D1: 1,7 => UNS * DIS # E1: 1,7 => CTR => E1: 5 * INC # E1: 5 => UNS * PRF # D3: 1,7 => SOL * INC # D3: 3,8 => UNS * INC # E8: 1,7 => UNS * DIS # E8: 4 => CTR => E8: 1,7 * DIS # I1: 3,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * INC # I1: 3,7 => UNS * DIS # I1: 8 => CTR => I1: 3,7 * PRF # D3: 3,7 => SOL * INC # D3: 1,8 => UNS * DIS # B5: 6,8 => CTR => B5: 5 * INC # B5: 5 => UNS * INC # I6: 4,8 => UNS * DIS # I6: 3 => CTR => I6: 4,8 * DIS # C7: 4,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * INC # I5: 3,8 => UNS * DIS # I6: 3,8 => CTR => I6: 4 * INC # I6: 4 => UNS * INC # B7: 1,8 => UNS * DIS # B7: 4 => CTR => B7: 1,8 * INC # D8: 4,6 => UNS * DIS # D8: 1,7 => CTR => D8: 4,6 * DIS # D8: 4,7 => CTR => D8: 1,6 * INC # D8: 1,6 => UNS * INC # E8: 4,7 => UNS * INC # D8: 1,6 => UNS * DIS # D8: 4,7 => CTR => D8: 1,6 * DIS # D8: 1,7 => CTR => D8: 4,6 * INC # D8: 4,6 => UNS * INC # E8: 1,7 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 3,8 => UNS * DIS # B3: 1 => CTR => B3: 3,8 * PRF B3: 3,8 # D3: 1,7 => SOL * STA B3: 3,8 + D3: 1,7 * CNT 3 HDP CHAINS / 3 HYP OPENED