Analysis of zz-www.sudokuoftheday.co.uk-20060622-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.....1....6..7..3.4..8...4.....95..86..1..2..1........59.....8..17..97......2. initial
Autosolve
position: ..6.....1....6..7..3.4..8...4.....95..86..1..2..1...8....59..1..8..17..97.....52. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I5: 3,4 => CTR => I5: 2,7 * DIS # C3: 1,9 => CTR => C3: 2,5,7 * DIS # D4: 2,3 => CTR => D4: 7,8 * DIS # F9: 3,8 => CTR => F9: 4,6 * CNT 4 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I5: 3,4 => CTR => I5: 2,7 * DIS I5: 2,7 # H8: 3,4 => CTR => H8: 6 * DIS I5: 2,7 + H8: 6 # C3: 1,9 => CTR => C3: 2,7 * DIS I5: 2,7 + H8: 6 + C3: 2,7 # C8: 2,3 => CTR => C8: 4,5 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # D4: 3,8 => CTR => D4: 7 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # E1: 3,5,8 => CTR => E1: 2,7 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 # G1: 3,4 => CTR => G1: 2,9 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 # G2: 3,4 => CTR => G2: 2,9 * PRF I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 + G2: 2,9 # A4: 1,3 => SOL * STA I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 + G2: 2,9 + A4: 1,3 * CNT 9 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6.....1....6..7..3.4..8...4.....95..86..1..2..1........59.....8..17..97......2. | initial |
| ..6.....1....6..7..3.4..8...4.....95..86..1..2..1...8....59..1..8..17..97.....52. | autosolve |
| 456978231812365974937421856143782695578639142269154387624593718385217469791846523 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) H3: 5,6 I3: 2,6 H5: 3,4 B7: 2,6 B9: 1,9 C9: 1,9 D8: 2,3 D9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 1.. / F2 = 1 => 0 pairs (X) / F3 = 1 => 9 pairs (_) A4,C4: 1.. / A4 = 1 => 16 pairs (_) / C4 = 1 => 11 pairs (_) B9,C9: 1.. / B9 = 1 => 8 pairs (_) / C9 = 1 => 14 pairs (_) B2,B9: 1.. / B2 = 1 => 14 pairs (_) / B9 = 1 => 8 pairs (_) G4,I5: 2.. / G4 = 2 => 14 pairs (_) / I5 = 2 => 14 pairs (_) F7,D8: 2.. / F7 = 2 => 0 pairs (X) / D8 = 2 => 7 pairs (_) C8,D8: 2.. / C8 = 2 => 0 pairs (X) / D8 = 2 => 7 pairs (_) H1,H3: 5.. / H1 = 5 => 21 pairs (_) / H3 = 5 => 11 pairs (_) A8,C8: 5.. / A8 = 5 => 11 pairs (_) / C8 = 5 => 7 pairs (_) H3,I3: 6.. / H3 = 6 => 21 pairs (_) / I3 = 6 => 11 pairs (_) A4,B6: 6.. / A4 = 6 => 11 pairs (_) / B6 = 6 => 16 pairs (_) F7,F9: 6.. / F7 = 6 => 0 pairs (X) / F9 = 6 => 8 pairs (_) A4,G4: 6.. / A4 = 6 => 11 pairs (_) / G4 = 6 => 16 pairs (_) F9,I9: 6.. / F9 = 6 => 8 pairs (_) / I9 = 6 => 0 pairs (X) B6,B7: 6.. / B6 = 6 => 16 pairs (_) / B7 = 6 => 11 pairs (_) H3,H8: 6.. / H3 = 6 => 21 pairs (_) / H8 = 6 => 11 pairs (_) B1,C3: 7.. / B1 = 7 => 0 pairs (X) / C3 = 7 => 12 pairs (_) G7,I7: 7.. / G7 = 7 => 8 pairs (_) / I7 = 7 => 12 pairs (_) C3,E3: 7.. / C3 = 7 => 12 pairs (_) / E3 = 7 => 0 pairs (X) D1,D4: 7.. / D1 = 7 => 12 pairs (_) / D4 = 7 => 9 pairs (_) A1,A2: 8.. / A1 = 8 => 9 pairs (_) / A2 = 8 => 9 pairs (_) I7,I9: 8.. / I7 = 8 => 8 pairs (_) / I9 = 8 => 12 pairs (_) F7,I7: 8.. / F7 = 8 => 12 pairs (_) / I7 = 8 => 8 pairs (_) A3,C3: 9.. / A3 = 9 => 9 pairs (_) / C3 = 9 => 0 pairs (X) D1,D2: 9.. / D1 = 9 => 9 pairs (_) / D2 = 9 => 8 pairs (_) G1,G2: 9.. / G1 = 9 => 8 pairs (_) / G2 = 9 => 9 pairs (_) F5,F6: 9.. / F5 = 9 => 10 pairs (_) / F6 = 9 => 8 pairs (_) B9,C9: 9.. / B9 = 9 => 14 pairs (_) / C9 = 9 => 8 pairs (_) D1,G1: 9.. / D1 = 9 => 9 pairs (_) / G1 = 9 => 8 pairs (_) D2,G2: 9.. / D2 = 9 => 8 pairs (_) / G2 = 9 => 9 pairs (_) A3,A5: 9.. / A3 = 9 => 9 pairs (_) / A5 = 9 => 0 pairs (X) * DURATION: 0:00:29.011507 START: 00:01:32.115028 END: 00:02:01.126535 2019-05-01 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,C9,D8,D9,H3,H5,I3) * ..6.....1....6..7..3.4..8...4.....95..86..1..2..1...8....59..1..8..17..97.....52. * PAIR H5: 3,4 BLK 6 I5: 3,4,2,7 # reduction candidate for 3,4 I5: 3,4 => CTR * 8.6.....11.4.6..7.937451862641...2955786291..293145.86.62594.1..8..17..9719..652. I5: 2,7 # 9 pairs G6: 3,4,6,7 # reduction candidate for 3,4 G6: 3,4 # 13 pairs I6: 3,4,6,7 # reduction candidate for 3,4 I6: 3,4 # 12 pairs * PAIR H5: 3,4 ROW 5 E5: 3,4,2,5,7 # reduction candidate for 3,4 E5: 3,4 # 11 pairs F5: 3,4,2,5,9 # reduction candidate for 3,4 F5: 3,4 # 12 pairs * PAIR H5: 3,4 COL H H1: 3,4,5 # reduction candidate for 3,4 H1: 3,4 # 11 pairs H8: 3,4,6 # reduction candidate for 3,4 H8: 3,4 # 21 pairs * PAIR B7: 2,6 ROW 7 F7: 2,6,3,4,8 # reduction candidate for 2,6 F7: 2,6 # 14 pairs F7: 3,4,8 # 7 pairs * PAIR C9: 1,9 COL C C3: 1,9,2,5,7 # reduction candidate for 1,9 C3: 1,9 => CTR * .76.....1....6..7..3.47.8..6417..2953.86..1472.71...8.46.59.71.58..17469719...52. C3: 2,5,7 # 9 pairs * PAIR D8: 2,3 BLK 8 F7: 2,3,4,6,8 # reduction candidate for 2,3 F7: 2,3 # 15 pairs F7: 4,6,8 # 7 pairs * PAIR D8: 2,3 ROW 8 C8: 2,3,4,5 # reduction candidate for 2,3 C8: 2,3 # 21 pairs C8: 4,5 # 8 pairs * PAIR D8: 2,3 COL D D1: 2,3,7,8,9 # reduction candidate for 2,3 D1: 2,3 # 10 pairs D2: 2,3,8,9 # reduction candidate for 2,3 D2: 2,3 # 10 pairs D4: 2,3,7,8 # reduction candidate for 2,3 D4: 2,3 => CTR * ..678.9.18..96..7.9374.18..1432786955.86..1.22691...8....59.718.8..17..97..8..52. D4: 7,8 # 9 pairs * PAIR D9: 3,8 BLK 8 F7: 3,8,2,4,6 # reduction candidate for 3,8 F7: 3,8 # 12 pairs E9: 3,8,4 # reduction candidate for 3,8 E9: 3,8 # 12 pairs F9: 3,8,4,6 # reduction candidate for 3,8 F9: 3,8 => CTR * ..6.....1....6..7..3.4..862.4.....95..86..1..2..1...8....596.18685217..97...4.526 F9: 4,6 # 9 pairs * PAIR D9: 3,8 ROW 9 I9: 3,8,4,6 # reduction candidate for 3,8 I9: 3,8 # 12 pairs I9: 4,6 # 10 pairs * PAIR D9: 3,8 COL D D1: 3,8,2,7,9 # reduction candidate for 3,8 D1: 3,8 # 9 pairs D2: 3,8,2,9 # reduction candidate for 3,8 D2: 3,8 # 9 pairs D4: 3,8,2,7 # reduction candidate for 3,8 D4: 3,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060622-absurd-base-pr-000.dot * REASONING * DIS # I5: 3,4 => CTR => I5: 2,7 * DIS # C3: 1,9 => CTR => C3: 2,5,7 * DIS # D4: 2,3 => CTR => D4: 7,8 * DIS # F9: 3,8 => CTR => F9: 4,6 * CNT 4 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,C9,D8,D9,H3,H5,I3) * ..6.....1....6..7..3.4..8...4.....95..86..1..2..1...8....59..1..8..17..97.....52. * PAIR H5: 3,4 BLK 6 I5: 3,4,2,7 # reduction candidate for 3,4 I5: 3,4 => CTR * 8.6.....11.4.6..7.937451862641...2955786291..293145.86.62594.1..8..17..9719..652. G6: 3,4,6,7 # reduction candidate for 3,4 G6: 3,4 # 13 pairs I6: 3,4,6,7 # reduction candidate for 3,4 I6: 3,4 # 12 pairs * PAIR H5: 3,4 ROW 5 E5: 3,4,2,5,7 # reduction candidate for 3,4 E5: 3,4 # 11 pairs F5: 3,4,2,5,9 # reduction candidate for 3,4 F5: 3,4 # 12 pairs * PAIR H5: 3,4 COL H H1: 3,4,5 # reduction candidate for 3,4 H1: 3,4 # 12 pairs H8: 3,4,6 # reduction candidate for 3,4 H8: 3,4 => CTR * 8.6...4511.4.6.97393.4.1862641...295..86..1472..1..386.6.59.71.485217639719..652. * RESTART * PAIR RESTART * PAIR H5: 3,4 BLK 6 G6: 3,4,6,7 # reduction candidate for 3,4 G6: 3,4 # 17 pairs I6: 3,4,7 # reduction candidate for 3,4 I6: 3,4 # 14 pairs * PAIR H5: 3,4 ROW 5 E5: 3,4,2,5,7 # reduction candidate for 3,4 E5: 3,4 # 14 pairs F5: 3,4,2,5,9 # reduction candidate for 3,4 F5: 3,4 # 14 pairs * PAIR C9: 1,9 COL C C3: 1,9,2,7 # reduction candidate for 1,9 C3: 1,9 => CTR * .76...2.1....6197..3.472856.4.728.95..86..1.72.71...8....59.718.8.217.69719..652. * PAIR RESTART * PAIR D8: 2,3 BLK 8 F7: 2,3,4,8 # reduction candidate for 2,3 F7: 2,3 # 20 pairs F7: 4,8 # 13 pairs * PAIR D8: 2,3 ROW 8 C8: 2,3,4,5 # reduction candidate for 2,3 C8: 2,3 => CTR * 476..5.31815.6..74932471856147...6953.86.9142269154.8.62459..1.583217469791.4652. * PAIR RESTART * PAIR D9: 3,8 BLK 8 F7: 3,8,4 # reduction candidate for 3,8 F7: 3,8 # 16 pairs E9: 3,8,4 # reduction candidate for 3,8 E9: 3,8 # 19 pairs * PAIR D9: 3,8 ROW 9 I9: 3,8,4 # reduction candidate for 3,8 I9: 4 # 19 pairs I9: 3,8 # 16 pairs * PAIR D9: 3,8 COL D D1: 3,8,7,9 # reduction candidate for 3,8 D1: 3,8 # 16 pairs D2: 3,8,9 # reduction candidate for 3,8 D2: 3,8 # 14 pairs D4: 3,8,7 # reduction candidate for 3,8 D4: 3,8 => CTR * 8267..941154968.7.937421856641....955.86..13.2.31..684.6259.718.85217469719.46523 * PAIR RESTART * PAIR D9: 3,8 BLK 8 F7: 3,8,4 # reduction candidate for 3,8 F7: 3,8 # 18 pairs E9: 3,8,4 # reduction candidate for 3,8 E9: 3,8 # 20 pairs * PAIR D9: 3,8 ROW 9 I9: 3,8,4 # reduction candidate for 3,8 I9: 4 # 20 pairs I9: 3,8 # 18 pairs * PAIR D9: 3,8 COL D D1: 3,8,9 # reduction candidate for 3,8 D1: 3,8 # 16 pairs D2: 3,8,9 # reduction candidate for 3,8 D2: 3,8 # 14 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,B7,B9,C3,C4,C8,C9,D9,E3,G8,H1,H5,I5) * ..6.....1....6..7.93.4.1856.4.7...95..86..1..2..1...8....59..1..8.217.697....652. * PAIR C3: 2,7 BLK 1 B1: 2,7,5 # reduction candidate for 2,7 B1: 5 # 19 pairs B1: 2,7 # 15 pairs * PAIR E3: 2,7 BLK 2 E1: 2,7,3,5,8 # reduction candidate for 2,7 E1: 3,5,8 => CTR * .76.....1....6..72932471856.4.7..295..862.1.72671.9.8.62.59.71..8.217.69719..652. * PAIR H1: 3,4 BLK 3 G1: 3,4,2,9 # reduction candidate for 3,4 G1: 3,4 => CTR * .2697.431....6.9729374218566417..295.986.21472731.968..62594718.8.217.697.9..6524 G2: 3,4,2,9 # reduction candidate for 3,4 G2: 3,4 => CTR * .26.7.9.1...96.4729374218566417..295.986.21472731.968..62594718.8.217.697.9..6524 * RESTART * PAIR C4: 1,3 BLK 4 A4: 1,3,6 # reduction candidate for 1,3 A4: 1,3 => SOLVED * 456978231812365974937421856143782695578639142269154387624593718385217469791846523 * DURATION: 0:00:25.198450 START: 00:02:16.426563 END: 00:02:41.625013 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060622-absurd-base-pr-001.dot * REASONING * DIS # I5: 3,4 => CTR => I5: 2,7 * DIS I5: 2,7 # H8: 3,4 => CTR => H8: 6 * DIS I5: 2,7 + H8: 6 # C3: 1,9 => CTR => C3: 2,7 * DIS I5: 2,7 + H8: 6 + C3: 2,7 # C8: 2,3 => CTR => C8: 4,5 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # D4: 3,8 => CTR => D4: 7 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # E1: 3,5,8 => CTR => E1: 2,7 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 # G1: 3,4 => CTR => G1: 2,9 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 # G2: 3,4 => CTR => G2: 2,9 * PRF I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 + G2: 2,9 # A4: 1,3 => SOL * STA I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 + G2: 2,9 + A4: 1,3 * CNT 9 HDP CHAINS / 35 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060622, absurd
Solution
position: 456978231812365974937421856143782695578639142269154387624593718385217469791846523 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 # I5: 3,4 => CTR => I5: 2,7 * INC # I5: 2,7 => UNS * INC # G6: 3,4 => UNS * INC # I6: 3,4 => UNS * INC # E5: 3,4 => UNS * INC # F5: 3,4 => UNS * INC # H1: 3,4 => UNS * INC # H8: 3,4 => UNS * INC # F7: 2,6 => UNS * INC # F7: 3,4,8 => UNS * DIS # C3: 1,9 => CTR => C3: 2,5,7 * INC # C3: 2,5,7 => UNS * INC # F7: 2,3 => UNS * INC # F7: 4,6,8 => UNS * INC # C8: 2,3 => UNS * INC # C8: 4,5 => UNS * INC # D1: 2,3 => UNS * INC # D2: 2,3 => UNS * DIS # D4: 2,3 => CTR => D4: 7,8 * INC # D4: 7,8 => UNS * INC # F7: 3,8 => UNS * INC # E9: 3,8 => UNS * DIS # F9: 3,8 => CTR => F9: 4,6 * INC # F9: 4,6 => UNS * INC # I9: 3,8 => UNS * INC # I9: 4,6 => UNS * INC # D1: 3,8 => UNS * INC # D2: 3,8 => UNS * INC # D4: 3,8 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I5: 3,4 => CTR => I5: 2,7 * INC I5: 2,7 # G6: 3,4 => UNS * INC I5: 2,7 # I6: 3,4 => UNS * INC I5: 2,7 # E5: 3,4 => UNS * INC I5: 2,7 # F5: 3,4 => UNS * INC I5: 2,7 # H1: 3,4 => UNS * DIS I5: 2,7 # H8: 3,4 => CTR => H8: 6 * INC I5: 2,7 + H8: 6 # G6: 3,4 => UNS * INC I5: 2,7 + H8: 6 # I6: 3,4 => UNS * INC I5: 2,7 + H8: 6 # E5: 3,4 => UNS * INC I5: 2,7 + H8: 6 # F5: 3,4 => UNS * DIS I5: 2,7 + H8: 6 # C3: 1,9 => CTR => C3: 2,7 * INC I5: 2,7 + H8: 6 + C3: 2,7 # F7: 2,3 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 # F7: 4,8 => UNS * DIS I5: 2,7 + H8: 6 + C3: 2,7 # C8: 2,3 => CTR => C8: 4,5 * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # F7: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # E9: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # I9: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # I9: 4 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # D1: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # D2: 3,8 => UNS * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 # D4: 3,8 => CTR => D4: 7 * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # F7: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # E9: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # I9: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # I9: 4 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # D1: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # D2: 3,8 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # B1: 2,7 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # B1: 5 => UNS * INC I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # E1: 2,7 => UNS * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 # E1: 3,5,8 => CTR => E1: 2,7 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 # G1: 3,4 => CTR => G1: 2,9 * DIS I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 # G2: 3,4 => CTR => G2: 2,9 * PRF I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 + G2: 2,9 # A4: 1,3 => SOL * STA I5: 2,7 + H8: 6 + C3: 2,7 + C8: 4,5 + D4: 7 + E1: 2,7 + G1: 2,9 + G2: 2,9 + A4: 1,3 * CNT 35 HDP CHAINS / 35 HYP OPENED