Analysis of zz-www.sudokuoftheday.co.uk-20060501-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: ....4.....2.9..3.759.1.7....3..2.7......34892.........1...729.........2..6.89.1.. initial
Autosolve
position: ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 6,8 => CTR => H2: 1 * DIS # H3: 6,8 => CTR => H3: 4 * DIS # H1: 1,8 => CTR => H1: 5,6 * DIS # G6: 5,6 => CTR => G6: 4 * PRF # G6: 4 => SOL * DIS # A6: 6,7 => CTR => A6: 2,4,8,9 * DIS # C4: 5,6 => CTR => C4: 4,8,9 * DIS # I4: 5,6 => CTR => I4: 1,4 * DIS # A9: 2,4 => CTR => A9: 3 * PRF # A9: 3 => SOL * DIS # C6: 2,4 => CTR => C6: 5,6,7,8,9 * DIS # H7: 3,4 => CTR => H7: 5,6,8 * DIS # I7: 3,4 => CTR => I7: 5,6,8 * DIS # A8: 3,4 => CTR => A8: 7,8,9 * PRF # A8: 7,8,9 => SOL * PRF # I8: 3,4 => SOL * DIS # H7: 4,5 => CTR => H7: 3,6,8 * DIS # I7: 4,5 => CTR => I7: 3,6,8 * DIS # I8: 4,5 => CTR => I8: 3,8 * DIS # B8: 4,5 => CTR => B8: 7,8 * DIS # C8: 4,5 => CTR => C8: 7,8,9 * DIS # G6: 6 => CTR => G6: 4,5 * DIS # H7: 3,4 => CTR => H7: 5,6,8 * DIS # I7: 3,4 => CTR => I7: 5,6,8 * PRF # I8: 3,4 => SOL * DIS # A9: 2 => CTR => A9: 3,4 * DIS # I6: 3,4 => CTR => I6: 1,5,6 * CNT 27 HDP CHAINS / 62 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 6,8 => CTR => H2: 1 * DIS H2: 1 # H3: 6,8 => CTR => H3: 4 * PRF H2: 1 + H3: 4 # H1: 5,6 => SOL * STA H2: 1 + H3: 4 + H1: 5,6 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....4.....2.9..3.759.1.7....3..2.7......34892.........1...729.........2..6.89.1.. | initial |
| ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517. | autosolve |
| 718243659426958317593167248834529761651734892279681435145372986987416523362895174 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) F2: 6,8 E3: 6,8 G1: 5,6 A5: 6,7 D4: 5,6 E6: 1,8 C9: 2,4 D7: 3,4 D8: 3,4 E8: 1,6 F8: 1,6 G8: 4,5 I9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H2: 1.. / H1 = 1 => 0 pairs (X) / H2 = 1 => 13 pairs (_) B5,C5: 1.. / B5 = 1 => 14 pairs (_) / C5 = 1 => 14 pairs (_) I4,I6: 1.. / I4 = 1 => 14 pairs (_) / I6 = 1 => 0 pairs (X) E8,F8: 1.. / E8 = 1 => 14 pairs (_) / F8 = 1 => 0 pairs (X) C2,H2: 1.. / C2 = 1 => 0 pairs (X) / H2 = 1 => 13 pairs (_) F4,I4: 1.. / F4 = 1 => 0 pairs (X) / I4 = 1 => 14 pairs (_) B1,B5: 1.. / B1 = 1 => 14 pairs (_) / B5 = 1 => 14 pairs (_) E6,E8: 1.. / E6 = 1 => 0 pairs (X) / E8 = 1 => 14 pairs (_) A6,C6: 2.. / A6 = 2 => 13 pairs (_) / C6 = 2 => 0 pairs (X) A9,C9: 2.. / A9 = 2 => 0 pairs (X) / C9 = 2 => 13 pairs (_) A6,A9: 2.. / A6 = 2 => 13 pairs (_) / A9 = 2 => 0 pairs (X) C6,C9: 2.. / C6 = 2 => 0 pairs (X) / C9 = 2 => 13 pairs (_) H6,I6: 3.. / H6 = 3 => 13 pairs (_) / I6 = 3 => 0 pairs (X) A8,A9: 3.. / A8 = 3 => 0 pairs (X) / A9 = 3 => 0 pairs (_) D7,D8: 3.. / D7 = 3 => 0 pairs (*) / D8 = 3 => 0 pairs (X) A9,I9: 3.. / A9 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) H6,H7: 3.. / H6 = 3 => 13 pairs (_) / H7 = 3 => 0 pairs (X) A2,C2: 4.. / A2 = 4 => 14 pairs (_) / C2 = 4 => 17 pairs (_) H3,I3: 4.. / H3 = 4 => 16 pairs (_) / I3 = 4 => 0 pairs (X) D7,D8: 4.. / D7 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) G6,G8: 4.. / G6 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) G1,H1: 5.. / G1 = 5 => 0 pairs (X) / H1 = 5 => 16 pairs (_) F2,E3: 6.. / F2 = 6 => 0 pairs (X) / E3 = 6 => 14 pairs (_) E8,F8: 6.. / E8 = 6 => 0 pairs (X) / F8 = 6 => 14 pairs (_) H7,I7: 6.. / H7 = 6 => 17 pairs (_) / I7 = 6 => 14 pairs (_) E3,E8: 6.. / E3 = 6 => 14 pairs (_) / E8 = 6 => 0 pairs (X) F2,F8: 6.. / F2 = 6 => 0 pairs (X) / F8 = 6 => 14 pairs (_) G1,G6: 6.. / G1 = 6 => 16 pairs (_) / G6 = 6 => 0 pairs (X) D5,D6: 7.. / D5 = 7 => 17 pairs (_) / D6 = 7 => 14 pairs (_) F2,E3: 8.. / F2 = 8 => 14 pairs (_) / E3 = 8 => 0 pairs (X) E3,E6: 8.. / E3 = 8 => 0 pairs (X) / E6 = 8 => 14 pairs (_) F4,F6: 9.. / F4 = 9 => 18 pairs (_) / F6 = 9 => 14 pairs (_) A8,C8: 9.. / A8 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) * DURATION: 0:00:34.483886 START: 22:47:59.024726 END: 22:48:33.508612 2019-04-30 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C9,D4,D7,D8,E3,E6,E8,F2,F8,G1,G8,I9) * ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517. * PAIR F2: 6,8 ROW 2 A2: 6,8,4 # reduction candidate for 6,8 A2: 6,8 # 17 pairs C2: 6,8,1,4 # reduction candidate for 6,8 C2: 6,8 # 15 pairs H2: 6,8,1 # reduction candidate for 6,8 H2: 6,8 => CTR * ...24351942195.3.75931.72...3..2.7...1..34892......6..1...729........42..64895173 H2: 1 # 13 pairs * PAIR E3: 6,8 ROW 3 H3: 6,8,4 # reduction candidate for 6,8 H3: 6,8 => CTR * ...243659.2.95.317593167284.3..2.7......34892....8.43.14.3729..3.94..528.6.895173 H3: 4 # 16 pairs I3: 6,8,4 # reduction candidate for 6,8 I3: 6,8 # 16 pairs * PAIR G1: 5,6 BLK 3 H1: 5,6,1,8 # reduction candidate for 5,6 H1: 1,8 => CTR * ...2435.9.2.95.3.75931.72...3..2.7......34892......6..1...729........42..6.895173 H1: 5,6 # 16 pairs * PAIR G1: 5,6 COL G G6: 5,6,4 # reduction candidate for 5,6 G6: 5,6 => CTR * ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729........42..6.895173 G6: 4 => SOLVED * 718243659426958317593167248834529761651734892279681435145372986987416523362895174 * PAIR A5: 6,7 BLK 4 C5: 6,7,1,5 # reduction candidate for 6,7 C5: 6,7 # 15 pairs A6: 6,7,2,4,8,9 # reduction candidate for 6,7 A6: 6,7 => CTR * ...243..942.95.3.75931.72...3..2.7......34892.42.89.311..3729..3.9416528264895173 A6: 2,4,8,9 # 13 pairs C6: 6,7,2,4,5,8,9 # reduction candidate for 6,7 C6: 6,7 # 19 pairs * PAIR A5: 6,7 ROW 5 D5: 6,7,5 # reduction candidate for 6,7 D5: 6,7 # 16 pairs D5: 5 # 14 pairs * PAIR A5: 6,7 COL A A1: 6,7,8 # reduction candidate for 6,7 A1: 8 # 15 pairs A1: 6,7 # 15 pairs * PAIR D4: 5,6 BLK 5 D5: 5,6,7 # reduction candidate for 5,6 D5: 5,6 # 14 pairs D6: 5,6,7 # reduction candidate for 5,6 D6: 5,6 # 17 pairs * PAIR D4: 5,6 ROW 4 C4: 5,6,4,8,9 # reduction candidate for 5,6 C4: 5,6 => CTR * ...243..9.2.95.3.75931.72...3..2.741....34892...7.....1...729........42..6.895173 C4: 4,8,9 # 13 pairs H4: 5,6,4 # reduction candidate for 5,6 H4: 5,6 # 15 pairs I4: 5,6,1,4 # reduction candidate for 5,6 I4: 5,6 => CTR * ...243..9.2.9583.75931672...3..2174.....34892....89.311...729......1642..6.895173 I4: 1,4 # 14 pairs * PAIR E6: 1,8 BLK 5 F4: 1,8,9 # reduction candidate for 1,8 F4: 1,8 # 14 pairs F6: 1,8,9 # reduction candidate for 1,8 F6: 1,8 # 18 pairs * PAIR C9: 2,4 BLK 7 A9: 2,4,3 # reduction candidate for 2,4 A9: 2,4 => CTR * ...243659.2.95.317593167284.3..2.7......34892....8.43.14..729..3.94..528.6.895173 A9: 3 => SOLVED * 718243659426958317593167248834529761651734892279681435145372986987416523362895174 * PAIR C9: 2,4 COL C C6: 2,4,5,6,7,8,9 # reduction candidate for 2,4 C6: 2,4 => CTR * ...243..942.95.3.75931.72...3..2.7......34892.........1...729........42..64895173 C6: 5,6,7,8,9 # 13 pairs * PAIR D7: 3,4 ROW 7 H7: 3,4,5,6,8 # reduction candidate for 3,4 H7: 3,4 => CTR * ...243659.2.95.317593167284.3..2.7......34892....8.43.1..37294634....528.6.895173 H7: 5,6,8 # 13 pairs I7: 3,4,5,6,8 # reduction candidate for 3,4 I7: 3,4 => CTR * ...243659.2.95.317593167284.3..2.74.....34892.......3.1...7296.......528.6.89517. I7: 5,6,8 # 13 pairs * PAIR D8: 3,4 ROW 8 A8: 3,4,7,8,9 # reduction candidate for 3,4 A8: 3,4 => CTR * ...243659.2.95.317593167284.3..2.7......34892....8.4..14..729...79...528.6.89517. A8: 7,8,9 => SOLVED * 718243659426958317593167248834529761651734892279681435145372986987416523362895174 I8: 3,4,5,8 # reduction candidate for 3,4 I8: 3,4 => SOLVED * 718243659426958317593167248834529761651734892279681435145372986987416523362895174 I8: 5,8 # 14 pairs * PAIR G8: 4,5 BLK 9 H7: 4,5,3,6,8 # reduction candidate for 4,5 H7: 4,5 => CTR * ...243659.2.95.317593167284.3..2.76.....34892....8.43.14.3729.63.94..528.6.895173 H7: 3,6,8 # 13 pairs I7: 4,5,3,6,8 # reduction candidate for 4,5 I7: 4,5 => CTR * ...243659.2.95.317593167284.3..2.7......34892.......3.1..37296.3.94..528.6.895173 I7: 3,6,8 # 13 pairs I8: 4,5,3,8 # reduction candidate for 4,5 I8: 4,5 => CTR * ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517. I8: 3,8 # 14 pairs * PAIR G8: 4,5 ROW 8 B8: 4,5,7,8 # reduction candidate for 4,5 B8: 4,5 => CTR * ...243..9.2.95.3.75931.72...3..2.7......348922........1..4729...4.3..528362895174 B8: 7,8 # 14 pairs C8: 4,5,7,8,9 # reduction candidate for 4,5 C8: 4,5 => CTR * ...243..9.2.95.3.75931.7246.3..2.7......348922........1...729..97.....28362895174 C8: 7,8,9 # 13 pairs * PAIR G8: 4,5 COL G G6: 4,5,6 # reduction candidate for 4,5 G6: 6 => CTR * ...243..9.2.95.3.75931.72...3..2.7......34892......6..1...729........42..6.895173 G6: 4,5 # 16 pairs * PAIR I9: 3,4 BLK 9 H7: 3,4,5,6,8 # reduction candidate for 3,4 H7: 3,4 => CTR * ...243659.2.95.317593167284.3..2.7......34892....8.43.1..37294634....528.6.895173 H7: 5,6,8 # 13 pairs I7: 3,4,5,6,8 # reduction candidate for 3,4 I7: 3,4 => CTR * ...243659.2.95.317593167284.3..2.74.....34892.......3.1...7296.......528.6.89517. I7: 5,6,8 # 13 pairs I8: 3,4,5,8 # reduction candidate for 3,4 I8: 3,4 => SOLVED * 718243659426958317593167248834529761651734892279681435145372986987416523362895174 I8: 5,8 # 14 pairs * PAIR I9: 3,4 ROW 9 A9: 3,4,2 # reduction candidate for 3,4 A9: 2 => CTR * ...243659426958317593167284.3..2.74.....34892.........1...729..3.94..528264895173 A9: 3,4 # 13 pairs * PAIR I9: 3,4 COL I I6: 3,4,1,5,6 # reduction candidate for 3,4 I6: 3,4 => CTR * ...243..9.2.95.3.75931.72...3..2.7.1....34892.........1...729........42..6.895173 I6: 1,5,6 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060501-absurd-base-pr-000.dot * REASONING * DIS # H2: 6,8 => CTR => H2: 1 * DIS # H3: 6,8 => CTR => H3: 4 * DIS # H1: 1,8 => CTR => H1: 5,6 * DIS # G6: 5,6 => CTR => G6: 4 * PRF # G6: 4 => SOL * DIS # A6: 6,7 => CTR => A6: 2,4,8,9 * DIS # C4: 5,6 => CTR => C4: 4,8,9 * DIS # I4: 5,6 => CTR => I4: 1,4 * DIS # A9: 2,4 => CTR => A9: 3 * PRF # A9: 3 => SOL * DIS # C6: 2,4 => CTR => C6: 5,6,7,8,9 * DIS # H7: 3,4 => CTR => H7: 5,6,8 * DIS # I7: 3,4 => CTR => I7: 5,6,8 * DIS # A8: 3,4 => CTR => A8: 7,8,9 * PRF # A8: 7,8,9 => SOL * PRF # I8: 3,4 => SOL * DIS # H7: 4,5 => CTR => H7: 3,6,8 * DIS # I7: 4,5 => CTR => I7: 3,6,8 * DIS # I8: 4,5 => CTR => I8: 3,8 * DIS # B8: 4,5 => CTR => B8: 7,8 * DIS # C8: 4,5 => CTR => C8: 7,8,9 * DIS # G6: 6 => CTR => G6: 4,5 * DIS # H7: 3,4 => CTR => H7: 5,6,8 * DIS # I7: 3,4 => CTR => I7: 5,6,8 * PRF # I8: 3,4 => SOL * DIS # A9: 2 => CTR => A9: 3,4 * DIS # I6: 3,4 => CTR => I6: 1,5,6 * CNT 27 HDP CHAINS / 62 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C9,D4,D7,D8,E3,E6,E8,F2,F8,G1,G8,I9) * ...243..9.2.95.3.75931.72...3..2.7......34892.........1...729.........2..6.89517. * PAIR F2: 6,8 ROW 2 A2: 6,8,4 # reduction candidate for 6,8 A2: 6,8 # 17 pairs C2: 6,8,1,4 # reduction candidate for 6,8 C2: 6,8 # 15 pairs H2: 6,8,1 # reduction candidate for 6,8 H2: 6,8 => CTR * ...24351942195.3.75931.72...3..2.7...1..34892......6..1...729........42..64895173 * PAIR RESTART * PAIR F2: 6,8 ROW 2 A2: 6,8,4 # reduction candidate for 6,8 A2: 6,8 # 17 pairs C2: 6,8,4 # reduction candidate for 6,8 C2: 6,8 # 15 pairs * PAIR E3: 6,8 ROW 3 H3: 6,8,4 # reduction candidate for 6,8 H3: 6,8 => CTR * ...243659.2.95.317593167284.3..2.7......34892....8.43.14.3729..3.94..528.6.895173 * RESTART * PAIR RESTART * PAIR G1: 5,6 BLK 3 H1: 5,6,8 # reduction candidate for 5,6 H1: 5,6 => SOLVED * 718243659426958317593167248834529761651734892279681435145372986987416523362895174 * DURATION: 0:00:05.504763 START: 22:49:09.832983 END: 22:49:15.337746 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060501-absurd-base-pr-001.dot * REASONING * DIS # H2: 6,8 => CTR => H2: 1 * DIS H2: 1 # H3: 6,8 => CTR => H3: 4 * PRF H2: 1 + H3: 4 # H1: 5,6 => SOL * STA H2: 1 + H3: 4 + H1: 5,6 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060501, absurd
Solution
position: 718243659426958317593167248834529761651734892279681435145372986987416523362895174 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 # A2: 6,8 => UNS * INC # C2: 6,8 => UNS * DIS # H2: 6,8 => CTR => H2: 1 * INC # H2: 1 => UNS * DIS # H3: 6,8 => CTR => H3: 4 * INC # H3: 4 => UNS * INC # I3: 6,8 => UNS * INC # H1: 5,6 => UNS * DIS # H1: 1,8 => CTR => H1: 5,6 * DIS # G6: 5,6 => CTR => G6: 4 * PRF # G6: 4 => SOL * INC # C5: 6,7 => UNS * DIS # A6: 6,7 => CTR => A6: 2,4,8,9 * INC # A6: 2,4,8,9 => UNS * INC # C6: 6,7 => UNS * INC # D5: 6,7 => UNS * INC # D5: 5 => UNS * INC # A1: 6,7 => UNS * INC # A1: 8 => UNS * INC # D5: 5,6 => UNS * INC # D6: 5,6 => UNS * DIS # C4: 5,6 => CTR => C4: 4,8,9 * INC # C4: 4,8,9 => UNS * INC # H4: 5,6 => UNS * DIS # I4: 5,6 => CTR => I4: 1,4 * INC # I4: 1,4 => UNS * INC # F4: 1,8 => UNS * INC # F6: 1,8 => UNS * DIS # A9: 2,4 => CTR => A9: 3 * PRF # A9: 3 => SOL * DIS # C6: 2,4 => CTR => C6: 5,6,7,8,9 * INC # C6: 5,6,7,8,9 => UNS * DIS # H7: 3,4 => CTR => H7: 5,6,8 * INC # H7: 5,6,8 => UNS * DIS # I7: 3,4 => CTR => I7: 5,6,8 * INC # I7: 5,6,8 => UNS * DIS # A8: 3,4 => CTR => A8: 7,8,9 * PRF # A8: 7,8,9 => SOL * PRF # I8: 3,4 => SOL * INC # I8: 5,8 => UNS * DIS # H7: 4,5 => CTR => H7: 3,6,8 * INC # H7: 3,6,8 => UNS * DIS # I7: 4,5 => CTR => I7: 3,6,8 * INC # I7: 3,6,8 => UNS * DIS # I8: 4,5 => CTR => I8: 3,8 * INC # I8: 3,8 => UNS * DIS # B8: 4,5 => CTR => B8: 7,8 * INC # B8: 7,8 => UNS * DIS # C8: 4,5 => CTR => C8: 7,8,9 * INC # C8: 7,8,9 => UNS * INC # G6: 4,5 => UNS * DIS # G6: 6 => CTR => G6: 4,5 * DIS # H7: 3,4 => CTR => H7: 5,6,8 * INC # H7: 5,6,8 => UNS * DIS # I7: 3,4 => CTR => I7: 5,6,8 * INC # I7: 5,6,8 => UNS * PRF # I8: 3,4 => SOL * INC # I8: 5,8 => UNS * INC # A9: 3,4 => UNS * DIS # A9: 2 => CTR => A9: 3,4 * DIS # I6: 3,4 => CTR => I6: 1,5,6 * INC # I6: 1,5,6 => UNS * CNT 62 HDP CHAINS / 62 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 6,8 => UNS * INC # C2: 6,8 => UNS * DIS # H2: 6,8 => CTR => H2: 1 * INC H2: 1 # A2: 6,8 => UNS * INC H2: 1 # C2: 6,8 => UNS * DIS H2: 1 # H3: 6,8 => CTR => H3: 4 * PRF H2: 1 + H3: 4 # H1: 5,6 => SOL * STA H2: 1 + H3: 4 + H1: 5,6 * CNT 7 HDP CHAINS / 7 HYP OPENED