Analysis of zz-www.sudokuoftheday.co.uk-20190123-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: 1......7..5.8....97.95.46....2....3.....4.95........46943.8...7...1.....6....7..2 initial
Autosolve
position: 1......7..5.87...97.95.46.34.2...73.....4.95.......246943.8...7...1.....6..4.7..2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 6,8 => CTR => B1: 2,3 * DIS # C1: 8 => CTR => C1: 4,6 * DIS # H3: 1 => CTR => H3: 2,8 * PRF # B8: 2,8 => SOL * DIS # H3: 8 => CTR => H3: 1,2 * DIS # G1: 4,5 => CTR => G1: 8 * DIS # H3: 8 => CTR => H3: 1,2 * PRF # A6: 3,8 => SOL * DIS # F5: 3,8 => CTR => F5: 1,2,6 * DIS # E4: 6,9 => CTR => E4: 1,5 * DIS # F4: 6,9 => CTR => F4: 1,5,8 * DIS # B4: 1,8 => CTR => B4: 6,9 * DIS # B4: 1,8 => CTR => B4: 6,9 * DIS # B5: 1,8 => CTR => B5: 3,6,7 * PRF # C5: 1,8 => SOL * DIS # F5: 1,8 => CTR => F5: 2,3,6 * DIS # B4: 1,8 => CTR => B4: 6,9 * DIS # B5: 1,8 => CTR => B5: 3,6,7 * DIS # B6: 1,8 => CTR => B6: 3,7,9 * DIS # F7: 2,6 => CTR => F7: 5 * DIS # H8: 6 => CTR => H8: 8,9 * CNT 21 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 6,8 => CTR => B1: 2,3 * PRF B1: 2,3 # A6: 3,8 => SOL * STA B1: 2,3 + A6: 3,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1......7..5.8....97.95.46....2....3.....4.95........46943.8...7...1.....6....7..2 | initial |
| 1......7..5.87...97.95.46.34.2...73.....4.95.......246943.8...7...1.....6..4.7..2 | autosolve |
| 134926875256873419789514623492658731361742958875391246943285167527169384618437592 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A2: 2,3 C2: 4,6 B3: 2,8 E3: 1,2 I1: 4,5 G2: 1,4 H2: 1,2 A5: 3,8 D4: 6,9 I4: 1,8 I5: 1,8 B9: 1,8 D7: 2,6 G7: 1,5 H7: 1,6 I8: 4,5 H9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,E3: 1.. / F2 = 1 => 0 pairs (X) / E3 = 1 => 19 pairs (_) I4,I5: 1.. / I4 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) B9,C9: 1.. / B9 = 1 => 17 pairs (_) / C9 = 1 => 0 pairs (X) G7,H7: 1.. / G7 = 1 => 20 pairs (_) / H7 = 1 => 0 pairs (X) E3,H3: 1.. / E3 = 1 => 19 pairs (_) / H3 = 1 => 0 pairs (X) G2,G7: 1.. / G2 = 1 => 0 pairs (X) / G7 = 1 => 20 pairs (_) E1,E3: 2.. / E1 = 2 => 19 pairs (_) / E3 = 2 => 0 pairs (X) H2,H3: 2.. / H2 = 2 => 17 pairs (_) / H3 = 2 => 0 pairs (*) D5,F5: 2.. / D5 = 2 => 0 pairs (X) / F5 = 2 => 17 pairs (_) A8,B8: 2.. / A8 = 2 => 17 pairs (_) / B8 = 2 => 0 pairs (*) D7,F7: 2.. / D7 = 2 => 17 pairs (_) / F7 = 2 => 0 pairs (X) B1,E1: 2.. / B1 = 2 => 0 pairs (X) / E1 = 2 => 19 pairs (_) A2,H2: 2.. / A2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) A2,A8: 2.. / A2 = 2 => 0 pairs (*) / A8 = 2 => 0 pairs (X) D5,D7: 2.. / D5 = 2 => 0 pairs (X) / D7 = 2 => 17 pairs (_) F5,F7: 2.. / F5 = 2 => 17 pairs (_) / F7 = 2 => 0 pairs (X) B1,A2: 3.. / B1 = 3 => 0 pairs (*) / A2 = 3 => 0 pairs (X) G8,G9: 3.. / G8 = 3 => 18 pairs (_) / G9 = 3 => 19 pairs (_) A2,F2: 3.. / A2 = 3 => 17 pairs (_) / F2 = 3 => 0 pairs (*) E9,G9: 3.. / E9 = 3 => 18 pairs (_) / G9 = 3 => 19 pairs (_) C1,C2: 4.. / C1 = 4 => 20 pairs (_) / C2 = 4 => 0 pairs (X) G8,I8: 4.. / G8 = 4 => 0 pairs (X) / I8 = 4 => 16 pairs (_) C2,G2: 4.. / C2 = 4 => 0 pairs (X) / G2 = 4 => 20 pairs (_) I1,I8: 4.. / I1 = 4 => 0 pairs (X) / I8 = 4 => 16 pairs (_) G1,I1: 5.. / G1 = 5 => 0 pairs (X) / I1 = 5 => 16 pairs (_) A6,C6: 5.. / A6 = 5 => 18 pairs (_) / C6 = 5 => 0 pairs (*) E4,F4: 5.. / E4 = 5 => 18 pairs (_) / F4 = 5 => 0 pairs (X) F7,G7: 5.. / F7 = 5 => 20 pairs (_) / G7 = 5 => 0 pairs (X) A6,A8: 5.. / A6 = 5 => 18 pairs (_) / A8 = 5 => 0 pairs (*) I1,I8: 5.. / I1 = 5 => 16 pairs (_) / I8 = 5 => 0 pairs (X) H7,H8: 6.. / H7 = 6 => 20 pairs (_) / H8 = 6 => 0 pairs (X) C2,F2: 6.. / C2 = 6 => 20 pairs (_) / F2 = 6 => 0 pairs (X) D5,D6: 7.. / D5 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) B8,C8: 7.. / B8 = 7 => 18 pairs (_) / C8 = 7 => 0 pairs (*) G1,H3: 8.. / G1 = 8 => 20 pairs (_) / H3 = 8 => 0 pairs (X) I4,I5: 8.. / I4 = 8 => 15 pairs (_) / I5 = 8 => 0 pairs (*) B3,H3: 8.. / B3 = 8 => 20 pairs (_) / H3 = 8 => 0 pairs (X) B4,B6: 9.. / B4 = 9 => 19 pairs (_) / B6 = 9 => 19 pairs (_) H8,H9: 9.. / H8 = 9 => 19 pairs (_) / H9 = 9 => 18 pairs (_) E9,H9: 9.. / E9 = 9 => 19 pairs (_) / H9 = 9 => 18 pairs (_) * DURATION: 0:00:45.187853 START: 03:09:09.466050 END: 03:09:54.653903 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,B9,C2,D4,D7,E3,G2,G7,H2,H7,H9,I1,I4,I5,I8) * 1......7..5.87...97.95.46.34.2...73.....4.95.......246943.8...7...1.....6..4.7..2 * PAIR A2: 2,3 BLK 1 B1: 2,3,6,8 # reduction candidate for 2,3 B1: 6,8 => CTR * 1...2..7.35.8761297295146834.2.6.73.8...4.9515....8246943.8..172..1...6.6..4.7.92 B1: 2,3 # 20 pairs * PAIR C2: 4,6 BLK 1 C1: 4,6,8 # reduction candidate for 4,6 C1: 8 => CTR * 168.2.4753548761297295146834.2.6573.8.6.4.9515.....246943.8.5172..1...646..4.7.92 C1: 4,6 # 21 pairs * PAIR B3: 2,8 BLK 1 B1: 2,8,3,6 # reduction candidate for 2,8 B1: 2,8 # 23 pairs B1: 3,6 # 21 pairs * PAIR B3: 2,8 ROW 3 H3: 2,8,1 # reduction candidate for 2,8 H3: 1 => CTR * 124...8753568714297895246134.2...73.8...4.9515.17.824694328516727.1....461.4.7..2 H3: 2,8 # 19 pairs * PAIR B3: 2,8 COL B B8: 2,8,7 # reduction candidate for 2,8 B8: 2,8 => SOLVED * 134926875256873419789514623492658731361742958875391246943285167527169384618437592 B8: 7 # 18 pairs * PAIR E3: 1,2 ROW 3 H3: 1,2,8 # reduction candidate for 1,2 H3: 8 => CTR * 1...2..7.35.8761297295146834.2.6573.8...4.9515.....246943.8..172..1...6.6..4.7.92 H3: 1,2 # 20 pairs * PAIR I1: 4,5 BLK 3 G1: 4,5,8 # reduction candidate for 4,5 G1: 4,5 => CTR * 1...2..7.35.8761297295146834.2.6573.8...4.9515.....246943.8..172..1...6.6..4.7.92 G1: 8 # 20 pairs * PAIR H2: 1,2 BLK 3 H3: 1,2,8 # reduction candidate for 1,2 H3: 8 => CTR * 1...2..7.35.8761297295146834.2.6573.8...4.9515.....246943.8..172..1...6.6..4.7.92 H3: 1,2 # 20 pairs * PAIR A5: 3,8 BLK 4 B5: 3,8,1,6,7 # reduction candidate for 3,8 B5: 3,8 # 20 pairs A6: 3,8,5 # reduction candidate for 3,8 A6: 3,8 => SOLVED * 134926875256873419789514623492658731361742958875391246943285167527169384618437592 A6: 5 # 18 pairs B6: 3,8,1,7,9 # reduction candidate for 3,8 B6: 3,8 # 22 pairs * PAIR A5: 3,8 ROW 5 F5: 3,8,1,2,6 # reduction candidate for 3,8 F5: 3,8 => CTR * 1..3...7535.87.1297.95146834.29..73.8..24395....7..246943682517...1...646..4.7.92 F5: 1,2,6 # 17 pairs * PAIR D4: 6,9 BLK 5 E4: 6,9,1,5 # reduction candidate for 6,9 E4: 6,9 => CTR * 1...2.4753548761297295146834.2.6573.8...4.9515.....246943.8.5172..1...646..4.7.92 E4: 1,5 # 18 pairs F4: 6,9,1,5,8 # reduction candidate for 6,9 F4: 6,9 => CTR * 1.8....7..548761297295146834.265973...6.4.95..9..3.24694328...7...1.....6..4.7..2 F4: 1,5,8 # 17 pairs * PAIR D4: 6,9 ROW 4 B4: 6,9,1,8 # reduction candidate for 6,9 B4: 1,8 => CTR * 1.8.2..7..548761297295146834.2...73...6742951.97...246943.8...7...1.....6..4.7..2 B4: 6,9 # 19 pairs * PAIR D4: 6,9 COL D D1: 6,9,3 # reduction candidate for 6,9 D1: 6,9 # 21 pairs D1: 3 # 20 pairs * PAIR I4: 1,8 ROW 4 B4: 1,8,6,9 # reduction candidate for 1,8 B4: 1,8 => CTR * 1.8.2..7..548761297295146834.2...73...6742951.97...246943.8...7...1.....6..4.7..2 B4: 6,9 # 19 pairs F4: 1,8,5,6,9 # reduction candidate for 1,8 F4: 1,8 # 20 pairs * PAIR I5: 1,8 ROW 5 B5: 1,8,3,6,7 # reduction candidate for 1,8 B5: 1,8 => CTR * 1......7..5.87...97.95.46.34.2...73.....4.95.......246943.8...7...1.....6..4.7..2 B5: 3,6,7 # 17 pairs C5: 1,8,6,7 # reduction candidate for 1,8 C5: 1,8 => SOLVED * 134926875256873419789514623492658731361742958875391246943285167527169384618437592 C5: 6,7 # 18 pairs F5: 1,8,2,3,6 # reduction candidate for 1,8 F5: 1,8 => CTR * 1..3...7535.87.1297.95146834.29..73.83.24.95....7..246943682517...1...646..4.7.92 F5: 2,3,6 # 17 pairs * PAIR B9: 1,8 BLK 7 C9: 1,8,5 # reduction candidate for 1,8 C9: 1,8 # 23 pairs C9: 5 # 21 pairs * PAIR B9: 1,8 COL B B4: 1,8,6,9 # reduction candidate for 1,8 B4: 1,8 => CTR * 1.8.2..7..548761297295146834.2...73...6742951.97...246943.8...7...1.....6..4.7..2 B4: 6,9 # 19 pairs B5: 1,8,3,6,7 # reduction candidate for 1,8 B5: 1,8 => CTR * 1......7..5.87...97.95.46.34.2...73.....4.95.......246943.8...7...1.....6..4.7..2 B5: 3,6,7 # 17 pairs B6: 1,8,3,7,9 # reduction candidate for 1,8 B6: 1,8 => CTR * 1.8.2..7..548761297.95.46.34926..73.....4295.......24694328...7...1.....6..4.7..2 B6: 3,7,9 # 17 pairs * PAIR D7: 2,6 BLK 8 F7: 2,6,5 # reduction candidate for 2,6 F7: 2,6 => CTR * 1...2.4753548761297295146834.2.6573.8...4.9515.....246943.8.5172..1...646..4.7.92 F7: 5 # 20 pairs * PAIR D7: 2,6 COL D D5: 2,6,3,7 # reduction candidate for 2,6 D5: 2,6 # 24 pairs D5: 3,7 # 18 pairs * PAIR I8: 4,5 BLK 9 G8: 4,5,3,8 # reduction candidate for 4,5 G8: 4,5 # 19 pairs G8: 3,8 # 17 pairs * PAIR H9: 8,9 BLK 9 H8: 8,9,6 # reduction candidate for 8,9 H8: 6 => CTR * 1...2.4753548761297295146834.2.6573.8...4.9515.....246943.8.5172..1...646..4.7.92 H8: 8,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190123-absurd-base-pr-000.dot * REASONING * DIS # B1: 6,8 => CTR => B1: 2,3 * DIS # C1: 8 => CTR => C1: 4,6 * DIS # H3: 1 => CTR => H3: 2,8 * PRF # B8: 2,8 => SOL * DIS # H3: 8 => CTR => H3: 1,2 * DIS # G1: 4,5 => CTR => G1: 8 * DIS # H3: 8 => CTR => H3: 1,2 * PRF # A6: 3,8 => SOL * DIS # F5: 3,8 => CTR => F5: 1,2,6 * DIS # E4: 6,9 => CTR => E4: 1,5 * DIS # F4: 6,9 => CTR => F4: 1,5,8 * DIS # B4: 1,8 => CTR => B4: 6,9 * DIS # B4: 1,8 => CTR => B4: 6,9 * DIS # B5: 1,8 => CTR => B5: 3,6,7 * PRF # C5: 1,8 => SOL * DIS # F5: 1,8 => CTR => F5: 2,3,6 * DIS # B4: 1,8 => CTR => B4: 6,9 * DIS # B5: 1,8 => CTR => B5: 3,6,7 * DIS # B6: 1,8 => CTR => B6: 3,7,9 * DIS # F7: 2,6 => CTR => F7: 5 * DIS # H8: 6 => CTR => H8: 8,9 * CNT 21 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,B9,C2,D4,D7,E3,G2,G7,H2,H7,H9,I1,I4,I5,I8) * 1......7..5.87...97.95.46.34.2...73.....4.95.......246943.8...7...1.....6..4.7..2 * PAIR A2: 2,3 BLK 1 B1: 2,3,6,8 # reduction candidate for 2,3 B1: 6,8 => CTR * 1...2..7.35.8761297295146834.2.6.73.8...4.9515....8246943.8..172..1...6.6..4.7.92 * PAIR A5: 3,8 BLK 4 A6: 3,8,5 # reduction candidate for 3,8 A6: 3,8 => SOLVED * 134926875256873419789514623492658731361742958875391246943285167527169384618437592 * DURATION: 0:00:03.412605 START: 03:10:27.227900 END: 03:10:30.640505 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190123-absurd-base-pr-001.dot * REASONING * DIS # B1: 6,8 => CTR => B1: 2,3 * PRF B1: 2,3 # A6: 3,8 => SOL * STA B1: 2,3 + A6: 3,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190123, absurd
Solution
position: 134926875256873419789514623492658731361742958875391246943285167527169384618437592 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 # B1: 2,3 => UNS * DIS # B1: 6,8 => CTR => B1: 2,3 * INC # C1: 4,6 => UNS * DIS # C1: 8 => CTR => C1: 4,6 * INC # B1: 2,8 => UNS * INC # B1: 3,6 => UNS * INC # H3: 2,8 => UNS * DIS # H3: 1 => CTR => H3: 2,8 * PRF # B8: 2,8 => SOL * INC # B8: 7 => UNS * INC # H3: 1,2 => UNS * DIS # H3: 8 => CTR => H3: 1,2 * DIS # G1: 4,5 => CTR => G1: 8 * INC # G1: 8 => UNS * INC # H3: 1,2 => UNS * DIS # H3: 8 => CTR => H3: 1,2 * INC # B5: 3,8 => UNS * PRF # A6: 3,8 => SOL * INC # A6: 5 => UNS * INC # B6: 3,8 => UNS * DIS # F5: 3,8 => CTR => F5: 1,2,6 * INC # F5: 1,2,6 => UNS * DIS # E4: 6,9 => CTR => E4: 1,5 * INC # E4: 1,5 => UNS * DIS # F4: 6,9 => CTR => F4: 1,5,8 * INC # F4: 1,5,8 => UNS * INC # B4: 6,9 => UNS * DIS # B4: 1,8 => CTR => B4: 6,9 * INC # D1: 6,9 => UNS * INC # D1: 3 => UNS * DIS # B4: 1,8 => CTR => B4: 6,9 * INC # B4: 6,9 => UNS * INC # F4: 1,8 => UNS * DIS # B5: 1,8 => CTR => B5: 3,6,7 * INC # B5: 3,6,7 => UNS * PRF # C5: 1,8 => SOL * INC # C5: 6,7 => UNS * DIS # F5: 1,8 => CTR => F5: 2,3,6 * INC # F5: 2,3,6 => UNS * INC # C9: 1,8 => UNS * INC # C9: 5 => UNS * DIS # B4: 1,8 => CTR => B4: 6,9 * INC # B4: 6,9 => UNS * DIS # B5: 1,8 => CTR => B5: 3,6,7 * INC # B5: 3,6,7 => UNS * DIS # B6: 1,8 => CTR => B6: 3,7,9 * INC # B6: 3,7,9 => UNS * DIS # F7: 2,6 => CTR => F7: 5 * INC # F7: 5 => UNS * INC # D5: 2,6 => UNS * INC # D5: 3,7 => UNS * INC # G8: 4,5 => UNS * INC # G8: 3,8 => UNS * INC # H8: 8,9 => UNS * DIS # H8: 6 => CTR => H8: 8,9 * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 2,3 => UNS * DIS # B1: 6,8 => CTR => B1: 2,3 * PRF B1: 2,3 # A6: 3,8 => SOL * STA B1: 2,3 + A6: 3,8 * CNT 3 HDP CHAINS / 3 HYP OPENED