Analysis of zz-www.sudokuoftheday.co.uk-20060614-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: 6......34.4.3..8......4......913.4...1.49..85..5..6..1.67............25.3.19..6.. initial
Autosolve
position: 6.8....34.423..8....3.4......91354...1649.385435..6..1.67........4...25.3.19..6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 2,7 => CTR => A4: 8 * DIS # D6: 2,7 => CTR => D6: 8 * DIS # F9: 2,7 => CTR => F9: 4,8 * DIS # H6: 7,9 => CTR => H6: 2 * DIS # E7: 2,5 => CTR => E7: 8 * DIS # E9: 7,8 => CTR => E9: 2,5 * DIS # E8: 1 => CTR => E8: 6,7 * DIS # D3: 5,8 => CTR => D3: 6,7 * DIS # H7: 1,9 => CTR => H7: 4 * DIS # G1: 1,9 => CTR => G1: 5,7 * DIS # G3: 1,9 => CTR => G3: 5,7 * DIS # F8: 3,7 => CTR => F8: 1 * DIS # F9: 2,8 => CTR => F9: 4,7 * DIS # E9: 7,8 => CTR => E9: 2,5 * DIS # F9: 7,8 => CTR => F9: 2,4 * CNT 15 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 2,7 => CTR => A4: 8 * DIS A4: 8 # D6: 2,7 => CTR => D6: 8 * DIS A4: 8 + D6: 8 # F9: 2,7 => CTR => F9: 4 * PRF A4: 8 + D6: 8 + F9: 4 # F1: 1,9 => SOL * STA A4: 8 + D6: 8 + F9: 4 + F1: 1,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6......34.4.3..8......4......913.4...1.49..85..5..6..1.67............25.3.19..6.. | initial |
| 6.8....34.423..8....3.4......91354...1649.385435..6..1.67........4...25.3.19..6.. | autosolve |
| 678219534142357896593648712829135467716492385435876921267583149984761253351924678 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A5: 2,7 F5: 2,7 G6: 7,9 A7: 2,5 A8: 8,9 B8: 8,9 B9: 2,5 D8: 6,7 G7: 1,9 I8: 3,7 H9: 4,7 I9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 0 pairs (*) / A3 = 1 => 0 pairs (X) E8,F8: 1.. / E8 = 1 => 0 pairs (X) / F8 = 1 => 14 pairs (_) G7,H7: 1.. / G7 = 1 => 14 pairs (_) / H7 = 1 => 0 pairs (X) H3,I3: 2.. / H3 = 2 => 0 pairs (X) / I3 = 2 => 13 pairs (_) A7,B9: 2.. / A7 = 2 => 24 pairs (_) / B9 = 2 => 0 pairs (X) A5,F5: 2.. / A5 = 2 => 0 pairs (X) / F5 = 2 => 25 pairs (_) B4,B9: 2.. / B4 = 2 => 24 pairs (_) / B9 = 2 => 0 pairs (X) I3,I4: 2.. / I3 = 2 => 13 pairs (_) / I4 = 2 => 0 pairs (X) F7,F8: 3.. / F7 = 3 => 14 pairs (_) / F8 = 3 => 0 pairs (X) I7,I8: 3.. / I7 = 3 => 0 pairs (X) / I8 = 3 => 14 pairs (_) F7,I7: 3.. / F7 = 3 => 14 pairs (_) / I7 = 3 => 0 pairs (X) F8,I8: 3.. / F8 = 3 => 0 pairs (X) / I8 = 3 => 14 pairs (_) F7,F9: 4.. / F7 = 4 => 0 pairs (X) / F9 = 4 => 14 pairs (_) H7,H9: 4.. / H7 = 4 => 14 pairs (_) / H9 = 4 => 0 pairs (X) F7,H7: 4.. / F7 = 4 => 0 pairs (X) / H7 = 4 => 14 pairs (_) F9,H9: 4.. / F9 = 4 => 14 pairs (_) / H9 = 4 => 0 pairs (X) G1,G3: 5.. / G1 = 5 => 17 pairs (_) / G3 = 5 => 13 pairs (_) A7,B9: 5.. / A7 = 5 => 0 pairs (X) / B9 = 5 => 24 pairs (_) A2,E2: 5.. / A2 = 5 => 24 pairs (_) / E2 = 5 => 0 pairs (*) B9,E9: 5.. / B9 = 5 => 24 pairs (_) / E9 = 5 => 0 pairs (X) E2,D3: 6.. / E2 = 6 => 0 pairs (X) / D3 = 6 => 16 pairs (_) H4,I4: 6.. / H4 = 6 => 13 pairs (_) / I4 = 6 => 14 pairs (_) D8,E8: 6.. / D8 = 6 => 0 pairs (X) / E8 = 6 => 16 pairs (_) D3,D8: 6.. / D3 = 6 => 16 pairs (_) / D8 = 6 => 0 pairs (X) E2,E8: 6.. / E2 = 6 => 0 pairs (X) / E8 = 6 => 16 pairs (_) A5,F5: 7.. / A5 = 7 => 25 pairs (_) / F5 = 7 => 0 pairs (X) D3,F3: 8.. / D3 = 8 => 0 pairs (X) / F3 = 8 => 12 pairs (_) A4,B4: 8.. / A4 = 8 => 11 pairs (_) / B4 = 8 => 0 pairs (X) D6,E6: 8.. / D6 = 8 => 15 pairs (_) / E6 = 8 => 0 pairs (X) A8,B8: 8.. / A8 = 8 => 0 pairs (X) / B8 = 8 => 11 pairs (_) I7,I9: 8.. / I7 = 8 => 0 pairs (X) / I9 = 8 => 12 pairs (_) A4,A8: 8.. / A4 = 8 => 11 pairs (_) / A8 = 8 => 0 pairs (X) B4,B8: 8.. / B4 = 8 => 0 pairs (X) / B8 = 8 => 11 pairs (_) G6,H6: 9.. / G6 = 9 => 17 pairs (_) / H6 = 9 => 0 pairs (X) A8,B8: 9.. / A8 = 9 => 11 pairs (_) / B8 = 9 => 0 pairs (X) * DURATION: 0:00:41.923282 START: 23:50:08.650881 END: 23:50:50.574163 2019-04-30 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,A8,B8,B9,D8,F5,G6,G7,H9,I8,I9) * 6.8....34.423..8....3.4......91354...1649.385435..6..1.67........4...25.3.19..6.. * PAIR A5: 2,7 BLK 4 A4: 2,7,8 # reduction candidate for 2,7 A4: 2,7 => CTR * 6.8....345423..8....3.4.....891354...1649.385435..6..1.67......894...25.32195.6.. A4: 8 # 11 pairs B4: 2,7,8 # reduction candidate for 2,7 B4: 2,7 # 11 pairs * PAIR F5: 2,7 BLK 5 D6: 2,7,8 # reduction candidate for 2,7 D6: 2,7 => CTR * 6.82..53454236.81.1.35487.28291354.671649238543578692126785.1..9846..257351927648 D6: 8 # 15 pairs E6: 2,7,8 # reduction candidate for 2,7 E6: 2,7 # 15 pairs * PAIR F5: 2,7 COL F F1: 2,7,1,9 # reduction candidate for 2,7 F1: 2,7 # 15 pairs F9: 2,7,4,8 # reduction candidate for 2,7 F9: 2,7 => CTR * 6.8..91345423618791937485....91354...1649.385435..6791267..4913984613257351972648 F9: 4,8 # 14 pairs * PAIR G6: 7,9 BLK 6 H6: 7,9,2 # reduction candidate for 7,9 H6: 7,9 => CTR * 6.8....34.423..8....3.4......91354..216497385435..6..1567........4...25.32195.6.. H6: 2 # 25 pairs * PAIR G6: 7,9 COL G G1: 7,9,1,5 # reduction candidate for 7,9 G1: 7,9 # 19 pairs G3: 7,9,1,5 # reduction candidate for 7,9 G3: 7,9 # 19 pairs * PAIR A7: 2,5 ROW 7 D7: 2,5,8 # reduction candidate for 2,5 D7: 2,5 # 15 pairs E7: 2,5,8 # reduction candidate for 2,5 E7: 2,5 => CTR * 6.82..53454236.81.1.35487.28291354.671649238543578692126785.1..9846..257351927648 E7: 8 # 15 pairs * PAIR B9: 2,5 ROW 9 E9: 2,5,7,8 # reduction candidate for 2,5 E9: 7,8 => CTR * 6.8....34.423..8....3.4.....291354..71649.385435..6..1.67........4...25.3519.264. E9: 2,5 # 13 pairs * PAIR D8: 6,7 BLK 8 E8: 6,7,1 # reduction candidate for 6,7 E8: 1 => CTR * 6982.1.3454236.819173.49562829135476716492385435786921267...19.98461.25.35192.64. E8: 6,7 # 14 pairs * PAIR D8: 6,7 COL D D3: 6,7,5,8 # reduction candidate for 6,7 D3: 5,8 => CTR * 6.82..53454236.81.1.354876282913547671649238543578692126785.1939846.3257351927648 D3: 6,7 # 15 pairs * PAIR G7: 1,9 BLK 9 H7: 1,9,4 # reduction candidate for 1,9 H7: 1,9 => CTR * 6.8..91345423618791937485....91354...1649.385435..6791267..4913984613257351972648 H7: 4 # 14 pairs * PAIR G7: 1,9 COL G G1: 1,9,5,7 # reduction candidate for 1,9 G1: 1,9 => CTR * 6.8....34.423..8....3.4.5....91354..216497385435..6791567........4...25.32195.6.. G1: 5,7 # 14 pairs G3: 1,9,5,7 # reduction candidate for 1,9 G3: 1,9 => CTR * 6.8...534.423..8....3.4......91354..216497385435..6791567........4...25.32195.6.. G3: 5,7 # 13 pairs * PAIR I8: 3,7 ROW 8 F8: 3,7,1 # reduction candidate for 3,7 F8: 3,7 => CTR * 6982.1.3454236.819173.49562829135476716492385435786921267...19.98461.25.35192.64. F8: 1 # 14 pairs * PAIR H9: 4,7 ROW 9 F9: 4,7,2,8 # reduction candidate for 4,7 F9: 2,8 => CTR * 6.8....34.4236.8.9..3.48....291354.671649.385435..6..1.67..4..3..4613257351972648 F9: 4,7 # 14 pairs * PAIR I9: 7,8 ROW 9 E9: 7,8,2,5 # reduction candidate for 7,8 E9: 7,8 => CTR * 6.8....34.423..8....3.4.....291354..71649.385435..6..1.67........4...25.3519.264. E9: 2,5 # 13 pairs F9: 7,8,2,4 # reduction candidate for 7,8 F9: 7,8 => CTR * 6.8..9134.4236.8.9..3.48.....91354..716492385435..6.21.67..4.93..46132573.19.7648 F9: 2,4 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060614-absurd-base-pr-000.dot * REASONING * DIS # A4: 2,7 => CTR => A4: 8 * DIS # D6: 2,7 => CTR => D6: 8 * DIS # F9: 2,7 => CTR => F9: 4,8 * DIS # H6: 7,9 => CTR => H6: 2 * DIS # E7: 2,5 => CTR => E7: 8 * DIS # E9: 7,8 => CTR => E9: 2,5 * DIS # E8: 1 => CTR => E8: 6,7 * DIS # D3: 5,8 => CTR => D3: 6,7 * DIS # H7: 1,9 => CTR => H7: 4 * DIS # G1: 1,9 => CTR => G1: 5,7 * DIS # G3: 1,9 => CTR => G3: 5,7 * DIS # F8: 3,7 => CTR => F8: 1 * DIS # F9: 2,8 => CTR => F9: 4,7 * DIS # E9: 7,8 => CTR => E9: 2,5 * DIS # F9: 7,8 => CTR => F9: 2,4 * CNT 15 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,A8,B8,B9,D8,F5,G6,G7,H9,I8,I9) * 6.8....34.423..8....3.4......91354...1649.385435..6..1.67........4...25.3.19..6.. * PAIR A5: 2,7 BLK 4 A4: 2,7,8 # reduction candidate for 2,7 A4: 2,7 => CTR * 6.8....345423..8....3.4.....891354...1649.385435..6..1.67......894...25.32195.6.. * RESTART * PAIR F5: 2,7 BLK 5 D6: 2,7,8 # reduction candidate for 2,7 D6: 2,7 => CTR * 6.82..53454236.81.1.35487.28291354.671649238543578692126785.1..9846..257351927648 * RESTART * PAIR F5: 2,7 COL F F1: 2,7,1,9 # reduction candidate for 2,7 F1: 2,7 # 16 pairs F9: 2,7,4 # reduction candidate for 2,7 F9: 2,7 => CTR * 6.8..91345423618791937485..8791354...1649.3854358.6..1.67.84..39846132573.19..648 * RESTART * PAIR F5: 2,7 COL F F1: 2,7,1,9 # reduction candidate for 2,7 F1: 1,9 => SOLVED * 678219534142357896593648712829135467716492385435876921267583149984761253351924678 * DURATION: 0:00:05.802155 START: 23:51:13.518014 END: 23:51:19.320169 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060614-absurd-base-pr-001.dot * REASONING * DIS # A4: 2,7 => CTR => A4: 8 * DIS A4: 8 # D6: 2,7 => CTR => D6: 8 * DIS A4: 8 + D6: 8 # F9: 2,7 => CTR => F9: 4 * PRF A4: 8 + D6: 8 + F9: 4 # F1: 1,9 => SOL * STA A4: 8 + D6: 8 + F9: 4 + F1: 1,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060614, absurd
Solution
position: 678219534142357896593648712829135467716492385435876921267583149984761253351924678 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:
* DIS # A4: 2,7 => CTR => A4: 8 * INC # A4: 8 => UNS * INC # B4: 2,7 => UNS * DIS # D6: 2,7 => CTR => D6: 8 * INC # D6: 8 => UNS * INC # E6: 2,7 => UNS * INC # F1: 2,7 => UNS * DIS # F9: 2,7 => CTR => F9: 4,8 * INC # F9: 4,8 => UNS * DIS # H6: 7,9 => CTR => H6: 2 * INC # H6: 2 => UNS * INC # G1: 7,9 => UNS * INC # G3: 7,9 => UNS * INC # D7: 2,5 => UNS * DIS # E7: 2,5 => CTR => E7: 8 * INC # E7: 8 => UNS * INC # E9: 2,5 => UNS * DIS # E9: 7,8 => CTR => E9: 2,5 * INC # E8: 6,7 => UNS * DIS # E8: 1 => CTR => E8: 6,7 * INC # D3: 6,7 => UNS * DIS # D3: 5,8 => CTR => D3: 6,7 * DIS # H7: 1,9 => CTR => H7: 4 * INC # H7: 4 => UNS * DIS # G1: 1,9 => CTR => G1: 5,7 * INC # G1: 5,7 => UNS * DIS # G3: 1,9 => CTR => G3: 5,7 * INC # G3: 5,7 => UNS * DIS # F8: 3,7 => CTR => F8: 1 * INC # F8: 1 => UNS * INC # F9: 4,7 => UNS * DIS # F9: 2,8 => CTR => F9: 4,7 * DIS # E9: 7,8 => CTR => E9: 2,5 * INC # E9: 2,5 => UNS * DIS # F9: 7,8 => CTR => F9: 2,4 * INC # F9: 2,4 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A4: 2,7 => CTR => A4: 8 * DIS A4: 8 # D6: 2,7 => CTR => D6: 8 * INC A4: 8 + D6: 8 # F1: 2,7 => UNS * DIS A4: 8 + D6: 8 # F9: 2,7 => CTR => F9: 4 * INC A4: 8 + D6: 8 + F9: 4 # F1: 2,7 => UNS * PRF A4: 8 + D6: 8 + F9: 4 # F1: 1,9 => SOL * STA A4: 8 + D6: 8 + F9: 4 + F1: 1,9 * CNT 6 HDP CHAINS / 6 HYP OPENED