Analysis of zz-www.sudokuoftheday.co.uk-20060621-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: .18.3....9..71...........9.25...14.94.7.9.......47..8..............6.15..23..5... initial
Autosolve
position: .18.39...9..71........5..9125638147948759..1....47..8.....27.......63152.23.45.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 2,4 => CTR => C2: 5 * DIS # C7: 5 => CTR => C7: 1,9 * PRF # I1: 5,6 => SOL * PRF # B8: 7 => SOL * DIS # A7: 1,8 => CTR => A7: 5,6 * DIS # D9: 9 => CTR => D9: 1,8 * DIS # I7: 8 => CTR => I7: 3,4 * DIS # G9: 7,8 => CTR => G9: 9 * CNT 8 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 # C2: 2,4 => CTR => C2: 5 * DIS C2: 5 # G5: 3 => CTR => G5: 2,6 * DIS C2: 5 + G5: 2,6 # G6: 2,6 => CTR => G6: 5 * PRF C2: 5 + G5: 2,6 + G6: 5 => SOL * STA C2: 5 + G5: 2,6 + G6: 5 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .18.3....9..71...........9.25...14.94.7.9.......47..8..............6.15..23..5... | initial |
| .18.39...9..71........5..9125638147948759..1....47..8.....27.......63152.23.45.6. | autosolve |
| 618239745935714628742658391256381479487596213391472586569127834874963152123845967 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) C3: 2,4 D1: 2,6 F2: 4,8 D3: 2,6 F3: 4,8 H1: 2,4 H2: 2,3 A6: 1,3 B6: 3,9 C6: 1,9 F5: 2,6 F6: 2,6 I5: 3,6 I6: 5,6 B7: 6,9 A8: 7,8 C8: 4,9 A9: 1,8 D8: 8,9 H7: 3,4 I9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A6,C6: 1.. / A6 = 1 => 0 pairs (X) / C6 = 1 => 22 pairs (_) D7,D9: 1.. / D7 = 1 => 23 pairs (_) / D9 = 1 => 27 pairs (_) A9,D9: 1.. / A9 = 1 => 23 pairs (_) / D9 = 1 => 27 pairs (_) C6,C7: 1.. / C6 = 1 => 22 pairs (_) / C7 = 1 => 0 pairs (X) C2,C3: 2.. / C2 = 2 => 0 pairs (X) / C3 = 2 => 21 pairs (_) D1,D3: 2.. / D1 = 2 => 21 pairs (_) / D3 = 2 => 0 pairs (X) H1,H2: 2.. / H1 = 2 => 0 pairs (X) / H2 = 2 => 21 pairs (_) F5,F6: 2.. / F5 = 2 => 19 pairs (_) / F6 = 2 => 20 pairs (_) G5,G6: 2.. / G5 = 2 => 20 pairs (_) / G6 = 2 => 19 pairs (_) D1,H1: 2.. / D1 = 2 => 21 pairs (_) / H1 = 2 => 0 pairs (X) C2,H2: 2.. / C2 = 2 => 0 pairs (X) / H2 = 2 => 21 pairs (_) C3,D3: 2.. / C3 = 2 => 21 pairs (_) / D3 = 2 => 0 pairs (X) F5,G5: 2.. / F5 = 2 => 19 pairs (_) / G5 = 2 => 20 pairs (_) F6,G6: 2.. / F6 = 2 => 20 pairs (_) / G6 = 2 => 19 pairs (_) A6,B6: 3.. / A6 = 3 => 22 pairs (_) / B6 = 3 => 0 pairs (X) G5,I5: 3.. / G5 = 3 => 22 pairs (_) / I5 = 3 => 22 pairs (_) A3,A6: 3.. / A3 = 3 => 0 pairs (X) / A6 = 3 => 22 pairs (_) H2,H7: 3.. / H2 = 3 => 0 pairs (X) / H7 = 3 => 21 pairs (_) F2,F3: 4.. / F2 = 4 => 23 pairs (_) / F3 = 4 => 0 pairs (X) H1,I1: 4.. / H1 = 4 => 21 pairs (_) / I1 = 4 => 0 pairs (X) B8,C8: 4.. / B8 = 4 => 0 pairs (X) / C8 = 4 => 21 pairs (_) H7,I7: 4.. / H7 = 4 => 0 pairs (X) / I7 = 4 => 21 pairs (_) H1,H7: 4.. / H1 = 4 => 21 pairs (_) / H7 = 4 => 0 pairs (X) I1,I7: 4.. / I1 = 4 => 0 pairs (X) / I7 = 4 => 21 pairs (_) A1,C2: 5.. / A1 = 5 => 0 pairs (X) / C2 = 5 => 21 pairs (_) G6,I6: 5.. / G6 = 5 => 20 pairs (_) / I6 = 5 => 21 pairs (_) A7,C7: 5.. / A7 = 5 => 21 pairs (_) / C7 = 5 => 0 pairs (X) A1,A7: 5.. / A1 = 5 => 0 pairs (X) / A7 = 5 => 21 pairs (_) C2,C7: 5.. / C2 = 5 => 21 pairs (_) / C7 = 5 => 0 pairs (X) D1,D3: 6.. / D1 = 6 => 0 pairs (X) / D3 = 6 => 21 pairs (_) F5,F6: 6.. / F5 = 6 => 20 pairs (_) / F6 = 6 => 19 pairs (_) A7,B7: 6.. / A7 = 6 => 0 pairs (X) / B7 = 6 => 22 pairs (_) A8,B8: 7.. / A8 = 7 => 27 pairs (_) / B8 = 7 => 0 pairs (*) G9,I9: 7.. / G9 = 7 => 0 pairs (X) / I9 = 7 => 21 pairs (_) B3,B8: 7.. / B3 = 7 => 27 pairs (_) / B8 = 7 => 0 pairs (*) I1,I9: 7.. / I1 = 7 => 0 pairs (X) / I9 = 7 => 21 pairs (_) F2,F3: 8.. / F2 = 8 => 0 pairs (X) / F3 = 8 => 23 pairs (_) F3,G3: 8.. / F3 = 8 => 23 pairs (_) / G3 = 8 => 0 pairs (X) A8,D8: 8.. / A8 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) B6,C6: 9.. / B6 = 9 => 22 pairs (_) / C6 = 9 => 0 pairs (X) G7,G9: 9.. / G7 = 9 => 0 pairs (X) / G9 = 9 => 23 pairs (_) D9,G9: 9.. / D9 = 9 => 0 pairs (X) / G9 = 9 => 23 pairs (_) * DURATION: 0:00:53.376551 START: 00:00:03.723006 END: 00:00:57.099557 2019-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,A9,B6,B7,C3,C6,C8,D1,D3,D8,F2,F3,F5,F6,H1,H2,H7,I5,I6,I9) * .18.39...9..71........5..9125638147948759..1....47..8.....27.......63152.23.45.6. * PAIR C3: 2,4 BLK 1 C2: 2,4,5 # reduction candidate for 2,4 C2: 2,4 => CTR * 518.39...93.71..2.672.5..9125638147948759..1.39147..8..65.27...749863152.23.45.6. C2: 5 # 21 pairs * PAIR C6: 1,9 COL C C7: 1,9,5 # reduction candidate for 1,9 C7: 5 => CTR * 518.39...93.71..2.672.5..9125638147948759..1.39147..8..65.27...749863152.23.45.6. C7: 1,9 # 21 pairs * PAIR F5: 2,6 ROW 5 G5: 2,6,3 # reduction candidate for 2,6 G5: 3 # 22 pairs G5: 2,6 # 22 pairs * PAIR F6: 2,6 ROW 6 G6: 2,6,5 # reduction candidate for 2,6 G6: 2,6 # 21 pairs G6: 5 # 20 pairs * PAIR I5: 3,6 BLK 6 G5: 3,6,2 # reduction candidate for 3,6 G5: 2 # 20 pairs G5: 3,6 # 19 pairs * PAIR I5: 3,6 COL I I2: 3,6,5,8 # reduction candidate for 3,6 I2: 3,6 # 26 pairs I2: 5,8 # 22 pairs * PAIR I6: 5,6 BLK 6 G6: 5,6,2 # reduction candidate for 5,6 G6: 5,6 # 20 pairs G6: 2 # 19 pairs * PAIR I6: 5,6 COL I I1: 5,6,4,7 # reduction candidate for 5,6 I1: 5,6 => SOLVED * 618239745935714628742658391256381479487596213391472586569127834874963152123845967 I1: 4,7 # 22 pairs I2: 5,6,3,8 # reduction candidate for 5,6 I2: 5,6 # 26 pairs * PAIR C8: 4,9 BLK 7 B8: 4,9,7 # reduction candidate for 4,9 B8: 7 => SOLVED * 618239745935714628742658391256381479487596213391472586569127834874963152123845967 B8: 4,9 # 27 pairs * PAIR A9: 1,8 BLK 7 A7: 1,8,5,6 # reduction candidate for 1,8 A7: 1,8 => CTR * 518.39...9..71....67.25.39125638147948759..1339147..8..65.27.34749863152.23.45.6. A7: 5,6 # 22 pairs * PAIR A9: 1,8 ROW 9 D9: 1,8,9 # reduction candidate for 1,8 D9: 9 => CTR * 518.39...93.71..2.672.5..9125638147948759..1.39147..8.8651279..749863152123945.6. D9: 1,8 # 23 pairs * PAIR D8: 8,9 BLK 8 D7: 8,9,1 # reduction candidate for 8,9 D7: 8,9 # 27 pairs D9: 8,9,1 # reduction candidate for 8,9 D9: 8,9 # 23 pairs * PAIR H7: 3,4 BLK 9 I7: 3,4,8 # reduction candidate for 3,4 I7: 8 => CTR * .18.39.249.271..3...4258.9125638147948759..13...47..8...5.27348.49863152823145967 I7: 3,4 # 23 pairs * PAIR I9: 7,8 BLK 9 G9: 7,8,9 # reduction candidate for 7,8 G9: 7,8 => CTR * 518.39...93.71..2.672.5..9125638147948759..1.39147..8.8651279..749863152123945.6. G9: 9 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060621-absurd-base-pr-000.dot * REASONING * DIS # C2: 2,4 => CTR => C2: 5 * DIS # C7: 5 => CTR => C7: 1,9 * PRF # I1: 5,6 => SOL * PRF # B8: 7 => SOL * DIS # A7: 1,8 => CTR => A7: 5,6 * DIS # D9: 9 => CTR => D9: 1,8 * DIS # I7: 8 => CTR => I7: 3,4 * DIS # G9: 7,8 => CTR => G9: 9 * CNT 8 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,A9,B6,B7,C3,C6,C8,D1,D3,D8,F2,F3,F5,F6,H1,H2,H7,I5,I6,I9) * .18.39...9..71........5..9125638147948759..1....47..8.....27.......63152.23.45.6. * PAIR C3: 2,4 BLK 1 C2: 2,4,5 # reduction candidate for 2,4 C2: 2,4 => CTR * 518.39...93.71..2.672.5..9125638147948759..1.39147..8..65.27...749863152.23.45.6. * PAIR F5: 2,6 ROW 5 G5: 2,6,3 # reduction candidate for 2,6 G5: 3 => CTR * 6182395479.571.623..265.891256381479487592316...47628556.8279348.4.63152.23.45.6. * PAIR RESTART * PAIR F6: 2,6 ROW 6 G6: 2,6,5 # reduction candidate for 2,6 G6: 2,6 => CTR * 6182395479.571..26..265..9125638147948759..13...47..8556.8279348.4.63152.23.45768 G6: 5 => SOLVED * 618239745935714628742658391256381479487596213391472586569127834874963152123845967 * DURATION: 0:00:05.938914 START: 00:01:17.316971 END: 00:01:23.255885 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060621-absurd-base-pr-001.dot * REASONING * DIS # C2: 2,4 => CTR => C2: 5 * DIS C2: 5 # G5: 3 => CTR => G5: 2,6 * DIS C2: 5 + G5: 2,6 # G6: 2,6 => CTR => G6: 5 * PRF C2: 5 + G5: 2,6 + G6: 5 => SOL * STA C2: 5 + G5: 2,6 + G6: 5 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060621, absurd
Solution
position: 618239745935714628742658391256381479487596213391472586569127834874963152123845967 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 # C2: 2,4 => CTR => C2: 5 * INC # C2: 5 => UNS * INC # C7: 1,9 => UNS * DIS # C7: 5 => CTR => C7: 1,9 * INC # G5: 2,6 => UNS * INC # G5: 3 => UNS * INC # G6: 2,6 => UNS * INC # G6: 5 => UNS * INC # G5: 3,6 => UNS * INC # G5: 2 => UNS * INC # I2: 3,6 => UNS * INC # I2: 5,8 => UNS * INC # G6: 5,6 => UNS * INC # G6: 2 => UNS * PRF # I1: 5,6 => SOL * INC # I1: 4,7 => UNS * INC # I2: 5,6 => UNS * INC # B8: 4,9 => UNS * PRF # B8: 7 => SOL * DIS # A7: 1,8 => CTR => A7: 5,6 * INC # A7: 5,6 => UNS * INC # D9: 1,8 => UNS * DIS # D9: 9 => CTR => D9: 1,8 * INC # D7: 8,9 => UNS * INC # D9: 8,9 => UNS * INC # I7: 3,4 => UNS * DIS # I7: 8 => CTR => I7: 3,4 * DIS # G9: 7,8 => CTR => G9: 9 * INC # G9: 9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 2,4 => CTR => C2: 5 * INC C2: 5 # G5: 2,6 => UNS * DIS C2: 5 # G5: 3 => CTR => G5: 2,6 * DIS C2: 5 + G5: 2,6 # G6: 2,6 => CTR => G6: 5 * PRF C2: 5 + G5: 2,6 + G6: 5 => SOL * STA C2: 5 + G5: 2,6 + G6: 5 * CNT 5 HDP CHAINS / 4 HYP OPENED