Analysis of zz-www.sudokuoftheday.co.uk-20060413-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .....5..8..54..7...1..3.....4....9..38.1.......6....516..5..1.4.9.7..52.1.324..9. initial
Autosolve
position: .....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 3,6 => CTR => H1: 1,4 * PRF # F2: 2,8 => SOL * DIS # H2: 1 => CTR => H2: 3,6 * DIS # E1: 6,9 => CTR => E1: 1,2,7 * DIS # G1: 4,6 => CTR => G1: 2,3 * DIS # H1: 4,6 => CTR => H1: 1,3 * DIS # G3: 4,6 => CTR => G3: 2 * DIS # H5: 4,6 => CTR => H5: 7 * DIS # F6: 2,7 => CTR => F6: 4,8,9 * DIS # H5: 4,6 => CTR => H5: 7 * DIS # G1: 4,6 => CTR => G1: 2,3 * DIS # G3: 4,6 => CTR => G3: 2 * PRF # I4: 2,6 => SOL * DIS # I4: 3 => CTR => I4: 2,6 * DIS # F7: 8,9 => CTR => F7: 3 * PRF # F7: 3 => SOL * PRF # F8: 1,6 => SOL * DIS # F8: 3 => CTR => F8: 1,6 * DIS # E1: 1,6 => CTR => E1: 2,7,9 * PRF # E2: 1,6 => SOL * DIS # F2: 6,8 => CTR => F2: 1,2 * DIS # F7: 9 => CTR => F7: 3,8 * DIS # H4: 6,7 => CTR => H4: 3,8 * PRF # F8: 1 => SOL * PRF # I4: 2 => SOL * CNT 25 HDP CHAINS / 68 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 3,6 => CTR => H1: 1,4 * DIS H1: 1,4 # G1: 2,4 => CTR => G1: 3,6 * PRF H1: 1,4 + G1: 3,6 # F2: 2,8 => SOL * STA H1: 1,4 + G1: 3,6 + F2: 2,8 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....5..8..54..7...1..3.....4....9..38.1.......6....516..5..1.4.9.7..52.1.324..9. | initial |
| .....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97 | autosolve |
| 264975318835412769719836245541687932382159476976324851627593184498761523153248697 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 3,6 A2: 2,8 B2: 3,6 D1: 6,9 H3: 4,6 B6: 2,7 G5: 4,6 I5: 2,6 B7: 2,7 C7: 2,7 A8: 4,8 C8: 4,8 E7: 8,9 E8: 1,6 F9: 6,8 H7: 3,8 I8: 3,6 G9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H2: 1.. / H1 = 1 => 19 pairs (_) / H2 = 1 => 0 pairs (X) E8,F8: 1.. / E8 = 1 => 21 pairs (_) / F8 = 1 => 0 pairs (*) E1,H1: 1.. / E1 = 1 => 0 pairs (X) / H1 = 1 => 19 pairs (_) F2,F8: 1.. / F2 = 1 => 21 pairs (_) / F8 = 1 => 0 pairs (*) G1,G3: 2.. / G1 = 2 => 0 pairs (X) / G3 = 2 => 18 pairs (_) I4,I5: 2.. / I4 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) B7,C7: 2.. / B7 = 2 => 17 pairs (_) / C7 = 2 => 17 pairs (_) B6,B7: 2.. / B6 = 2 => 17 pairs (_) / B7 = 2 => 17 pairs (_) B1,B2: 3.. / B1 = 3 => 0 pairs (X) / B2 = 3 => 18 pairs (_) D4,D6: 3.. / D4 = 3 => 0 pairs (X) / D6 = 3 => 22 pairs (_) F7,F8: 3.. / F7 = 3 => 0 pairs (*) / F8 = 3 => 0 pairs (X) H7,I8: 3.. / H7 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) B2,H2: 3.. / B2 = 3 => 18 pairs (_) / H2 = 3 => 0 pairs (X) D6,G6: 3.. / D6 = 3 => 22 pairs (_) / G6 = 3 => 0 pairs (X) F7,H7: 3.. / F7 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) F8,I8: 3.. / F8 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) G1,G6: 3.. / G1 = 3 => 22 pairs (_) / G6 = 3 => 0 pairs (X) I4,I8: 3.. / I4 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) F5,F6: 4.. / F5 = 4 => 0 pairs (X) / F6 = 4 => 19 pairs (_) A8,C8: 4.. / A8 = 4 => 16 pairs (_) / C8 = 4 => 26 pairs (_) F6,G6: 4.. / F6 = 4 => 19 pairs (_) / G6 = 4 => 0 pairs (X) B1,B2: 6.. / B1 = 6 => 18 pairs (_) / B2 = 6 => 0 pairs (X) I8,G9: 6.. / I8 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) F9,G9: 6.. / F9 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) E1,F3: 7.. / E1 = 7 => 19 pairs (_) / F3 = 7 => 18 pairs (_) H4,H5: 7.. / H4 = 7 => 0 pairs (X) / H5 = 7 => 20 pairs (_) B7,C7: 7.. / B7 = 7 => 17 pairs (_) / C7 = 7 => 17 pairs (_) B6,B7: 7.. / B6 = 7 => 17 pairs (_) / B7 = 7 => 17 pairs (_) H4,G6: 8.. / H4 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) A8,C8: 8.. / A8 = 8 => 26 pairs (_) / C8 = 8 => 16 pairs (_) H7,G9: 8.. / H7 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) F9,G9: 8.. / F9 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) C3,C8: 8.. / C3 = 8 => 26 pairs (_) / C8 = 8 => 16 pairs (_) G6,G9: 8.. / G6 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) H4,H7: 8.. / H4 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) C5,A6: 9.. / C5 = 9 => 20 pairs (_) / A6 = 9 => 24 pairs (_) E7,F7: 9.. / E7 = 9 => 18 pairs (_) / F7 = 9 => 0 pairs (X) C5,F5: 9.. / C5 = 9 => 20 pairs (_) / F5 = 9 => 24 pairs (_) * DURATION: 0:00:42.308233 START: 22:21:26.052902 END: 22:22:08.361135 2019-04-30 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,B2,B6,B7,C7,C8,D1,E7,E8,F9,G5,G9,H3,H7,I5,I8) * .....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97 * PAIR B1: 3,6 ROW 1 G1: 3,6,2,4 # reduction candidate for 3,6 G1: 3,6 # 22 pairs H1: 3,6,1,4 # reduction candidate for 3,6 H1: 3,6 => CTR * ....15..8.354.6719.1..37.655416.29..38.15......6....516..5..1.4.9.761523153248697 H1: 1,4 # 19 pairs * PAIR A2: 2,8 BLK 1 A3: 2,8,4,7,9 # reduction candidate for 2,8 A3: 2,8 # 19 pairs C3: 2,8,4,7,9 # reduction candidate for 2,8 C3: 2,8 # 19 pairs * PAIR A2: 2,8 ROW 2 E2: 2,8,1,6 # reduction candidate for 2,8 E2: 2,8 # 20 pairs F2: 2,8,1,6 # reduction candidate for 2,8 F2: 2,8 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 F2: 1,6 # 20 pairs * PAIR B2: 3,6 ROW 2 H2: 3,6,1 # reduction candidate for 3,6 H2: 1 => CTR * .6.915..8.354..719.1..37.655416..93238.15.476..63.48516..5.3184.9.761523153248697 H2: 3,6 # 19 pairs * PAIR D1: 6,9 BLK 2 E1: 6,9,1,2,7 # reduction candidate for 6,9 E1: 6,9 => CTR * .....5.188.54..739.1.837..5541...9..38.15......6...3516..5.31844987..523153248697 E1: 1,2,7 # 18 pairs D3: 6,9,8 # reduction candidate for 6,9 D3: 6,9 # 24 pairs F3: 6,9,2,7,8 # reduction candidate for 6,9 F3: 6,9 # 22 pairs * PAIR H3: 4,6 BLK 3 G1: 4,6,2,3 # reduction candidate for 4,6 G1: 4,6 => CTR * .....5..8..54..7.9.1..3.2.5541...9..38.15......6...3516..5..1.4.9.7..52315324..97 G1: 2,3 # 19 pairs H1: 4,6,1,3 # reduction candidate for 4,6 H1: 4,6 => CTR * ....153.8.354.6719.1..372655416.29..38.15......6....516..5..1.4.9.761523153248697 H1: 1,3 # 19 pairs G3: 4,6,2 # reduction candidate for 4,6 G3: 4,6 => CTR * .....52.8..54..7.9.1..3...5541...9..38.15......6...3516..5..1.4.9.7..52315324..97 G3: 2 # 18 pairs * PAIR H3: 4,6 COL H H5: 4,6,7 # reduction candidate for 4,6 H5: 4,6 => CTR * .....5..8..54..7.9.1..3...5541...97.38.15......6...8516..5..184.9.7..523153248697 H5: 7 # 20 pairs * PAIR B6: 2,7 BLK 4 C5: 2,7,9 # reduction candidate for 2,7 C5: 2,7 # 24 pairs A6: 2,7,9 # reduction candidate for 2,7 A6: 2,7 # 20 pairs * PAIR B6: 2,7 ROW 6 E6: 2,7,8,9 # reduction candidate for 2,7 E6: 2,7 # 24 pairs F6: 2,7,4,8,9 # reduction candidate for 2,7 F6: 2,7 => CTR * .....53.8.354..7.9.1..3.2.5541...983389154672..63..4516..5..1.4.9.7..526153246897 F6: 4,8,9 # 18 pairs * PAIR G5: 4,6 BLK 6 H5: 4,6,7 # reduction candidate for 4,6 H5: 4,6 => CTR * .....5..8..54..7.9.1..3...5541...97.38.15......6...8516..5..184.9.7..523153248697 H5: 7 # 20 pairs * PAIR G5: 4,6 ROW 5 F5: 4,6,2,7,9 # reduction candidate for 4,6 F5: 4,6 # 24 pairs F5: 2,7,9 # 20 pairs * PAIR G5: 4,6 COL G G1: 4,6,2,3 # reduction candidate for 4,6 G1: 4,6 => CTR * .....5..8..54..7.9.1..3.2.5541...9..38.15......6...3516..5..1.4.9.7..52315324..97 G1: 2,3 # 19 pairs G3: 4,6,2 # reduction candidate for 4,6 G3: 4,6 => CTR * .....52.8..54..7.9.1..3...5541...9..38.15......6...3516..5..1.4.9.7..52315324..97 G3: 2 # 18 pairs * PAIR I5: 2,6 BLK 6 I4: 2,6,3 # reduction candidate for 2,6 I4: 2,6 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 I4: 3 => CTR * .....53.8.354.1769.1.63.24554186297338.15...2..63...516..5..134.9.7.3526153246897 * PAIR I5: 2,6 ROW 5 F5: 2,6,4,7,9 # reduction candidate for 2,6 F5: 2,6 # 22 pairs F5: 4,7,9 # 19 pairs * PAIR C7: 2,7 COL C C1: 2,7,4,9 # reduction candidate for 2,7 C1: 2,7 # 22 pairs C3: 2,7,4,8,9 # reduction candidate for 2,7 C3: 2,7 # 19 pairs C5: 2,7,9 # reduction candidate for 2,7 C5: 2,7 # 24 pairs * PAIR A8: 4,8 COL A A3: 4,8,2,7,9 # reduction candidate for 4,8 A3: 4,8 # 29 pairs A3: 2,7,9 # 18 pairs * PAIR C8: 4,8 COL C C3: 4,8,2,7,9 # reduction candidate for 4,8 C3: 4,8 # 19 pairs C3: 2,7,9 # 16 pairs * PAIR E7: 8,9 BLK 8 F7: 8,9,3 # reduction candidate for 8,9 F7: 8,9 => CTR * .....53.8.354.1769.1.63.245541.6.98338.15......6....516..5..134.9.7.3526153246897 F7: 3 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 * PAIR E7: 8,9 COL E E6: 8,9,2,7 # reduction candidate for 8,9 E6: 2,7 # 24 pairs E6: 8,9 # 19 pairs * PAIR E8: 1,6 BLK 8 F8: 1,6,3 # reduction candidate for 1,6 F8: 1,6 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 F8: 3 => CTR * .....5318.354.1769.1..3...5541...98338.15..72..63..4516..5..134.9.713526153246897 * PAIR E8: 1,6 COL E E1: 1,6,2,7,9 # reduction candidate for 1,6 E1: 1,6 => CTR * .6.9153488354..7199148372655416..9..38915..7...63...516..5..1.4498761523153248697 E1: 2,7,9 # 19 pairs E2: 1,6,2,8 # reduction candidate for 1,6 E2: 1,6 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 E2: 2,8 # 20 pairs * PAIR F9: 6,8 COL F F2: 6,8,1,2 # reduction candidate for 6,8 F2: 6,8 => CTR * .....53.8.354.6719.1..3.26554168.93238.152476..63948516..5.3184.9.761523153248697 F2: 1,2 # 19 pairs F3: 6,8,2,7,9 # reduction candidate for 6,8 F3: 6,8 # 25 pairs F4: 6,8,2,7 # reduction candidate for 6,8 F4: 6,8 # 23 pairs * PAIR H7: 3,8 ROW 7 F7: 3,8,9 # reduction candidate for 3,8 F7: 9 => CTR * .....53.8.354.1769.1.63.245541.6.98338.15......6....516..5.9134.9.7.3526153246897 F7: 3,8 # 18 pairs * PAIR H7: 3,8 COL H H4: 3,8,6,7 # reduction candidate for 3,8 H4: 6,7 => CTR * .....5..8..54..7.9.1..3...5541...9..38.15......6...8516..5..184.9.7..523153248697 H4: 3,8 # 22 pairs * PAIR I8: 3,6 ROW 8 F8: 3,6,1 # reduction candidate for 3,6 F8: 1 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 F8: 3,6 # 21 pairs * PAIR I8: 3,6 COL I I4: 3,6,2 # reduction candidate for 3,6 I4: 2 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 I4: 3,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060413-absurd-base-pr-000.dot * REASONING * DIS # H1: 3,6 => CTR => H1: 1,4 * PRF # F2: 2,8 => SOL * DIS # H2: 1 => CTR => H2: 3,6 * DIS # E1: 6,9 => CTR => E1: 1,2,7 * DIS # G1: 4,6 => CTR => G1: 2,3 * DIS # H1: 4,6 => CTR => H1: 1,3 * DIS # G3: 4,6 => CTR => G3: 2 * DIS # H5: 4,6 => CTR => H5: 7 * DIS # F6: 2,7 => CTR => F6: 4,8,9 * DIS # H5: 4,6 => CTR => H5: 7 * DIS # G1: 4,6 => CTR => G1: 2,3 * DIS # G3: 4,6 => CTR => G3: 2 * PRF # I4: 2,6 => SOL * DIS # I4: 3 => CTR => I4: 2,6 * DIS # F7: 8,9 => CTR => F7: 3 * PRF # F7: 3 => SOL * PRF # F8: 1,6 => SOL * DIS # F8: 3 => CTR => F8: 1,6 * DIS # E1: 1,6 => CTR => E1: 2,7,9 * PRF # E2: 1,6 => SOL * DIS # F2: 6,8 => CTR => F2: 1,2 * DIS # F7: 9 => CTR => F7: 3,8 * DIS # H4: 6,7 => CTR => H4: 3,8 * PRF # F8: 1 => SOL * PRF # I4: 2 => SOL * CNT 25 HDP CHAINS / 68 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,B2,B6,B7,C7,C8,D1,E7,E8,F9,G5,G9,H3,H7,I5,I8) * .....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97 * PAIR B1: 3,6 ROW 1 G1: 3,6,2,4 # reduction candidate for 3,6 G1: 3,6 # 22 pairs H1: 3,6,1,4 # reduction candidate for 3,6 H1: 3,6 => CTR * ....15..8.354.6719.1..37.655416.29..38.15......6....516..5..1.4.9.761523153248697 * RESTART * PAIR B1: 3,6 ROW 1 G1: 3,6,2,4 # reduction candidate for 3,6 G1: 2,4 => CTR * .3...5..8.654..739.1..3...5541...9..38.15......6...3516..5.3184.9.7..523153248697 * PAIR RESTART * PAIR A2: 2,8 ROW 2 E2: 2,8,1,6 # reduction candidate for 2,8 E2: 2,8 # 24 pairs F2: 2,8,1,6 # reduction candidate for 2,8 F2: 2,8 => SOLVED * 264975318835412769719836245541687932382159476976324851627593184498761523153248697 * DURATION: 0:00:04.785998 START: 22:22:48.881977 END: 22:22:53.667975 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060413-absurd-base-pr-001.dot * REASONING * DIS # H1: 3,6 => CTR => H1: 1,4 * DIS H1: 1,4 # G1: 2,4 => CTR => G1: 3,6 * PRF H1: 1,4 + G1: 3,6 # F2: 2,8 => SOL * STA H1: 1,4 + G1: 3,6 + F2: 2,8 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060413, absurd
Solution
position: 264975318835412769719836245541687932382159476976324851627593184498761523153248697 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 # G1: 3,6 => UNS * DIS # H1: 3,6 => CTR => H1: 1,4 * INC # H1: 1,4 => UNS * INC # A3: 2,8 => UNS * INC # C3: 2,8 => UNS * INC # E2: 2,8 => UNS * PRF # F2: 2,8 => SOL * INC # F2: 1,6 => UNS * INC # H2: 3,6 => UNS * DIS # H2: 1 => CTR => H2: 3,6 * DIS # E1: 6,9 => CTR => E1: 1,2,7 * INC # E1: 1,2,7 => UNS * INC # D3: 6,9 => UNS * INC # F3: 6,9 => UNS * DIS # G1: 4,6 => CTR => G1: 2,3 * INC # G1: 2,3 => UNS * DIS # H1: 4,6 => CTR => H1: 1,3 * INC # H1: 1,3 => UNS * DIS # G3: 4,6 => CTR => G3: 2 * INC # G3: 2 => UNS * DIS # H5: 4,6 => CTR => H5: 7 * INC # H5: 7 => UNS * INC # C5: 2,7 => UNS * INC # A6: 2,7 => UNS * INC # E6: 2,7 => UNS * DIS # F6: 2,7 => CTR => F6: 4,8,9 * INC # F6: 4,8,9 => UNS * DIS # H5: 4,6 => CTR => H5: 7 * INC # H5: 7 => UNS * INC # F5: 4,6 => UNS * INC # F5: 2,7,9 => UNS * DIS # G1: 4,6 => CTR => G1: 2,3 * INC # G1: 2,3 => UNS * DIS # G3: 4,6 => CTR => G3: 2 * INC # G3: 2 => UNS * PRF # I4: 2,6 => SOL * DIS # I4: 3 => CTR => I4: 2,6 * INC # F5: 2,6 => UNS * INC # F5: 4,7,9 => UNS * INC # C1: 2,7 => UNS * INC # C3: 2,7 => UNS * INC # C5: 2,7 => UNS * INC # A3: 4,8 => UNS * INC # A3: 2,7,9 => UNS * INC # C3: 4,8 => UNS * INC # C3: 2,7,9 => UNS * DIS # F7: 8,9 => CTR => F7: 3 * PRF # F7: 3 => SOL * INC # E6: 8,9 => UNS * INC # E6: 2,7 => UNS * PRF # F8: 1,6 => SOL * DIS # F8: 3 => CTR => F8: 1,6 * DIS # E1: 1,6 => CTR => E1: 2,7,9 * INC # E1: 2,7,9 => UNS * PRF # E2: 1,6 => SOL * INC # E2: 2,8 => UNS * DIS # F2: 6,8 => CTR => F2: 1,2 * INC # F2: 1,2 => UNS * INC # F3: 6,8 => UNS * INC # F4: 6,8 => UNS * INC # F7: 3,8 => UNS * DIS # F7: 9 => CTR => F7: 3,8 * INC # H4: 3,8 => UNS * DIS # H4: 6,7 => CTR => H4: 3,8 * INC # F8: 3,6 => UNS * PRF # F8: 1 => SOL * INC # I4: 3,6 => UNS * PRF # I4: 2 => SOL * CNT 68 HDP CHAINS / 68 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 3,6 => UNS * DIS # H1: 3,6 => CTR => H1: 1,4 * INC H1: 1,4 # G1: 3,6 => UNS * DIS H1: 1,4 # G1: 2,4 => CTR => G1: 3,6 * INC H1: 1,4 + G1: 3,6 # E2: 2,8 => UNS * PRF H1: 1,4 + G1: 3,6 # F2: 2,8 => SOL * STA H1: 1,4 + G1: 3,6 + F2: 2,8 * CNT 6 HDP CHAINS / 6 HYP OPENED