Analysis of zz-www.sudokuoftheday.co.uk-20060519-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: .8.6.3.......1....5..4.8..9........5..2...7...9...64.8..8.5..4113.....9.7....16.. initial
Autosolve
position: .8.693.......1....5..4.8..9......9.5..2...7..39...64.8..8.5..4113..6..977....16.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,4 => CTR => A2: 6,9 * PRF # C3: 1,7 => SOL * DIS # C4: 1,7 => CTR => C4: 4,6 * DIS # F2: 2,7 => CTR => F2: 5 * DIS # I2: 2,4 => CTR => I2: 3,6 * DIS # D4: 2,7 => CTR => D4: 1,3,8 * PRF # D6: 2,7 => SOL * DIS # I2: 2,4 => CTR => I2: 3,6 * DIS # D6: 1,2 => CTR => D6: 5,7 * DIS # A7: 9 => CTR => A7: 2,6 * DIS # B2: 2,6 => CTR => B2: 4,7 * DIS # C9: 4,5 => CTR => C9: 9 * DIS # D7: 3 => CTR => D7: 7,9 * DIS # F4: 7 => CTR => F4: 2,4 * DIS # G2: 2,3 => CTR => G2: 8 * CNT 15 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,4 => CTR => A2: 6,9 * PRF A2: 6,9 # C3: 1,7 => SOL * STA A2: 6,9 + C3: 1,7 * CNT 2 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.6.3.......1....5..4.8..9........5..2...7...9...64.8..8.5..4113.....9.7....16.. | initial |
| .8.693.......1....5..4.8..9......9.5..2...7..39...64.8..8.5..4113..6..977....16.. | autosolve |
| 287693154943215876561478239876134925412589763395726418628957341134862597759341682 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 2,4 C1: 1,7 E3: 2,7 G1: 1,5 H1: 5,7 I1: 2,4 E6: 2,7 I5: 3,6 H6: 1,2 B7: 2,6 C8: 4,5 F7: 7,9 D8: 2,8 F8: 2,4 G7: 2,3 G8: 5,8 H9: 5,8 I9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G3: 1.. / G1 = 1 => 22 pairs (_) / G3 = 1 => 0 pairs (X) C1,G1: 1.. / C1 = 1 => 0 pairs (X) / G1 = 1 => 22 pairs (_) H4,H6: 2.. / H4 = 2 => 24 pairs (_) / H6 = 2 => 22 pairs (_) D8,F8: 2.. / D8 = 2 => 0 pairs (X) / F8 = 2 => 22 pairs (_) G7,I9: 2.. / G7 = 2 => 0 pairs (X) / I9 = 2 => 21 pairs (_) A1,I1: 2.. / A1 = 2 => 17 pairs (_) / I1 = 2 => 0 pairs (X) B9,I9: 2.. / B9 = 2 => 0 pairs (X) / I9 = 2 => 21 pairs (_) E3,E6: 2.. / E3 = 2 => 22 pairs (_) / E6 = 2 => 28 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) G7,I9: 3.. / G7 = 3 => 21 pairs (_) / I9 = 3 => 0 pairs (X) D7,G7: 3.. / D7 = 3 => 0 pairs (X) / G7 = 3 => 21 pairs (_) I1,I2: 4.. / I1 = 4 => 17 pairs (_) / I2 = 4 => 0 pairs (X) F8,E9: 4.. / F8 = 4 => 0 pairs (X) / E9 = 4 => 22 pairs (_) A1,I1: 4.. / A1 = 4 => 0 pairs (X) / I1 = 4 => 17 pairs (_) C8,F8: 4.. / C8 = 4 => 22 pairs (_) / F8 = 4 => 0 pairs (X) D2,F2: 5.. / D2 = 5 => 0 pairs (X) / F2 = 5 => 20 pairs (_) G1,H1: 5.. / G1 = 5 => 0 pairs (X) / H1 = 5 => 22 pairs (_) B5,C6: 5.. / B5 = 5 => 25 pairs (_) / C6 = 5 => 0 pairs (*) G8,H9: 5.. / G8 = 5 => 22 pairs (_) / H9 = 5 => 0 pairs (X) C6,D6: 5.. / C6 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) C8,G8: 5.. / C8 = 5 => 0 pairs (X) / G8 = 5 => 22 pairs (_) B5,B9: 5.. / B5 = 5 => 25 pairs (_) / B9 = 5 => 0 pairs (*) F2,F5: 5.. / F2 = 5 => 20 pairs (_) / F5 = 5 => 0 pairs (X) G1,G8: 5.. / G1 = 5 => 0 pairs (X) / G8 = 5 => 22 pairs (_) H1,H9: 5.. / H1 = 5 => 22 pairs (_) / H9 = 5 => 0 pairs (X) A7,B7: 6.. / A7 = 6 => 21 pairs (_) / B7 = 6 => 20 pairs (_) I2,I5: 6.. / I2 = 6 => 24 pairs (_) / I5 = 6 => 20 pairs (_) D7,F7: 7.. / D7 = 7 => 21 pairs (_) / F7 = 7 => 20 pairs (_) C1,H1: 7.. / C1 = 7 => 22 pairs (_) / H1 = 7 => 0 pairs (X) E3,E6: 7.. / E3 = 7 => 28 pairs (_) / E6 = 7 => 22 pairs (_) G2,H2: 8.. / G2 = 8 => 22 pairs (_) / H2 = 8 => 0 pairs (X) A4,A5: 8.. / A4 = 8 => 20 pairs (_) / A5 = 8 => 20 pairs (_) G8,H9: 8.. / G8 = 8 => 0 pairs (X) / H9 = 8 => 22 pairs (_) D8,G8: 8.. / D8 = 8 => 22 pairs (_) / G8 = 8 => 0 pairs (X) G2,G8: 8.. / G2 = 8 => 22 pairs (_) / G8 = 8 => 0 pairs (X) H2,H9: 8.. / H2 = 8 => 0 pairs (X) / H9 = 8 => 22 pairs (_) A2,C2: 9.. / A2 = 9 => 21 pairs (_) / C2 = 9 => 0 pairs (X) D5,F5: 9.. / D5 = 9 => 21 pairs (_) / F5 = 9 => 20 pairs (_) A7,C9: 9.. / A7 = 9 => 0 pairs (X) / C9 = 9 => 21 pairs (_) C9,D9: 9.. / C9 = 9 => 21 pairs (_) / D9 = 9 => 0 pairs (X) A2,A7: 9.. / A2 = 9 => 21 pairs (_) / A7 = 9 => 0 pairs (X) C2,C9: 9.. / C2 = 9 => 0 pairs (X) / C9 = 9 => 21 pairs (_) F5,F7: 9.. / F5 = 9 => 20 pairs (_) / F7 = 9 => 21 pairs (_) * DURATION: 0:00:50.773631 START: 23:15:23.593264 END: 23:16:14.366895 2019-04-30 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,C1,C8,D8,E3,E6,F7,F8,G1,G7,G8,H1,H6,H9,I1,I5,I9) * .8.693.......1....5..4.8..9......9.5..2...7..39...64.8..8.5..4113..6..977....16.. * PAIR A1: 2,4 BLK 1 A2: 2,4,6,9 # reduction candidate for 2,4 A2: 2,4 => CTR * .8.693.....9.1....5.34.8..9..6...9.5..2...7..39...64.8..8.5..4113..6..977....16.. A2: 6,9 # 19 pairs B2: 2,4,6,7 # reduction candidate for 2,4 B2: 2,4 # 20 pairs * PAIR C1: 1,7 BLK 1 B3: 1,7,2,6 # reduction candidate for 1,7 B3: 1,7 # 20 pairs C3: 1,7,3,6 # reduction candidate for 1,7 C3: 1,7 => SOLVED * 287693154943215876561478239876134925412589763395726418628957341134862597759341682 C3: 3,6 # 19 pairs * PAIR C1: 1,7 COL C C4: 1,7,4,6 # reduction candidate for 1,7 C4: 1,7 => CTR * 28.69315494..1.8..51.4.82.9.71..49.5462...7.3395.26418..8.5..41134.62597759.41682 C4: 4,6 # 21 pairs C6: 1,7,5 # reduction candidate for 1,7 C6: 1,7 # 25 pairs * PAIR E3: 2,7 BLK 2 D2: 2,7,5 # reduction candidate for 2,7 D2: 2,7 # 20 pairs F2: 2,7,5 # reduction candidate for 2,7 F2: 2,7 => CTR * 28.6931.....51....5..4.8..9......9.5..2..57..395..64.8..8.59.41134.62597759.41682 F2: 5 # 20 pairs * PAIR E3: 2,7 ROW 3 B3: 2,7,1,6 # reduction candidate for 2,7 B3: 2,7 # 23 pairs B3: 1,6 # 19 pairs * PAIR I1: 2,4 BLK 3 I2: 2,4,3,6 # reduction candidate for 2,4 I2: 2,4 => CTR * .8.693.....9.1....5.34281.9..6...9.5.52..97.639.57642896835724113..6..9772.9.16.3 I2: 3,6 # 21 pairs * PAIR E6: 2,7 BLK 5 D4: 2,7,1,3,8 # reduction candidate for 2,7 D4: 2,7 => CTR * .8769315.....1.8..5..428379.7.2.49.5..2...7..39..76428..8357241134862597725941683 D4: 1,3,8 # 18 pairs F4: 2,7,4 # reduction candidate for 2,7 F4: 2,7 # 20 pairs D6: 2,7,1,5 # reduction candidate for 2,7 D6: 2,7 => SOLVED * 287693154943215876561478239876134925412589763395726418628957341134862597759341682 D6: 1,5 # 19 pairs * PAIR I5: 3,6 BLK 6 H4: 3,6,1,2 # reduction candidate for 3,6 H4: 3,6 # 26 pairs H5: 3,6,1 # reduction candidate for 3,6 H5: 3,6 # 24 pairs * PAIR I5: 3,6 COL I I2: 3,6,2,4 # reduction candidate for 3,6 I2: 2,4 => CTR * .8.693.....9.1....5.34281.9..6...9.5.52..97.639.57642896835724113..6..9772.9.16.3 I2: 3,6 # 21 pairs * PAIR H6: 1,2 BLK 6 H4: 1,2,3,6 # reduction candidate for 1,2 H4: 3,6 # 26 pairs H4: 1,2 # 24 pairs * PAIR H6: 1,2 ROW 6 D6: 1,2,5,7 # reduction candidate for 1,2 D6: 1,2 => CTR * 28.69315494..1.8..5..4283.9......9.5..2...7..395.764.8..8.5..41134.62597759.41682 D6: 5,7 # 19 pairs * PAIR B7: 2,6 BLK 7 A7: 2,6,9 # reduction candidate for 2,6 A7: 9 => CTR * .8.693.....9.1....5.3428169..6...9.5.52..97.639.57642896835724113..6..9772.9.16.3 A7: 2,6 # 21 pairs * PAIR B7: 2,6 COL B B2: 2,6,4,7 # reduction candidate for 2,6 B2: 2,6 => CTR * 28.693574964.1.283573428169.16..2935.52..9716397..64.8628.5.341135.64897749..1652 B2: 4,7 # 19 pairs B3: 2,6,1,7 # reduction candidate for 2,6 B3: 2,6 # 26 pairs * PAIR C8: 4,5 BLK 7 B9: 4,5,2 # reduction candidate for 4,5 B9: 4,5 # 21 pairs C9: 4,5,9 # reduction candidate for 4,5 C9: 4,5 => CTR * .8.693...6.9.1.38.5.3428169..6...9.5.52..97.639.57642896835724113..6.89772.981653 C9: 9 # 21 pairs * PAIR F7: 7,9 BLK 8 D7: 7,9,3 # reduction candidate for 7,9 D7: 3 => CTR * .8.693.....9.1....5.34281.9..6...9.5.52..97.639.57642896835724113..6..9772.9.16.3 D7: 7,9 # 21 pairs * PAIR D8: 2,8 COL D D4: 2,8,1,3,7 # reduction candidate for 2,8 D4: 2,8 # 24 pairs D4: 1,3,7 # 18 pairs * PAIR F8: 2,4 COL F F4: 2,4,7 # reduction candidate for 2,4 F4: 7 => CTR * 2816935......1....5..4.8..9.....79.5..2...7..397526418..875934113..6..977.9..16.2 F4: 2,4 # 21 pairs * PAIR G7: 2,3 COL G G2: 2,3,8 # reduction candidate for 2,3 G2: 2,3 => CTR * .8169357....715.8.5..4281.9.1...29.5.521.97..3975.64.8..8.5..411352648977....165. G2: 8 # 22 pairs G3: 2,3,1 # reduction candidate for 2,3 G3: 2,3 # 22 pairs * PAIR I9: 2,3 COL I I2: 2,3,4,6 # reduction candidate for 2,3 I2: 2,3 # 20 pairs I2: 4,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060519-absurd-base-pr-000.dot * REASONING * DIS # A2: 2,4 => CTR => A2: 6,9 * PRF # C3: 1,7 => SOL * DIS # C4: 1,7 => CTR => C4: 4,6 * DIS # F2: 2,7 => CTR => F2: 5 * DIS # I2: 2,4 => CTR => I2: 3,6 * DIS # D4: 2,7 => CTR => D4: 1,3,8 * PRF # D6: 2,7 => SOL * DIS # I2: 2,4 => CTR => I2: 3,6 * DIS # D6: 1,2 => CTR => D6: 5,7 * DIS # A7: 9 => CTR => A7: 2,6 * DIS # B2: 2,6 => CTR => B2: 4,7 * DIS # C9: 4,5 => CTR => C9: 9 * DIS # D7: 3 => CTR => D7: 7,9 * DIS # F4: 7 => CTR => F4: 2,4 * DIS # G2: 2,3 => CTR => G2: 8 * CNT 15 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,C1,C8,D8,E3,E6,F7,F8,G1,G7,G8,H1,H6,H9,I1,I5,I9) * .8.693.......1....5..4.8..9......9.5..2...7..39...64.8..8.5..4113..6..977....16.. * PAIR A1: 2,4 BLK 1 A2: 2,4,6,9 # reduction candidate for 2,4 A2: 2,4 => CTR * .8.693.....9.1....5.34.8..9..6...9.5..2...7..39...64.8..8.5..4113..6..977....16.. B2: 2,4,6,7 # reduction candidate for 2,4 B2: 2,4 # 20 pairs * RESTART * PAIR A1: 2,4 BLK 1 B2: 2,4,6,7 # reduction candidate for 2,4 B2: 6,7 # 20 pairs B2: 2,4 # 20 pairs * PAIR C1: 1,7 BLK 1 B3: 1,7,2,6 # reduction candidate for 1,7 B3: 1,7 # 21 pairs C3: 1,7,3,6 # reduction candidate for 1,7 C3: 1,7 => SOLVED * 287693154943215876561478239876134925412589763395726418628957341134862597759341682 * DURATION: 0:00:04.504374 START: 23:16:44.463188 END: 23:16:48.967562 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060519-absurd-base-pr-001.dot * REASONING * DIS # A2: 2,4 => CTR => A2: 6,9 * PRF A2: 6,9 # C3: 1,7 => SOL * STA A2: 6,9 + C3: 1,7 * CNT 2 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060519, absurd
Solution
position: 287693154943215876561478239876134925412589763395726418628957341134862597759341682 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 # A2: 2,4 => CTR => A2: 6,9 * INC # A2: 6,9 => UNS * INC # B2: 2,4 => UNS * INC # B3: 1,7 => UNS * PRF # C3: 1,7 => SOL * INC # C3: 3,6 => UNS * DIS # C4: 1,7 => CTR => C4: 4,6 * INC # C4: 4,6 => UNS * INC # C6: 1,7 => UNS * INC # D2: 2,7 => UNS * DIS # F2: 2,7 => CTR => F2: 5 * INC # F2: 5 => UNS * INC # B3: 2,7 => UNS * INC # B3: 1,6 => UNS * DIS # I2: 2,4 => CTR => I2: 3,6 * INC # I2: 3,6 => UNS * DIS # D4: 2,7 => CTR => D4: 1,3,8 * INC # D4: 1,3,8 => UNS * INC # F4: 2,7 => UNS * PRF # D6: 2,7 => SOL * INC # D6: 1,5 => UNS * INC # H4: 3,6 => UNS * INC # H5: 3,6 => UNS * INC # I2: 3,6 => UNS * DIS # I2: 2,4 => CTR => I2: 3,6 * INC # H4: 1,2 => UNS * INC # H4: 3,6 => UNS * DIS # D6: 1,2 => CTR => D6: 5,7 * INC # D6: 5,7 => UNS * INC # A7: 2,6 => UNS * DIS # A7: 9 => CTR => A7: 2,6 * DIS # B2: 2,6 => CTR => B2: 4,7 * INC # B2: 4,7 => UNS * INC # B3: 2,6 => UNS * INC # B9: 4,5 => UNS * DIS # C9: 4,5 => CTR => C9: 9 * INC # C9: 9 => UNS * INC # D7: 7,9 => UNS * DIS # D7: 3 => CTR => D7: 7,9 * INC # D4: 2,8 => UNS * INC # D4: 1,3,7 => UNS * INC # F4: 2,4 => UNS * DIS # F4: 7 => CTR => F4: 2,4 * DIS # G2: 2,3 => CTR => G2: 8 * INC # G2: 8 => UNS * INC # G3: 2,3 => UNS * INC # I2: 2,3 => UNS * INC # I2: 4,6 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 2,4 => CTR => A2: 6,9 * INC A2: 6,9 # B2: 2,4 => UNS * INC A2: 6,9 # B2: 2,4 => UNS * INC A2: 6,9 # B2: 6,7 => UNS * INC A2: 6,9 # B3: 1,7 => UNS * PRF A2: 6,9 # C3: 1,7 => SOL * STA A2: 6,9 + C3: 1,7 * CNT 6 HDP CHAINS / 6 HYP OPENED