Analysis of zz-www.sudokuoftheday.co.uk-20190417-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: ..4............5.7....39..4.3.......24.7....37..18..2.95...21.....8..2..8..56.... initial
Autosolve
position: ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 8,9 => CTR => H1: 1,3 * DIS # H1: 8,9 => CTR => H1: 1,3 * DIS # H2: 9 => CTR => H2: 3,6 * PRF # H3: 6,8 => SOL * DIS # B3: 6,8 => CTR => B3: 7 * DIS # C6: 5,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * DIS # H4: 7 => CTR => H4: 5,6 * PRF # A3: 1 => SOL * PRF # C6: 6,9 => SOL * DIS # C6: 5 => CTR => C6: 6,9 * PRF # B2: 6,9 => SOL * PRF # H4: 6,7 => SOL * DIS # H4: 5 => CTR => H4: 6,7 * DIS # G1: 3 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 1,3 * DIS # H4: 7 => CTR => H4: 5,6 * DIS # C6: 5,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * DIS # C8: 6,7 => CTR => C8: 3 * DIS # C3: 6,7 => CTR => C3: 5 * PRF # C3: 5 => SOL * DIS # B8: 6 => CTR => B8: 1,7 * PRF # B9: 2 => SOL * DIS # H8: 6,7 => CTR => H8: 3,5 * PRF # H4: 6,7 => SOL * DIS # H4: 5 => CTR => H4: 6,7 * DIS # H8: 3,7 => CTR => H8: 5,6 * DIS # H8: 3,7 => CTR => H8: 5,6 * PRF # C9: 3,7 => SOL * CNT 30 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 8,9 => CTR => H1: 1,3 * DIS H1: 1,3 # C6: 5,6 => CTR => C6: 9 * PRF H1: 1,3 + C6: 9 => SOL * STA H1: 1,3 + C6: 9 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4............5.7....39..4.3.......24.7....37..18..2.95...21.....8..2..8..56.... | initial |
| ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49 | autosolve |
| 384675912692418537175239684538924761241756893769183425956342178413897256827561349 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 1,3 B1: 8,9 A2: 3,6 G3: 6,8 A4: 5,6 B6: 6,9 G4: 6,7 G5: 8,9 H5: 8,9 I6: 5,6 C7: 6,7 F8: 1,7 F9: 1,7 H7: 6,7 I8: 5,6 G9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 16 pairs (_) / A3 = 1 => 0 pairs (*) H1,H3: 1.. / H1 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) B8,B9: 1.. / B8 = 1 => 19 pairs (_) / B9 = 1 => 21 pairs (_) F8,F9: 1.. / F8 = 1 => 21 pairs (_) / F9 = 1 => 19 pairs (_) A1,H1: 1.. / A1 = 1 => 16 pairs (_) / H1 = 1 => 0 pairs (*) A3,H3: 1.. / A3 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) B8,F8: 1.. / B8 = 1 => 19 pairs (_) / F8 = 1 => 21 pairs (_) B9,F9: 1.. / B9 = 1 => 21 pairs (_) / F9 = 1 => 19 pairs (_) B2,C2: 2.. / B2 = 2 => 23 pairs (_) / C2 = 2 => 0 pairs (*) B9,C9: 2.. / B9 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) B2,B9: 2.. / B2 = 2 => 23 pairs (_) / B9 = 2 => 0 pairs (*) C2,C9: 2.. / C2 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) A1,A2: 3.. / A1 = 3 => 0 pairs (*) / A2 = 3 => 0 pairs (X) C8,C9: 3.. / C8 = 3 => 22 pairs (_) / C9 = 3 => 0 pairs (X) H8,G9: 3.. / H8 = 3 => 0 pairs (X) / G9 = 3 => 22 pairs (_) A2,H2: 3.. / A2 = 3 => 16 pairs (_) / H2 = 3 => 0 pairs (*) C8,H8: 3.. / C8 = 3 => 22 pairs (_) / H8 = 3 => 0 pairs (X) C9,G9: 3.. / C9 = 3 => 0 pairs (X) / G9 = 3 => 22 pairs (_) G1,G9: 3.. / G1 = 3 => 0 pairs (X) / G9 = 3 => 22 pairs (_) A3,C3: 5.. / A3 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) A4,C6: 5.. / A4 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) H4,I6: 5.. / H4 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) H8,I8: 5.. / H8 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) A4,H4: 5.. / A4 = 5 => 0 pairs (*) / H4 = 5 => 0 pairs (X) C6,I6: 5.. / C6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) A3,A4: 5.. / A3 = 5 => 0 pairs (X) / A4 = 5 => 0 pairs (_) C3,C6: 5.. / C3 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) H4,H8: 5.. / H4 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) I6,I8: 5.. / I6 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) C7,H7: 6.. / C7 = 6 => 24 pairs (_) / H7 = 6 => 0 pairs (X) G3,G4: 6.. / G3 = 6 => 22 pairs (_) / G4 = 6 => 0 pairs (X) I6,I8: 6.. / I6 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) B3,C3: 7.. / B3 = 7 => 24 pairs (_) / C3 = 7 => 0 pairs (X) G4,H4: 7.. / G4 = 7 => 22 pairs (_) / H4 = 7 => 0 pairs (X) F8,F9: 7.. / F8 = 7 => 19 pairs (_) / F9 = 7 => 21 pairs (_) C7,H7: 7.. / C7 = 7 => 0 pairs (X) / H7 = 7 => 24 pairs (_) G4,G9: 7.. / G4 = 7 => 22 pairs (_) / G9 = 7 => 0 pairs (X) B1,B3: 8.. / B1 = 8 => 22 pairs (_) / B3 = 8 => 0 pairs (X) G5,H5: 8.. / G5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) B6,C6: 9.. / B6 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) G5,H5: 9.. / G5 = 9 => 16 pairs (_) / H5 = 9 => 0 pairs (*) C2,C6: 9.. / C2 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) G1,G5: 9.. / G1 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) * DURATION: 0:00:50.977164 START: 05:21:56.699364 END: 05:22:47.676528 2019-05-01 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A4,B1,B6,C7,F8,F9,G3,G4,G5,G9,H5,H7,I6,I8) * ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49 * PAIR A1: 1,3 ROW 1 H1: 1,3,8,9 # reduction candidate for 1,3 H1: 8,9 => CTR * 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749 H1: 1,3 # 22 pairs * PAIR B1: 8,9 ROW 1 G1: 8,9,3 # reduction candidate for 8,9 G1: 8,9 # 22 pairs H1: 8,9,1,3 # reduction candidate for 8,9 H1: 8,9 => CTR * 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749 H1: 1,3 # 22 pairs * PAIR A2: 3,6 ROW 2 H2: 3,6,9 # reduction candidate for 3,6 H2: 9 => CTR * 1946758323..418597.8.239..4.38924..12417569837.918342595.3421.84..89.2568..56.349 H2: 3,6 # 22 pairs * PAIR G3: 6,8 BLK 3 H3: 6,8,1 # reduction candidate for 6,8 H3: 6,8 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 H3: 1 # 16 pairs * PAIR G3: 6,8 ROW 3 B3: 6,8,7 # reduction candidate for 6,8 B3: 6,8 => CTR * ..4675..2.29418537567239..4.38924..1241756..37.51834269563421784.389.2658.256.349 B3: 7 # 24 pairs * PAIR A4: 5,6 BLK 4 C6: 5,6,9 # reduction candidate for 5,6 C6: 5,6 => CTR * .846759.2.294185.7...239684.389247.124175689379.18342.95.3421.8463891275812567349 C6: 9 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 * PAIR A4: 5,6 ROW 4 H4: 5,6,7 # reduction candidate for 5,6 H4: 7 => CTR * ..4675..2...4185.7...239..4538924671241756..37..1834259573421684..89.2..8..56..49 H4: 5,6 # 22 pairs * PAIR A4: 5,6 COL A A3: 5,6,1 # reduction candidate for 5,6 A3: 1 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 A3: 5,6 # 16 pairs * PAIR B6: 6,9 BLK 4 C6: 6,9,5 # reduction candidate for 6,9 C6: 6,9 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 C6: 5 => CTR * .846759.2.294185.75..2396.4.38924..1241756..379518342695.3421.84..89.2.58.256.349 * PAIR B6: 6,9 COL B B2: 6,9,2 # reduction candidate for 6,9 B2: 6,9 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 B2: 2 # 23 pairs * PAIR G4: 6,7 BLK 6 H4: 6,7,5 # reduction candidate for 6,7 H4: 6,7 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 H4: 5 => CTR * ..4675..2..94185.75..239614638924751241756..379518342695.3421.84..89.2.58..56.349 * PAIR G5: 8,9 COL G G1: 8,9,3 # reduction candidate for 8,9 G1: 3 => CTR * ..46753.23..4185.7...239..4.38924..12417569837..18342.95.3421.84..89.2358.356.749 G1: 8,9 # 22 pairs * PAIR H5: 8,9 COL H H1: 8,9,1,3 # reduction candidate for 8,9 H1: 8,9 => CTR * 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749 H1: 1,3 # 22 pairs * PAIR I6: 5,6 BLK 6 H4: 5,6,7 # reduction candidate for 5,6 H4: 7 => CTR * ..4675..2...4185.7...239..4538924671241756..37..1834259573421684..89.2..8..56..49 H4: 5,6 # 22 pairs * PAIR I6: 5,6 ROW 6 C6: 5,6,9 # reduction candidate for 5,6 C6: 5,6 => CTR * .846759.2.294185.7...239684.389247.124175689379.18342.95.3421.8463891275812567349 C6: 9 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 * PAIR C7: 6,7 BLK 7 B8: 6,7,1 # reduction candidate for 6,7 B8: 6,7 # 21 pairs C8: 6,7,3 # reduction candidate for 6,7 C8: 6,7 => CTR * ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2358.356.749 C8: 3 # 22 pairs * PAIR C7: 6,7 COL C C3: 6,7,5 # reduction candidate for 6,7 C3: 6,7 => CTR * 1846759.2...4185.75..239.14638924751241756..379518342695.3421.84..89.2.58..56.349 C3: 5 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 * PAIR F8: 1,7 ROW 8 B8: 1,7,6 # reduction candidate for 1,7 B8: 6 => CTR * .846759.2.29418537576239..4.38924751241756..3795183426957342168463891275812567349 B8: 1,7 # 21 pairs * PAIR F9: 1,7 ROW 9 B9: 1,7,2 # reduction candidate for 1,7 B9: 2 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 B9: 1,7 # 23 pairs * PAIR H7: 6,7 BLK 9 H8: 6,7,3,5 # reduction candidate for 6,7 H8: 6,7 => CTR * ..4675..2..94185.75..239614638924751241756..379518342695.3421.84.389.2.58..56.349 H8: 3,5 # 17 pairs * PAIR H7: 6,7 COL H H4: 6,7,5 # reduction candidate for 6,7 H4: 6,7 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 H4: 5 => CTR * ..4675..2..94185.75..239614638924751241756..379518342695.3421.84..89.2.58..56.349 * PAIR I8: 5,6 BLK 9 H8: 5,6,3,7 # reduction candidate for 5,6 H8: 3,7 => CTR * ..4675..2..941853757.239..4.38924.51241756..37.518342695.3421684..89.2758..567349 H8: 5,6 # 24 pairs * PAIR G9: 3,7 BLK 9 H8: 3,7,5,6 # reduction candidate for 3,7 H8: 3,7 => CTR * ..4675..2..941853757.239..4.38924.51241756..37.518342695.3421684..89.2758..567349 H8: 5,6 # 24 pairs * PAIR G9: 3,7 ROW 9 C9: 3,7,2 # reduction candidate for 3,7 C9: 3,7 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 C9: 2 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190417-absurd-base-pr-000.dot * REASONING * DIS # H1: 8,9 => CTR => H1: 1,3 * DIS # H1: 8,9 => CTR => H1: 1,3 * DIS # H2: 9 => CTR => H2: 3,6 * PRF # H3: 6,8 => SOL * DIS # B3: 6,8 => CTR => B3: 7 * DIS # C6: 5,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * DIS # H4: 7 => CTR => H4: 5,6 * PRF # A3: 1 => SOL * PRF # C6: 6,9 => SOL * DIS # C6: 5 => CTR => C6: 6,9 * PRF # B2: 6,9 => SOL * PRF # H4: 6,7 => SOL * DIS # H4: 5 => CTR => H4: 6,7 * DIS # G1: 3 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 1,3 * DIS # H4: 7 => CTR => H4: 5,6 * DIS # C6: 5,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * DIS # C8: 6,7 => CTR => C8: 3 * DIS # C3: 6,7 => CTR => C3: 5 * PRF # C3: 5 => SOL * DIS # B8: 6 => CTR => B8: 1,7 * PRF # B9: 2 => SOL * DIS # H8: 6,7 => CTR => H8: 3,5 * PRF # H4: 6,7 => SOL * DIS # H4: 5 => CTR => H4: 6,7 * DIS # H8: 3,7 => CTR => H8: 5,6 * DIS # H8: 3,7 => CTR => H8: 5,6 * PRF # C9: 3,7 => SOL * CNT 30 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A4,B1,B6,C7,F8,F9,G3,G4,G5,G9,H5,H7,I6,I8) * ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49 * PAIR A1: 1,3 ROW 1 H1: 1,3,8,9 # reduction candidate for 1,3 H1: 8,9 => CTR * 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749 * PAIR RESTART * PAIR A4: 5,6 BLK 4 C6: 5,6,9 # reduction candidate for 5,6 C6: 5,6 => CTR * 38467591262941853717523968453892476124175689379618342.95.3421.84.389.2..8.256.349 C6: 9 => SOLVED * 384675912692418537175239684538924761241756893769183425956342178413897256827561349 * DURATION: 0:00:03.846094 START: 05:23:22.555789 END: 05:23:26.401883 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190417-absurd-base-pr-001.dot * REASONING * DIS # H1: 8,9 => CTR => H1: 1,3 * DIS H1: 1,3 # C6: 5,6 => CTR => C6: 9 * PRF H1: 1,3 + C6: 9 => SOL * STA H1: 1,3 + C6: 9 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190417, absurd
Solution
position: 384675912692418537175239684538924761241756893769183425956342178413897256827561349 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 # H1: 1,3 => UNS * DIS # H1: 8,9 => CTR => H1: 1,3 * INC # G1: 8,9 => UNS * DIS # H1: 8,9 => CTR => H1: 1,3 * INC # H1: 1,3 => UNS * INC # H2: 3,6 => UNS * DIS # H2: 9 => CTR => H2: 3,6 * PRF # H3: 6,8 => SOL * INC # H3: 1 => UNS * DIS # B3: 6,8 => CTR => B3: 7 * INC # B3: 7 => UNS * DIS # C6: 5,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * INC # H4: 5,6 => UNS * DIS # H4: 7 => CTR => H4: 5,6 * INC # A3: 5,6 => UNS * PRF # A3: 1 => SOL * PRF # C6: 6,9 => SOL * DIS # C6: 5 => CTR => C6: 6,9 * PRF # B2: 6,9 => SOL * INC # B2: 2 => UNS * PRF # H4: 6,7 => SOL * DIS # H4: 5 => CTR => H4: 6,7 * INC # G1: 8,9 => UNS * DIS # G1: 3 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 1,3 * INC # H1: 1,3 => UNS * INC # H4: 5,6 => UNS * DIS # H4: 7 => CTR => H4: 5,6 * DIS # C6: 5,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * INC # B8: 6,7 => UNS * DIS # C8: 6,7 => CTR => C8: 3 * INC # C8: 3 => UNS * DIS # C3: 6,7 => CTR => C3: 5 * PRF # C3: 5 => SOL * INC # B8: 1,7 => UNS * DIS # B8: 6 => CTR => B8: 1,7 * INC # B9: 1,7 => UNS * PRF # B9: 2 => SOL * DIS # H8: 6,7 => CTR => H8: 3,5 * INC # H8: 3,5 => UNS * PRF # H4: 6,7 => SOL * DIS # H4: 5 => CTR => H4: 6,7 * INC # H8: 5,6 => UNS * DIS # H8: 3,7 => CTR => H8: 5,6 * DIS # H8: 3,7 => CTR => H8: 5,6 * INC # H8: 5,6 => UNS * PRF # C9: 3,7 => SOL * INC # C9: 2 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 1,3 => UNS * DIS # H1: 8,9 => CTR => H1: 1,3 * DIS H1: 1,3 # C6: 5,6 => CTR => C6: 9 * PRF H1: 1,3 + C6: 9 => SOL * STA H1: 1,3 + C6: 9 * CNT 4 HDP CHAINS / 3 HYP OPENED