Analysis of zz-www.sudokuoftheday.co.uk-20060802-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: ..6.3.....8.4.67......91........514........8...5.8..6..4.9....19.1..847.63...489. initial
Autosolve
position: ..683...4.8.4.67....4.916.8....7514.....4..8.4.5.8..6..4.96...19.13.847663..1489. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,7 => CTR => A3: 2,3 * PRF # G5: 3,9 => SOL * PRF # A7: 2,5 => SOL * DIS # A7: 7,8 => CTR => A7: 2,5 * DIS # B1: 2,5 => CTR => B1: 1,7,9 * PRF # A7: 2,7 => SOL * DIS # C7: 2,7 => CTR => C7: 8 * PRF # A7: 2,7 => SOL * DIS # C7: 2,7 => CTR => C7: 8 * CNT 9 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5,7 => CTR => A3: 2,3 * PRF A3: 2,3 # B3: 2 => SOL * STA A3: 2,3 + B3: 2 * CNT 2 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6.3.....8.4.67......91........514........8...5.8..6..4.9....19.1..847.63...489. | initial |
| ..683...4.8.4.67....4.916.8....7514.....4..8.4.5.8..6..4.96...19.13.847663..1489. | autosolve |
| 576832914189456723324791658863275149712649385495183267248967531951328476637514892 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) F1: 2,7 E2: 2,5 D3: 5,7 D4: 2,6 F5: 3,9 D6: 1,2 F6: 3,9 B8: 2,5 C9: 2,7 F7: 2,7 E8: 2,5 D9: 5,7 I9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H2: 1.. / H1 = 1 => 15 pairs (_) / H2 = 1 => 14 pairs (_) D5,D6: 1.. / D5 = 1 => 13 pairs (_) / D6 = 1 => 13 pairs (_) A2,H2: 1.. / A2 = 1 => 15 pairs (_) / H2 = 1 => 14 pairs (_) B6,D6: 1.. / B6 = 1 => 13 pairs (_) / D6 = 1 => 13 pairs (_) F1,E2: 2.. / F1 = 2 => 0 pairs (*) / E2 = 2 => 0 pairs (X) F7,E8: 2.. / F7 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) B8,E8: 2.. / B8 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) C9,I9: 2.. / C9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) E2,E8: 2.. / E2 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) F1,F7: 2.. / F1 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) F5,F6: 3.. / F5 = 3 => 15 pairs (_) / F6 = 3 => 12 pairs (_) G7,H7: 3.. / G7 = 3 => 15 pairs (_) / H7 = 3 => 18 pairs (_) A3,H3: 3.. / A3 = 3 => 16 pairs (_) / H3 = 3 => 16 pairs (_) E2,D3: 5.. / E2 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) G5,I5: 5.. / G5 = 5 => 15 pairs (_) / I5 = 5 => 0 pairs (*) A7,B8: 5.. / A7 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) E8,D9: 5.. / E8 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) B8,E8: 5.. / B8 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) D9,I9: 5.. / D9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) D3,D9: 5.. / D3 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) E2,E8: 5.. / E2 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) B4,B5: 6.. / B4 = 6 => 13 pairs (_) / B5 = 6 => 14 pairs (_) D4,D5: 6.. / D4 = 6 => 14 pairs (_) / D5 = 6 => 13 pairs (_) B4,D4: 6.. / B4 = 6 => 13 pairs (_) / D4 = 6 => 14 pairs (_) B5,D5: 6.. / B5 = 6 => 14 pairs (_) / D5 = 6 => 13 pairs (_) F1,D3: 7.. / F1 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) I5,I6: 7.. / I5 = 7 => 19 pairs (_) / I6 = 7 => 13 pairs (_) F7,D9: 7.. / F7 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) B6,I6: 7.. / B6 = 7 => 19 pairs (_) / I6 = 7 => 13 pairs (_) C9,D9: 7.. / C9 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) D3,D9: 7.. / D3 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) F1,F7: 7.. / F1 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) A4,C4: 8.. / A4 = 8 => 13 pairs (_) / C4 = 8 => 0 pairs (X) A7,C7: 8.. / A7 = 8 => 0 pairs (X) / C7 = 8 => 13 pairs (_) A4,A7: 8.. / A4 = 8 => 13 pairs (_) / A7 = 8 => 0 pairs (X) C4,C7: 8.. / C4 = 8 => 0 pairs (X) / C7 = 8 => 13 pairs (_) B1,C2: 9.. / B1 = 9 => 19 pairs (_) / C2 = 9 => 15 pairs (_) G1,I2: 9.. / G1 = 9 => 15 pairs (_) / I2 = 9 => 19 pairs (_) F5,F6: 9.. / F5 = 9 => 12 pairs (_) / F6 = 9 => 15 pairs (_) B1,G1: 9.. / B1 = 9 => 19 pairs (_) / G1 = 9 => 15 pairs (_) C2,I2: 9.. / C2 = 9 => 15 pairs (_) / I2 = 9 => 19 pairs (_) * DURATION: 0:00:46.611923 START: 01:30:03.637878 END: 01:30:50.249801 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C9,D3,D4,D6,D9,E2,E8,F1,F5,F6,F7,I9) * ..683...4.8.4.67....4.916.8....7514.....4..8.4.5.8..6..4.96...19.13.847663..1489. * PAIR F1: 2,7 ROW 1 A1: 2,7,1,5 # reduction candidate for 2,7 A1: 2,7 # 16 pairs B1: 2,7,1,5,9 # reduction candidate for 2,7 B1: 2,7 # 23 pairs * PAIR E2: 2,5 ROW 2 A2: 2,5,1,3 # reduction candidate for 2,5 A2: 2,5 # 17 pairs H2: 2,5,1,3 # reduction candidate for 2,5 H2: 2,5 # 18 pairs I2: 2,5,3,9 # reduction candidate for 2,5 I2: 2,5 # 20 pairs * PAIR D3: 5,7 ROW 3 A3: 5,7,2,3 # reduction candidate for 5,7 A3: 5,7 => CTR * .96832514183456729524791638.69275143372.4..854.5.83.67.4.967351951328476637514892 A3: 2,3 # 14 pairs B3: 5,7,2 # reduction candidate for 5,7 B3: 5,7 # 16 pairs * PAIR D4: 2,6 BLK 5 D5: 2,6,1 # reduction candidate for 2,6 D5: 2,6 # 13 pairs D5: 1 # 13 pairs * PAIR D4: 2,6 ROW 4 B4: 2,6,9 # reduction candidate for 2,6 B4: 9 # 19 pairs B4: 2,6 # 16 pairs * PAIR F5: 3,9 ROW 5 C5: 3,9,2,7 # reduction candidate for 3,9 C5: 3,9 # 15 pairs G5: 3,9,2,5 # reduction candidate for 3,9 G5: 3,9 => SOLVED * 576832914189456723324791658863275149712649385495183267248967531951328476637514892 G5: 2,5 # 14 pairs I5: 3,9,2,5,7 # reduction candidate for 3,9 I5: 3,9 # 18 pairs * PAIR D6: 1,2 BLK 5 D5: 1,2,6 # reduction candidate for 1,2 D5: 1,2 # 14 pairs D5: 6 # 13 pairs * PAIR D6: 1,2 ROW 6 B6: 1,2,7,9 # reduction candidate for 1,2 B6: 7,9 # 15 pairs B6: 1,2 # 15 pairs * PAIR F6: 3,9 ROW 6 G6: 3,9,2 # reduction candidate for 3,9 G6: 3,9 # 15 pairs I6: 3,9,2,7 # reduction candidate for 3,9 I6: 3,9 # 24 pairs * PAIR B8: 2,5 BLK 7 A7: 2,5,7,8 # reduction candidate for 2,5 A7: 2,5 => SOLVED * 576832914189456723324791658863275149712649385495183267248967531951328476637514892 A7: 7,8 => CTR * .768329141894567233247916.8..8.7514.....4..854.5.8..67842967..1951328476637514892 * PAIR B8: 2,5 COL B B1: 2,5,1,7,9 # reduction candidate for 2,5 B1: 2,5 => CTR * ..683.9.4.894.67...745916.8....7514.....4..8.4.5.8..67.4.96...19.135847663.714895 B1: 1,7,9 # 13 pairs B3: 2,5,7 # reduction candidate for 2,5 B3: 2,5 # 15 pairs * PAIR C9: 2,7 BLK 7 A7: 2,7,5,8 # reduction candidate for 2,7 A7: 2,7 => SOLVED * 576832914189456723324791658863275149712649385495183267248967531951328476637514892 A7: 5,8 # 14 pairs C7: 2,7,8 # reduction candidate for 2,7 C7: 2,7 => CTR * .768329141894567233247916.8..8.7514.....4..854.5.8..67842967..1951328476637514892 C7: 8 # 13 pairs * PAIR C9: 2,7 COL C C5: 2,7,3,9 # reduction candidate for 2,7 C5: 2,7 # 16 pairs C5: 3,9 # 15 pairs * PAIR F7: 2,7 ROW 7 A7: 2,7,5,8 # reduction candidate for 2,7 A7: 2,7 => SOLVED * 576832914189456723324791658863275149712649385495183267248967531951328476637514892 A7: 5,8 # 14 pairs C7: 2,7,8 # reduction candidate for 2,7 C7: 2,7 => CTR * .768329141894567233247916.8..8.7514.....4..854.5.8..67842967..1951328476637514892 C7: 8 # 13 pairs * PAIR I9: 2,5 BLK 9 G7: 2,5,3 # reduction candidate for 2,5 G7: 2,5 # 18 pairs H7: 2,5,3 # reduction candidate for 2,5 H7: 2,5 # 15 pairs * PAIR I9: 2,5 COL I I2: 2,5,3,9 # reduction candidate for 2,5 I2: 2,5 # 20 pairs I5: 2,5,3,7,9 # reduction candidate for 2,5 I5: 2,5 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060802-absurd-base-pr-000.dot * REASONING * DIS # A3: 5,7 => CTR => A3: 2,3 * PRF # G5: 3,9 => SOL * PRF # A7: 2,5 => SOL * DIS # A7: 7,8 => CTR => A7: 2,5 * DIS # B1: 2,5 => CTR => B1: 1,7,9 * PRF # A7: 2,7 => SOL * DIS # C7: 2,7 => CTR => C7: 8 * PRF # A7: 2,7 => SOL * DIS # C7: 2,7 => CTR => C7: 8 * CNT 9 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C9,D3,D4,D6,D9,E2,E8,F1,F5,F6,F7,I9) * ..683...4.8.4.67....4.916.8....7514.....4..8.4.5.8..6..4.96...19.13.847663..1489. * PAIR F1: 2,7 ROW 1 A1: 2,7,1,5 # reduction candidate for 2,7 A1: 2,7 # 16 pairs B1: 2,7,1,5,9 # reduction candidate for 2,7 B1: 2,7 # 23 pairs * PAIR E2: 2,5 ROW 2 A2: 2,5,1,3 # reduction candidate for 2,5 A2: 2,5 # 17 pairs H2: 2,5,1,3 # reduction candidate for 2,5 H2: 2,5 # 18 pairs I2: 2,5,3,9 # reduction candidate for 2,5 I2: 2,5 # 20 pairs * PAIR D3: 5,7 ROW 3 A3: 5,7,2,3 # reduction candidate for 5,7 A3: 5,7 => CTR * .96832514183456729524791638.69275143372.4..854.5.83.67.4.967351951328476637514892 B3: 5,7,2 # reduction candidate for 5,7 B3: 5,7 # 16 pairs * RESTART * PAIR D3: 5,7 ROW 3 B3: 5,7,2 # reduction candidate for 5,7 B3: 2 => SOLVED * 576832914189456723324791658863275149712649385495183267248967531951328476637514892 * DURATION: 0:00:06.609076 START: 01:31:15.911256 END: 01:31:22.520332 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060802-absurd-base-pr-001.dot * REASONING * DIS # A3: 5,7 => CTR => A3: 2,3 * PRF A3: 2,3 # B3: 2 => SOL * STA A3: 2,3 + B3: 2 * CNT 2 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060802, absurd
Solution
position: 576832914189456723324791658863275149712649385495183267248967531951328476637514892 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 # A1: 2,7 => UNS * INC # B1: 2,7 => UNS * INC # A2: 2,5 => UNS * INC # H2: 2,5 => UNS * INC # I2: 2,5 => UNS * DIS # A3: 5,7 => CTR => A3: 2,3 * INC # A3: 2,3 => UNS * INC # B3: 5,7 => UNS * INC # D5: 2,6 => UNS * INC # D5: 1 => UNS * INC # B4: 2,6 => UNS * INC # B4: 9 => UNS * INC # C5: 3,9 => UNS * PRF # G5: 3,9 => SOL * INC # G5: 2,5 => UNS * INC # I5: 3,9 => UNS * INC # D5: 1,2 => UNS * INC # D5: 6 => UNS * INC # B6: 1,2 => UNS * INC # B6: 7,9 => UNS * INC # G6: 3,9 => UNS * INC # I6: 3,9 => UNS * PRF # A7: 2,5 => SOL * DIS # A7: 7,8 => CTR => A7: 2,5 * DIS # B1: 2,5 => CTR => B1: 1,7,9 * INC # B1: 1,7,9 => UNS * INC # B3: 2,5 => UNS * PRF # A7: 2,7 => SOL * INC # A7: 5,8 => UNS * DIS # C7: 2,7 => CTR => C7: 8 * INC # C7: 8 => UNS * INC # C5: 2,7 => UNS * INC # C5: 3,9 => UNS * PRF # A7: 2,7 => SOL * INC # A7: 5,8 => UNS * DIS # C7: 2,7 => CTR => C7: 8 * INC # C7: 8 => UNS * INC # G7: 2,5 => UNS * INC # H7: 2,5 => UNS * INC # I2: 2,5 => UNS * INC # I5: 2,5 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,7 => UNS * INC # B1: 2,7 => UNS * INC # A2: 2,5 => UNS * INC # H2: 2,5 => UNS * INC # I2: 2,5 => UNS * DIS # A3: 5,7 => CTR => A3: 2,3 * INC A3: 2,3 # B3: 5,7 => UNS * INC A3: 2,3 # B3: 5,7 => UNS * PRF A3: 2,3 # B3: 2 => SOL * STA A3: 2,3 + B3: 2 * CNT 9 HDP CHAINS / 9 HYP OPENED