Analysis of zz-www.sudokuoftheday.co.uk-20060420-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: ...........78..41..48.1..7..........46..2.....827...498....17..6..2.89...7594..6. initial
Autosolve
position: ..64.7.9...789.41.948.1..7.7...84...46..29.87.827...498....17..6..2789...75943.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I1: 3,5 => CTR => I1: 2,8 * DIS # B4: 1,3 => CTR => B4: 5,9 * DIS # C4: 1,3 => CTR => C4: 9 * DIS # G5: 1,3 => CTR => G5: 5 * DIS # D4: 5,6 => CTR => D4: 1,3 * DIS # G6: 5,6 => CTR => G6: 1,3 * DIS # B4: 1,3 => CTR => B4: 5,9 * DIS # D4: 5,6 => CTR => D4: 1,3 * DIS # E6: 3 => CTR => E6: 5,6 * DIS # B7: 2,3 => CTR => B7: 9 * DIS # H4: 5 => CTR => H4: 2,3 * CNT 11 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I1: 3,5 => CTR => I1: 2,8 * PRF I1: 2,8 # E6: 6 => SOL * STA I1: 2,8 + E6: 6 * CNT 2 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...........78..41..48.1..7..........46..2.....827...498....17..6..2.89...7594..6. | initial |
| ..64.7.9...789.41.948.1..7.7...84...46..29.87.827...498....17..6..2789...75943.6. | autosolve |
| 516437298327896415948512673759384126463129587182765349894651732631278954275943861 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) E1: 3,5 C5: 1,3 F6: 5,6 B8: 1,3 A9: 1,2 D7: 5,6 E7: 5,6 H7: 2,3 H8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 12 pairs (_) / B1 = 1 => 15 pairs (_) D4,D5: 1.. / D4 = 1 => 12 pairs (_) / D5 = 1 => 13 pairs (_) A6,G6: 1.. / A6 = 1 => 17 pairs (_) / G6 = 1 => 12 pairs (_) F2,F3: 2.. / F2 = 2 => 17 pairs (_) / F3 = 2 => 10 pairs (_) B7,A9: 2.. / B7 = 2 => 0 pairs (X) / A9 = 2 => 12 pairs (_) H4,H7: 2.. / H4 = 2 => 11 pairs (_) / H7 = 2 => 13 pairs (_) E1,D3: 3.. / E1 = 3 => 22 pairs (_) / D3 = 3 => 0 pairs (X) E1,E6: 3.. / E1 = 3 => 22 pairs (_) / E6 = 3 => 0 pairs (X) C7,C8: 4.. / C7 = 4 => 13 pairs (_) / C8 = 4 => 13 pairs (_) I7,I8: 4.. / I7 = 4 => 13 pairs (_) / I8 = 4 => 13 pairs (_) C7,I7: 4.. / C7 = 4 => 13 pairs (_) / I7 = 4 => 13 pairs (_) C8,I8: 4.. / C8 = 4 => 13 pairs (_) / I8 = 4 => 13 pairs (_) B4,A6: 5.. / B4 = 5 => 15 pairs (_) / A6 = 5 => 0 pairs (X) D7,E7: 5.. / D7 = 5 => 16 pairs (_) / E7 = 5 => 19 pairs (_) H8,I8: 5.. / H8 = 5 => 9 pairs (_) / I8 = 5 => 0 pairs (X) D5,G5: 5.. / D5 = 5 => 0 pairs (X) / G5 = 5 => 10 pairs (_) H4,H8: 5.. / H4 = 5 => 0 pairs (X) / H8 = 5 => 9 pairs (_) D7,E7: 6.. / D7 = 6 => 19 pairs (_) / E7 = 6 => 16 pairs (_) F2,I2: 6.. / F2 = 6 => 18 pairs (_) / I2 = 6 => 10 pairs (_) E6,E7: 6.. / E6 = 6 => 19 pairs (_) / E7 = 6 => 16 pairs (_) G1,I1: 8.. / G1 = 8 => 10 pairs (_) / I1 = 8 => 10 pairs (_) G9,I9: 8.. / G9 = 8 => 10 pairs (_) / I9 = 8 => 10 pairs (_) G1,G9: 8.. / G1 = 8 => 10 pairs (_) / G9 = 8 => 10 pairs (_) I1,I9: 8.. / I1 = 8 => 10 pairs (_) / I9 = 8 => 10 pairs (_) B4,C4: 9.. / B4 = 9 => 0 pairs (X) / C4 = 9 => 12 pairs (_) B7,C7: 9.. / B7 = 9 => 12 pairs (_) / C7 = 9 => 0 pairs (X) B4,B7: 9.. / B4 = 9 => 0 pairs (X) / B7 = 9 => 12 pairs (_) C4,C7: 9.. / C4 = 9 => 12 pairs (_) / C7 = 9 => 0 pairs (X) * DURATION: 0:00:30.417407 START: 22:30:58.475506 END: 22:31:28.892913 2019-04-30 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,C5,D7,E1,E7,F6,H7,H8) * ..64.7.9...789.41.948.1..7.7...84...46..29.87.827...498....17..6..2789...75943.6. * PAIR E1: 3,5 BLK 2 D3: 3,5,6 # reduction candidate for 3,5 D3: 6 # 22 pairs D3: 3,5 # 19 pairs * PAIR E1: 3,5 ROW 1 A1: 3,5,1,2 # reduction candidate for 3,5 A1: 3,5 # 19 pairs B1: 3,5,1,2 # reduction candidate for 3,5 B1: 3,5 # 14 pairs G1: 3,5,2,8 # reduction candidate for 3,5 G1: 3,5 # 22 pairs I1: 3,5,2,8 # reduction candidate for 3,5 I1: 3,5 => CTR * 2164.789.35789.41.948.1..7.79..84.2.46..29.87582736149829.61734634278951175943268 I1: 2,8 # 10 pairs * PAIR E1: 3,5 COL E E6: 3,5,6 # reduction candidate for 3,5 E6: 6 # 19 pairs E6: 3,5 # 16 pairs * PAIR C5: 1,3 BLK 4 B4: 1,3,5,9 # reduction candidate for 1,3 B4: 1,3 => CTR * 1.6457.9835789241.948.1..7.7.9.84...46..29.875827.614989..617..6..2789..275943861 B4: 5,9 # 10 pairs C4: 1,3,9 # reduction candidate for 1,3 C4: 1,3 => CTR * ..6457.9..5789241.948.1..7.79..84...46..29.875827.61498.9.617.46.42789...75943.6. C4: 9 # 12 pairs A6: 1,3,5 # reduction candidate for 1,3 A6: 1,3 # 15 pairs * PAIR C5: 1,3 ROW 5 D5: 1,3,5 # reduction candidate for 1,3 D5: 1,3 # 10 pairs G5: 1,3,5 # reduction candidate for 1,3 G5: 1,3 => CTR * ..64.7.9...789.41.948.1..7.7...84...46.529.87.827.6.498..6.17..6..2789...75943.6. G5: 5 # 10 pairs * PAIR C5: 1,3 COL C C8: 1,3,4 # reduction candidate for 1,3 C8: 4 # 13 pairs C8: 1,3 # 13 pairs * PAIR F6: 5,6 BLK 5 D4: 5,6,1,3 # reduction candidate for 5,6 D4: 5,6 => CTR * ..6457.9.5.789.416948316275759684...4631295871827356498945617..631278954275943.6. D4: 1,3 # 10 pairs E6: 5,6,3 # reduction candidate for 5,6 E6: 5,6 # 22 pairs * PAIR F6: 5,6 ROW 6 G6: 5,6,1,3 # reduction candidate for 5,6 G6: 5,6 => CTR * .16457.9.527896413948312.7.759684...4631295871827356498...617..6.12789.4275943.6. G6: 1,3 # 10 pairs * PAIR F6: 5,6 COL F F2: 5,6,2 # reduction candidate for 5,6 F2: 5,6 # 10 pairs F3: 5,6,2 # reduction candidate for 5,6 F3: 5,6 # 17 pairs * PAIR B8: 1,3 BLK 7 C8: 1,3,4 # reduction candidate for 1,3 C8: 4 # 13 pairs C8: 1,3 # 13 pairs * PAIR B8: 1,3 ROW 8 I8: 1,3,4,5 # reduction candidate for 1,3 I8: 1,3 # 14 pairs I8: 4,5 # 13 pairs * PAIR B8: 1,3 COL B B1: 1,3,2,5 # reduction candidate for 1,3 B1: 1,3 # 13 pairs B4: 1,3,5,9 # reduction candidate for 1,3 B4: 1,3 => CTR * 1.6457.9835789241.948.1..7.7.9.84...46..29.875827.614989..617..6..2789..275943861 B4: 5,9 # 10 pairs * PAIR A9: 1,2 ROW 9 G9: 1,2,8 # reduction candidate for 1,2 G9: 1,2 # 10 pairs I9: 1,2,8 # reduction candidate for 1,2 I9: 1,2 # 10 pairs * PAIR A9: 1,2 COL A A1: 1,2,3,5 # reduction candidate for 1,2 A1: 3,5 # 19 pairs A1: 1,2 # 14 pairs * PAIR D7: 5,6 COL D D3: 5,6,3 # reduction candidate for 5,6 D3: 5,6 # 22 pairs D4: 5,6,1,3 # reduction candidate for 5,6 D4: 5,6 => CTR * ..6457.9.5.789.416948316275759684...4631295871827356498945617..631278954275943.6. D4: 1,3 # 10 pairs * PAIR E7: 5,6 COL E E6: 5,6,3 # reduction candidate for 5,6 E6: 3 => CTR * ..6457.9.5.789.41.94831.275759684...4631295871827356498945617..631278954.75943.6. E6: 5,6 # 22 pairs * PAIR H7: 2,3 BLK 9 I7: 2,3,4 # reduction candidate for 2,3 I7: 4 # 13 pairs I7: 2,3 # 13 pairs * PAIR H7: 2,3 ROW 7 B7: 2,3,9 # reduction candidate for 2,3 B7: 2,3 => CTR * ..6457.9..5789241.948.1..7.79..84...46..29.875827.61498.9.617.46.42789...75943.6. B7: 9 # 12 pairs * PAIR H7: 2,3 COL H H4: 2,3,5 # reduction candidate for 2,3 H4: 5 => CTR * ..64.7.9...789.41.948.1..7.7...84.5.46.529.875827.61498..6.17..6..2789...75943.6. H4: 2,3 # 9 pairs * PAIR H8: 3,5 BLK 9 I8: 3,5,1,4 # reduction candidate for 3,5 I8: 3,5 # 15 pairs I8: 1,4 # 12 pairs * PAIR H8: 3,5 COL H H4: 3,5,2 # reduction candidate for 3,5 H4: 3,5 # 13 pairs H4: 2 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060420-absurd-base-pr-000.dot * REASONING * DIS # I1: 3,5 => CTR => I1: 2,8 * DIS # B4: 1,3 => CTR => B4: 5,9 * DIS # C4: 1,3 => CTR => C4: 9 * DIS # G5: 1,3 => CTR => G5: 5 * DIS # D4: 5,6 => CTR => D4: 1,3 * DIS # G6: 5,6 => CTR => G6: 1,3 * DIS # B4: 1,3 => CTR => B4: 5,9 * DIS # D4: 5,6 => CTR => D4: 1,3 * DIS # E6: 3 => CTR => E6: 5,6 * DIS # B7: 2,3 => CTR => B7: 9 * DIS # H4: 5 => CTR => H4: 2,3 * CNT 11 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,C5,D7,E1,E7,F6,H7,H8) * ..64.7.9...789.41.948.1..7.7...84...46..29.87.827...498....17..6..2789...75943.6. * PAIR E1: 3,5 BLK 2 D3: 3,5,6 # reduction candidate for 3,5 D3: 6 # 22 pairs D3: 3,5 # 19 pairs * PAIR E1: 3,5 ROW 1 A1: 3,5,1,2 # reduction candidate for 3,5 A1: 3,5 # 19 pairs B1: 3,5,1,2 # reduction candidate for 3,5 B1: 3,5 # 14 pairs G1: 3,5,2,8 # reduction candidate for 3,5 G1: 3,5 # 22 pairs I1: 3,5,2,8 # reduction candidate for 3,5 I1: 3,5 => CTR * 2164.789.35789.41.948.1..7.79..84.2.46..29.87582736149829.61734634278951175943268 * PAIR E1: 3,5 COL E E6: 3,5,6 # reduction candidate for 3,5 E6: 6 => SOLVED * 516437298327896415948512673759384126463129587182765349894651732631278954275943861 * DURATION: 0:00:06.241510 START: 22:31:59.032234 END: 22:32:05.273744 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060420-absurd-base-pr-001.dot * REASONING * DIS # I1: 3,5 => CTR => I1: 2,8 * PRF I1: 2,8 # E6: 6 => SOL * STA I1: 2,8 + E6: 6 * CNT 2 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060420, absurd
Solution
position: 516437298327896415948512673759384126463129587182765349894651732631278954275943861 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 # D3: 3,5 => UNS * INC # D3: 6 => UNS * INC # A1: 3,5 => UNS * INC # B1: 3,5 => UNS * INC # G1: 3,5 => UNS * DIS # I1: 3,5 => CTR => I1: 2,8 * INC # I1: 2,8 => UNS * INC # E6: 3,5 => UNS * INC # E6: 6 => UNS * DIS # B4: 1,3 => CTR => B4: 5,9 * INC # B4: 5,9 => UNS * DIS # C4: 1,3 => CTR => C4: 9 * INC # C4: 9 => UNS * INC # A6: 1,3 => UNS * INC # D5: 1,3 => UNS * DIS # G5: 1,3 => CTR => G5: 5 * INC # G5: 5 => UNS * INC # C8: 1,3 => UNS * INC # C8: 4 => UNS * DIS # D4: 5,6 => CTR => D4: 1,3 * INC # D4: 1,3 => UNS * INC # E6: 5,6 => UNS * DIS # G6: 5,6 => CTR => G6: 1,3 * INC # G6: 1,3 => UNS * INC # F2: 5,6 => UNS * INC # F3: 5,6 => UNS * INC # C8: 1,3 => UNS * INC # C8: 4 => UNS * INC # I8: 1,3 => UNS * INC # I8: 4,5 => UNS * INC # B1: 1,3 => UNS * DIS # B4: 1,3 => CTR => B4: 5,9 * INC # B4: 5,9 => UNS * INC # G9: 1,2 => UNS * INC # I9: 1,2 => UNS * INC # A1: 1,2 => UNS * INC # A1: 3,5 => UNS * INC # D3: 5,6 => UNS * DIS # D4: 5,6 => CTR => D4: 1,3 * INC # D4: 1,3 => UNS * INC # E6: 5,6 => UNS * DIS # E6: 3 => CTR => E6: 5,6 * INC # I7: 2,3 => UNS * INC # I7: 4 => UNS * DIS # B7: 2,3 => CTR => B7: 9 * INC # B7: 9 => UNS * INC # H4: 2,3 => UNS * DIS # H4: 5 => CTR => H4: 2,3 * INC # I8: 3,5 => UNS * INC # I8: 1,4 => UNS * INC # H4: 3,5 => UNS * INC # H4: 2 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 3,5 => UNS * INC # D3: 6 => UNS * INC # A1: 3,5 => UNS * INC # B1: 3,5 => UNS * INC # G1: 3,5 => UNS * DIS # I1: 3,5 => CTR => I1: 2,8 * INC I1: 2,8 # E6: 3,5 => UNS * PRF I1: 2,8 # E6: 6 => SOL * STA I1: 2,8 + E6: 6 * CNT 8 HDP CHAINS / 8 HYP OPENED