Analysis of zz-www.sudokuoftheday.co.uk-20060514-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: ........2..9...4.3.34..271.8...4.6...9.1.7.......2..9..432......15..8...7..3....1 initial
Autosolve
position: ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 5,6 => CTR => A1: 1 * DIS # H4: 5,7 => CTR => H4: 2,3 * DIS # I6: 5,7 => CTR => I6: 4,8 * CNT 3 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 5,6 => CTR => A1: 1 * DIS A1: 1 # H4: 5,7 => CTR => H4: 2,3 * DIS A1: 1 + H4: 2,3 # I6: 5,7 => CTR => I6: 4,8 * DIS A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,3 => CTR => H5: 4,5,8 * DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 4,6,7 => CTR => H8: 2,3 * DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 2 => CTR => A8: 6,9 * PRF A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 # E7: 6,9 => SOL * STA A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 + E7: 6,9 * CNT 7 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ........2..9...4.3.34..271.8...4.6...9.1.7.......2..9..432......15..8...7..3....1 | initial |
| ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1 | autosolve |
| 178934562269715483534862719821549637396187254457623198643291875915478326782356941 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A3: 5,6 A5: 3,4 C5: 2,6 A6: 3,4 C6: 6,7 D4: 5,9 I4: 5,7 A7: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 8 pairs (_) / A2 = 1 => 0 pairs (X) E7,F7: 1.. / E7 = 1 => 8 pairs (_) / F7 = 1 => 9 pairs (_) A2,B2: 2.. / A2 = 2 => 14 pairs (_) / B2 = 2 => 27 pairs (_) B4,C5: 2.. / B4 = 2 => 17 pairs (_) / C5 = 2 => 14 pairs (_) B4,H4: 2.. / B4 = 2 => 17 pairs (_) / H4 = 2 => 14 pairs (_) A2,A8: 2.. / A2 = 2 => 14 pairs (_) / A8 = 2 => 27 pairs (_) C5,C9: 2.. / C5 = 2 => 14 pairs (_) / C9 = 2 => 17 pairs (_) E1,F1: 3.. / E1 = 3 => 8 pairs (_) / F1 = 3 => 0 pairs (X) A5,A6: 3.. / A5 = 3 => 14 pairs (_) / A6 = 3 => 9 pairs (_) G8,H8: 3.. / G8 = 3 => 8 pairs (_) / H8 = 3 => 0 pairs (X) F4,H4: 3.. / F4 = 3 => 13 pairs (_) / H4 = 3 => 15 pairs (_) A6,F6: 3.. / A6 = 3 => 9 pairs (_) / F6 = 3 => 14 pairs (_) E1,E5: 3.. / E1 = 3 => 8 pairs (_) / E5 = 3 => 0 pairs (X) G5,G8: 3.. / G5 = 3 => 0 pairs (X) / G8 = 3 => 8 pairs (_) D1,F1: 4.. / D1 = 4 => 8 pairs (_) / F1 = 4 => 8 pairs (_) A5,A6: 4.. / A5 = 4 => 9 pairs (_) / A6 = 4 => 14 pairs (_) D8,F9: 4.. / D8 = 4 => 8 pairs (_) / F9 = 4 => 8 pairs (_) A6,I6: 4.. / A6 = 4 => 14 pairs (_) / I6 = 4 => 9 pairs (_) F9,H9: 4.. / F9 = 4 => 8 pairs (_) / H9 = 4 => 8 pairs (_) D1,D8: 4.. / D1 = 4 => 8 pairs (_) / D8 = 4 => 8 pairs (_) F1,F9: 4.. / F1 = 4 => 8 pairs (_) / F9 = 4 => 8 pairs (_) B4,B6: 5.. / B4 = 5 => 14 pairs (_) / B6 = 5 => 13 pairs (_) C5,E5: 6.. / C5 = 6 => 17 pairs (_) / E5 = 6 => 14 pairs (_) C1,C6: 7.. / C1 = 7 => 13 pairs (_) / C6 = 7 => 10 pairs (_) E5,D6: 8.. / E5 = 8 => 14 pairs (_) / D6 = 8 => 8 pairs (_) B9,C9: 8.. / B9 = 8 => 13 pairs (_) / C9 = 8 => 15 pairs (_) D6,I6: 8.. / D6 = 8 => 8 pairs (_) / I6 = 8 => 14 pairs (_) C1,C9: 8.. / C1 = 8 => 13 pairs (_) / C9 = 8 => 15 pairs (_) G1,I3: 9.. / G1 = 9 => 12 pairs (_) / I3 = 9 => 12 pairs (_) D4,F4: 9.. / D4 = 9 => 8 pairs (_) / F4 = 9 => 13 pairs (_) A7,A8: 9.. / A7 = 9 => 9 pairs (_) / A8 = 9 => 15 pairs (_) * DURATION: 0:00:31.649234 START: 23:08:13.167515 END: 23:08:44.816749 2019-04-30 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A6,A7,C5,C6,D4,I4) * ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1 * PAIR A3: 5,6 BLK 1 A1: 5,6,1 # reduction candidate for 5,6 A1: 5,6 => CTR * ....31..2129...4.3.34..271.8.1.4362..92167...3..82519494321....215..8...7..3..2.1 A1: 1 # 8 pairs A2: 5,6,1,2 # reduction candidate for 5,6 A2: 5,6 # 27 pairs * PAIR A3: 5,6 ROW 3 D3: 5,6,8,9 # reduction candidate for 5,6 D3: 5,6 # 11 pairs E3: 5,6,8,9 # reduction candidate for 5,6 E3: 5,6 # 11 pairs I3: 5,6,8,9 # reduction candidate for 5,6 I3: 5,6 # 15 pairs * PAIR A5: 3,4 ROW 5 H5: 3,4,2,5,8 # reduction candidate for 3,4 H5: 3,4 # 10 pairs H5: 2,5,8 # 8 pairs * PAIR C5: 2,6 COL C C9: 2,6,8 # reduction candidate for 2,6 C9: 8 # 15 pairs C9: 2,6 # 13 pairs * PAIR C6: 6,7 BLK 4 B6: 6,7,5 # reduction candidate for 6,7 B6: 6,7 # 14 pairs B6: 5 # 13 pairs * PAIR C6: 6,7 COL C C1: 6,7,8 # reduction candidate for 6,7 C1: 6,7 # 15 pairs C1: 8 # 13 pairs * PAIR D4: 5,9 BLK 5 F4: 5,9,3 # reduction candidate for 5,9 F4: 5,9 # 15 pairs F4: 3 # 13 pairs * PAIR D4: 5,9 COL D D1: 5,9,4,6,7,8 # reduction candidate for 5,9 D1: 5,9 # 11 pairs D3: 5,9,6,8 # reduction candidate for 5,9 D3: 5,9 # 10 pairs * PAIR I4: 5,7 BLK 6 H4: 5,7,2,3 # reduction candidate for 5,7 H4: 5,7 => CTR * 1.8.395622695714835346827198219436..496157..8357826194.43215876.15..8...7823....1 H4: 2,3 # 9 pairs I6: 5,7,4,8 # reduction candidate for 5,7 I6: 5,7 => CTR * ....3...2..9...4.3.34..271.821.4.63.39.167...4..82319..432......15..83..7..3....1 I6: 4,8 # 10 pairs * PAIR I4: 5,7 ROW 4 B4: 5,7,2 # reduction candidate for 5,7 B4: 2 # 17 pairs B4: 5,7 # 14 pairs * PAIR I4: 5,7 COL I I7: 5,7,6,8,9 # reduction candidate for 5,7 I7: 5,7 # 14 pairs I7: 6,8,9 # 8 pairs * PAIR A7: 6,9 BLK 7 A8: 6,9,2 # reduction candidate for 6,9 A8: 2 # 27 pairs A8: 6,9 # 14 pairs * PAIR A7: 6,9 ROW 7 E7: 6,9,1,5,7 # reduction candidate for 6,9 E7: 6,9 # 14 pairs F7: 6,9,1,5 # reduction candidate for 6,9 F7: 6,9 # 13 pairs I7: 6,9,5,7,8 # reduction candidate for 6,9 I7: 6,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060514-absurd-base-pr-000.dot * REASONING * DIS # A1: 5,6 => CTR => A1: 1 * DIS # H4: 5,7 => CTR => H4: 2,3 * DIS # I6: 5,7 => CTR => I6: 4,8 * CNT 3 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A6,A7,C5,C6,D4,I4) * ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1 * PAIR A3: 5,6 BLK 1 A1: 5,6,1 # reduction candidate for 5,6 A1: 5,6 => CTR * ....31..2129...4.3.34..271.8.1.4362..92167...3..82519494321....215..8...7..3..2.1 A2: 5,6,2 # reduction candidate for 5,6 A2: 5,6 # 27 pairs * RESTART * PAIR A3: 5,6 BLK 1 A2: 5,6,2 # reduction candidate for 5,6 A2: 5,6 # 27 pairs A2: 2 # 14 pairs * PAIR A3: 5,6 ROW 3 D3: 5,6,8,9 # reduction candidate for 5,6 D3: 5,6 # 11 pairs E3: 5,6,8,9 # reduction candidate for 5,6 E3: 5,6 # 11 pairs I3: 5,6,8,9 # reduction candidate for 5,6 I3: 5,6 # 15 pairs * PAIR A5: 3,4 ROW 5 H5: 3,4,2,5,8 # reduction candidate for 3,4 H5: 3,4 # 10 pairs H5: 2,5,8 # 8 pairs * PAIR C5: 2,6 COL C C9: 2,6,8 # reduction candidate for 2,6 C9: 8 # 15 pairs C9: 2,6 # 13 pairs * PAIR C6: 6,7 BLK 4 B6: 6,7,5 # reduction candidate for 6,7 B6: 6,7 # 14 pairs B6: 5 # 13 pairs * PAIR C6: 6,7 COL C C1: 6,7,8 # reduction candidate for 6,7 C1: 6,7 # 15 pairs C1: 8 # 13 pairs * PAIR D4: 5,9 BLK 5 F4: 5,9,3 # reduction candidate for 5,9 F4: 5,9 # 15 pairs F4: 3 # 13 pairs * PAIR D4: 5,9 COL D D1: 5,9,4,6,7,8 # reduction candidate for 5,9 D1: 5,9 # 11 pairs D3: 5,9,6,8 # reduction candidate for 5,9 D3: 5,9 # 10 pairs * PAIR I4: 5,7 BLK 6 H4: 5,7,2,3 # reduction candidate for 5,7 H4: 5,7 => CTR * 1.8.395622695714835346827198219436..496157..8357826194.43215876.15..8...7823....1 I6: 5,7,4,8 # reduction candidate for 5,7 I6: 5,7 => CTR * 1...3...2..9...4.3.34..271.821.4.63.39.167...4..82319..432......15..83..7..3....1 * PAIR A7: 6,9 BLK 7 A8: 6,9,2 # reduction candidate for 6,9 A8: 2 # 27 pairs A8: 6,9 # 16 pairs * PAIR A7: 6,9 ROW 7 E7: 6,9,1,5,7 # reduction candidate for 6,9 E7: 6,9 # 17 pairs F7: 6,9,1,5 # reduction candidate for 6,9 F7: 6,9 # 16 pairs I7: 6,9,5,8 # reduction candidate for 6,9 I7: 6,9 # 13 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A5,A6,A7,B4,C5,C6,D4,H4,I6) * 1.......2..9...4.3.34..271.8.1.4.6.7.9.1.7.......2.19..432......15..8...7..3....1 * PAIR A3: 5,6 BLK 1 A2: 5,6,2 # reduction candidate for 5,6 A2: 5,6 # 27 pairs A2: 2 # 16 pairs * PAIR A3: 5,6 ROW 3 D3: 5,6,8,9 # reduction candidate for 5,6 D3: 5,6 # 13 pairs E3: 5,6,8,9 # reduction candidate for 5,6 E3: 5,6 # 13 pairs I3: 5,6,8,9 # reduction candidate for 5,6 I3: 5,6 # 17 pairs * PAIR A5: 3,4 ROW 5 H5: 3,4,2,5,8 # reduction candidate for 3,4 H5: 3,4 # 13 pairs H5: 2,5,8 # 11 pairs * PAIR C5: 2,6 COL C C9: 2,6,8 # reduction candidate for 2,6 C9: 8 # 15 pairs C9: 2,6 # 14 pairs * PAIR C6: 6,7 BLK 4 B6: 6,7,5 # reduction candidate for 6,7 B6: 5 # 15 pairs B6: 6,7 # 14 pairs * PAIR C6: 6,7 COL C C1: 6,7,8 # reduction candidate for 6,7 C1: 6,7 # 15 pairs C1: 8 # 14 pairs * PAIR D4: 5,9 BLK 5 F4: 5,9,3 # reduction candidate for 5,9 F4: 5,9 # 15 pairs F4: 3 # 14 pairs * PAIR D4: 5,9 COL D D1: 5,9,4,6,7,8 # reduction candidate for 5,9 D1: 5,9 # 16 pairs D3: 5,9,6,8 # reduction candidate for 5,9 D3: 5,9 # 12 pairs * PAIR H4: 2,3 BLK 6 G5: 2,3,5,8 # reduction candidate for 2,3 G5: 2,3 # 11 pairs H5: 2,3,4,5,8 # reduction candidate for 2,3 H5: 2,3 => CTR * 1...3.9.2.29...4.3.34.927188519436274921678353..8251949432..5862156783.97..3..2.1 * RESTART * PAIR H4: 2,3 COL H H8: 2,3,4,6,7 # reduction candidate for 2,3 H8: 4,6,7 => CTR * 1.......2..9...4.3.34..271.8.1.4.637.9.1.72......2.19..432.....215..83..7..3...21 * PAIR RESTART * PAIR I6: 4,8 BLK 6 H5: 4,8,5 # reduction candidate for 4,8 H5: 4,8 # 13 pairs I5: 4,8,5 # reduction candidate for 4,8 I5: 4,8 # 23 pairs * PAIR A7: 6,9 BLK 7 A8: 6,9,2 # reduction candidate for 6,9 A8: 2 => CTR * 1...3...2.29...4.3.34..271.851943627.921673..3..8251949432...7.2154789367..3..241 * PAIR A7: 6,9 ROW 7 E7: 6,9,1,5 # reduction candidate for 6,9 E7: 6,9 => SOLVED * 178934562269715483534862719821549637396187254457623198643291875915478326782356941 * DURATION: 0:00:32.506753 START: 23:09:01.631236 END: 23:09:34.137989 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060514-absurd-base-pr-001.dot * REASONING * DIS # A1: 5,6 => CTR => A1: 1 * DIS A1: 1 # H4: 5,7 => CTR => H4: 2,3 * DIS A1: 1 + H4: 2,3 # I6: 5,7 => CTR => I6: 4,8 * DIS A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,3 => CTR => H5: 4,5,8 * DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 4,6,7 => CTR => H8: 2,3 * DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 2 => CTR => A8: 6,9 * PRF A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 # E7: 6,9 => SOL * STA A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 + E7: 6,9 * CNT 7 HDP CHAINS / 52 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060514, absurd
Solution
position: 178934562269715483534862719821549637396187254457623198643291875915478326782356941 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 # A1: 5,6 => CTR => A1: 1 * INC # A1: 1 => UNS * INC # A2: 5,6 => UNS * INC # D3: 5,6 => UNS * INC # E3: 5,6 => UNS * INC # I3: 5,6 => UNS * INC # H5: 3,4 => UNS * INC # H5: 2,5,8 => UNS * INC # C9: 2,6 => UNS * INC # C9: 8 => UNS * INC # B6: 6,7 => UNS * INC # B6: 5 => UNS * INC # C1: 6,7 => UNS * INC # C1: 8 => UNS * INC # F4: 5,9 => UNS * INC # F4: 3 => UNS * INC # D1: 5,9 => UNS * INC # D3: 5,9 => UNS * DIS # H4: 5,7 => CTR => H4: 2,3 * INC # H4: 2,3 => UNS * DIS # I6: 5,7 => CTR => I6: 4,8 * INC # I6: 4,8 => UNS * INC # B4: 5,7 => UNS * INC # B4: 2 => UNS * INC # I7: 5,7 => UNS * INC # I7: 6,8,9 => UNS * INC # A8: 6,9 => UNS * INC # A8: 2 => UNS * INC # E7: 6,9 => UNS * INC # F7: 6,9 => UNS * INC # I7: 6,9 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 5,6 => CTR => A1: 1 * INC A1: 1 # A2: 5,6 => UNS * INC A1: 1 # A2: 5,6 => UNS * INC A1: 1 # A2: 2 => UNS * INC A1: 1 # D3: 5,6 => UNS * INC A1: 1 # E3: 5,6 => UNS * INC A1: 1 # I3: 5,6 => UNS * INC A1: 1 # H5: 3,4 => UNS * INC A1: 1 # H5: 2,5,8 => UNS * INC A1: 1 # C9: 2,6 => UNS * INC A1: 1 # C9: 8 => UNS * INC A1: 1 # B6: 6,7 => UNS * INC A1: 1 # B6: 5 => UNS * INC A1: 1 # C1: 6,7 => UNS * INC A1: 1 # C1: 8 => UNS * INC A1: 1 # F4: 5,9 => UNS * INC A1: 1 # F4: 3 => UNS * INC A1: 1 # D1: 5,9 => UNS * INC A1: 1 # D3: 5,9 => UNS * DIS A1: 1 # H4: 5,7 => CTR => H4: 2,3 * DIS A1: 1 + H4: 2,3 # I6: 5,7 => CTR => I6: 4,8 * INC A1: 1 + H4: 2,3 + I6: 4,8 # A8: 6,9 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # A8: 2 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # E7: 6,9 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # F7: 6,9 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # I7: 6,9 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # A2: 5,6 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # A2: 2 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # D3: 5,6 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # E3: 5,6 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # I3: 5,6 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # H5: 3,4 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,5,8 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # C9: 2,6 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # C9: 8 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # B6: 6,7 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # B6: 5 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # C1: 6,7 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # C1: 8 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # F4: 5,9 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # F4: 3 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # D1: 5,9 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # D3: 5,9 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 # G5: 2,3 => UNS * DIS A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,3 => CTR => H5: 4,5,8 * INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 2,3 => UNS * DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 4,6,7 => CTR => H8: 2,3 * INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # H5: 4,8 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # I5: 4,8 => UNS * INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 6,9 => UNS * DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 2 => CTR => A8: 6,9 * PRF A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 # E7: 6,9 => SOL * STA A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 + E7: 6,9 * CNT 52 HDP CHAINS / 52 HYP OPENED