Analysis of zz-www.sudokuoftheday.co.uk-20190313-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: ..856...95....2...2......45786.5.......7...1....2.6..8.936.....65.3.1...8.7...9.. initial
Autosolve
position: ..856...95....2...2......4578615.....2.7...1....2.6..84936.....652391...8174259.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 2,7 => CTR => G1: 1,3 * PRF # C2: 1,9 => SOL * DIS # C2: 4 => CTR => C2: 1,9 * DIS # F1: 3,7 => CTR => F1: 4 * DIS # F5: 4,8 => CTR => F5: 3,9 * DIS # G5: 3,6 => CTR => G5: 4,5 * DIS # F4: 3,4 => CTR => F4: 9 * PRF # F4: 9 => SOL * DIS # E5: 3,4 => CTR => E5: 8 * PRF # F5: 3,4 => SOL * DIS # H6: 5,7 => CTR => H6: 9 * PRF # H6: 9 => SOL * DIS # G7: 1 => CTR => G7: 2,5 * DIS # G7: 5 => CTR => G7: 1,2 * DIS # I2: 3,6 => CTR => I2: 1,7 * CNT 15 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 # G1: 2,7 => CTR => G1: 1,3 * PRF G1: 1,3 # C2: 1,9 => SOL * STA G1: 1,3 + C2: 1,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..856...95....2...2......45786.5.......7...1....2.6..8.936.....65.3.1...8.7...9.. | initial |
| ..856...95....2...2......4578615.....2.7...1....2.6..84936.....652391...8174259.. | autosolve |
| 378564129541932687269817345786159432924783516135246798493678251652391874817425963 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A1: 1,3 C3: 1,9 D2: 8,9 D3: 8,9 F3: 3,7 A5: 3,9 C5: 4,5 A6: 1,9 B6: 3,4 C6: 1,5 E6: 3,4 G6: 5,7 E7: 7,8 F7: 7,8 H7: 2,5 I7: 1,2 H8: 7,8 I8: 4,7 H9: 3,6 I9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 28 pairs (_) / E3 = 1 => 18 pairs (_) A6,C6: 1.. / A6 = 1 => 0 pairs (*) / C6 = 1 => 0 pairs (X) G7,I7: 1.. / G7 = 1 => 0 pairs (X) / I7 = 1 => 22 pairs (_) A1,G1: 1.. / A1 = 1 => 0 pairs (X) / G1 = 1 => 0 pairs (_) A1,A6: 1.. / A1 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) I2,I7: 1.. / I2 = 1 => 0 pairs (X) / I7 = 1 => 22 pairs (_) G1,H1: 2.. / G1 = 2 => 0 pairs (X) / H1 = 2 => 22 pairs (_) I4,I7: 2.. / I4 = 2 => 22 pairs (_) / I7 = 2 => 0 pairs (X) A5,B6: 3.. / A5 = 3 => 0 pairs (X) / B6 = 3 => 0 pairs (_) H9,I9: 3.. / H9 = 3 => 0 pairs (X) / I9 = 3 => 20 pairs (_) B6,E6: 3.. / B6 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) A1,A5: 3.. / A1 = 3 => 0 pairs (*) / A5 = 3 => 0 pairs (X) F1,E2: 4.. / F1 = 4 => 25 pairs (_) / E2 = 4 => 0 pairs (X) C5,B6: 4.. / C5 = 4 => 0 pairs (*) / B6 = 4 => 0 pairs (X) G8,I8: 4.. / G8 = 4 => 19 pairs (_) / I8 = 4 => 26 pairs (_) B1,F1: 4.. / B1 = 4 => 0 pairs (X) / F1 = 4 => 25 pairs (_) B6,E6: 4.. / B6 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) C2,C5: 4.. / C2 = 4 => 0 pairs (X) / C5 = 4 => 0 pairs (_) C5,C6: 5.. / C5 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) G7,H7: 5.. / G7 = 5 => 0 pairs (X) / H7 = 5 => 21 pairs (_) C5,G5: 5.. / C5 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) H6,H7: 5.. / H6 = 5 => 0 pairs (X) / H7 = 5 => 21 pairs (_) B2,B3: 6.. / B2 = 6 => 19 pairs (_) / B3 = 6 => 20 pairs (_) G5,I5: 6.. / G5 = 6 => 0 pairs (X) / I5 = 6 => 20 pairs (_) H9,I9: 6.. / H9 = 6 => 20 pairs (_) / I9 = 6 => 0 pairs (X) B3,G3: 6.. / B3 = 6 => 20 pairs (_) / G3 = 6 => 19 pairs (_) H2,H9: 6.. / H2 = 6 => 0 pairs (X) / H9 = 6 => 20 pairs (_) G6,H6: 7.. / G6 = 7 => 21 pairs (_) / H6 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 19 pairs (_) / F7 = 7 => 0 pairs (X) I2,I8: 7.. / I2 = 7 => 26 pairs (_) / I8 = 7 => 19 pairs (_) D2,D3: 8.. / D2 = 8 => 0 pairs (X) / D3 = 8 => 18 pairs (_) E5,F5: 8.. / E5 = 8 => 19 pairs (_) / F5 = 8 => 0 pairs (X) E7,F7: 8.. / E7 = 8 => 0 pairs (X) / F7 = 8 => 19 pairs (_) G8,H8: 8.. / G8 = 8 => 19 pairs (_) / H8 = 8 => 20 pairs (_) D3,G3: 8.. / D3 = 8 => 18 pairs (_) / G3 = 8 => 0 pairs (X) E5,E7: 8.. / E5 = 8 => 19 pairs (_) / E7 = 8 => 0 pairs (X) F5,F7: 8.. / F5 = 8 => 0 pairs (X) / F7 = 8 => 19 pairs (_) H2,H8: 8.. / H2 = 8 => 19 pairs (_) / H8 = 8 => 20 pairs (_) C2,C3: 9.. / C2 = 9 => 0 pairs (X) / C3 = 9 => 18 pairs (_) D2,D3: 9.. / D2 = 9 => 18 pairs (_) / D3 = 9 => 0 pairs (X) A5,A6: 9.. / A5 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) F4,F5: 9.. / F4 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) H4,H6: 9.. / H4 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) C2,D2: 9.. / C2 = 9 => 0 pairs (X) / D2 = 9 => 18 pairs (_) C3,D3: 9.. / C3 = 9 => 18 pairs (_) / D3 = 9 => 0 pairs (X) F4,H4: 9.. / F4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) A5,F5: 9.. / A5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) A6,H6: 9.. / A6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) * DURATION: 0:01:11.938107 START: 04:28:47.429271 END: 04:29:59.367378 2019-05-01 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,A6,B6,C3,C5,C6,D2,D3,E6,E7,F3,F7,G6,H7,H8,H9,I7,I8,I9) * ..856...95....2...2......4578615.....2.7...1....2.6..84936.....652391...8174259.. * PAIR A1: 1,3 ROW 1 G1: 1,3,2,7 # reduction candidate for 1,3 G1: 2,7 => CTR * 1.8564..95....2...2.98...4578615....32.7.9.1.941236..84936.8...652391...8174259.. G1: 1,3 # 25 pairs * PAIR C3: 1,9 BLK 1 C2: 1,9,4 # reduction candidate for 1,9 C2: 1,9 => SOLVED * 378564129541932687269817345786159432924783516135246798493678251652391874817425963 C2: 4 => CTR * 1.8564..95.49.2...2.98.3.45786159....257...1..41236..84936.....652391...8174259.. * PAIR F3: 3,7 BLK 2 F1: 3,7,4 # reduction candidate for 3,7 F1: 3,7 => CTR * .4856...95...42...2...1..4578615.....247..516.3.2.6..84936.....652391...8174259.. F1: 4 # 25 pairs E2: 3,7,1,4 # reduction candidate for 3,7 E2: 3,7 # 24 pairs E3: 3,7,1 # reduction candidate for 3,7 E3: 3,7 # 28 pairs * PAIR F3: 3,7 ROW 3 B3: 3,7,6 # reduction candidate for 3,7 B3: 3,7 # 19 pairs G3: 3,7,1,6,8 # reduction candidate for 3,7 G3: 3,7 # 19 pairs * PAIR A5: 3,9 ROW 5 F5: 3,9,4,8 # reduction candidate for 3,9 F5: 4,8 => CTR * 3.856412954...2...26...3845786159.3.92473851613524679849368725.652391...8174259.. F5: 3,9 # 22 pairs * PAIR C5: 4,5 ROW 5 G5: 4,5,3,6 # reduction candidate for 4,5 G5: 3,6 => CTR * 1.8564..95.49.2...2.98.3.45786159....257...1..41236..84936.....652391...8174259.. G5: 4,5 # 23 pairs * PAIR B6: 3,4 COL B B1: 3,4,7 # reduction candidate for 3,4 B1: 3,4 # 25 pairs B2: 3,4,6,7 # reduction candidate for 3,4 B2: 3,4 # 26 pairs * PAIR E6: 3,4 BLK 5 F4: 3,4,9 # reduction candidate for 3,4 F4: 3,4 => CTR * 1.8564..95....2...2.98...4578615..9.325789.1.941236..8493678...652391...8174259.. F4: 9 => SOLVED * 378564129541932687269817345786159432924783516135246798493678251652391874817425963 E5: 3,4,8 # reduction candidate for 3,4 E5: 3,4 => CTR * 3.856412954...2...26..73845786159.3.92473851613524679849368725.652391...8174259.. E5: 8 # 19 pairs F5: 3,4,8,9 # reduction candidate for 3,4 F5: 3,4 => SOLVED * 378564129541932687269817345786159432924783516135246798493678251652391874817425963 F5: 8,9 # 21 pairs * PAIR E6: 3,4 COL E E2: 3,4,1,7 # reduction candidate for 3,4 E2: 1,7 # 28 pairs E2: 3,4 # 17 pairs * PAIR G6: 5,7 BLK 6 H6: 5,7,9 # reduction candidate for 5,7 H6: 5,7 => CTR * 1.8564..95....2...2.98...4578615..9.325789.1.941236..8493678...652391...8174259.. H6: 9 => SOLVED * 378564129541932687269817345786159432924783516135246798493678251652391874817425963 * PAIR H7: 2,5 BLK 9 G7: 2,5,1 # reduction candidate for 2,5 G7: 1 => CTR * 1.8564..95....2..12.981..4578615....32.7.9.1.9412365784936.8152652391.878174259.. G7: 2,5 # 22 pairs * PAIR I7: 1,2 BLK 9 G7: 1,2,5 # reduction candidate for 1,2 G7: 5 => CTR * 1.85642.95.49.2...2.98.3.45786159432.257...1..412367584936..521652391...8174259.. G7: 1,2 # 21 pairs * PAIR H8: 7,8 BLK 9 G8: 7,8,4 # reduction candidate for 7,8 G8: 7,8 # 26 pairs G8: 4 # 19 pairs * PAIR H8: 7,8 COL H H2: 7,8,3,6 # reduction candidate for 7,8 H2: 7,8 # 25 pairs H2: 3,6 # 23 pairs * PAIR I8: 4,7 BLK 9 G8: 4,7,8 # reduction candidate for 4,7 G8: 4,7 # 20 pairs G8: 8 # 19 pairs * PAIR H9: 3,6 COL H H2: 3,6,7,8 # reduction candidate for 3,6 H2: 7,8 # 25 pairs H2: 3,6 # 23 pairs * PAIR I9: 3,6 COL I I2: 3,6,1,7 # reduction candidate for 3,6 I2: 3,6 => CTR * ..8564..95.49.28..2.98.3.457861593.2.2.7...14.4.236..84936....16523914878174259.. I2: 1,7 # 21 pairs I5: 3,6,4 # reduction candidate for 3,6 I5: 3,6 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190313-absurd-base-pr-000.dot * REASONING * DIS # G1: 2,7 => CTR => G1: 1,3 * PRF # C2: 1,9 => SOL * DIS # C2: 4 => CTR => C2: 1,9 * DIS # F1: 3,7 => CTR => F1: 4 * DIS # F5: 4,8 => CTR => F5: 3,9 * DIS # G5: 3,6 => CTR => G5: 4,5 * DIS # F4: 3,4 => CTR => F4: 9 * PRF # F4: 9 => SOL * DIS # E5: 3,4 => CTR => E5: 8 * PRF # F5: 3,4 => SOL * DIS # H6: 5,7 => CTR => H6: 9 * PRF # H6: 9 => SOL * DIS # G7: 1 => CTR => G7: 2,5 * DIS # G7: 5 => CTR => G7: 1,2 * DIS # I2: 3,6 => CTR => I2: 1,7 * CNT 15 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,A6,B6,C3,C5,C6,D2,D3,E6,E7,F3,F7,G6,H7,H8,H9,I7,I8,I9) * ..856...95....2...2......4578615.....2.7...1....2.6..84936.....652391...8174259.. * PAIR A1: 1,3 ROW 1 G1: 1,3,2,7 # reduction candidate for 1,3 G1: 2,7 => CTR * 1.8564..95....2...2.98...4578615....32.7.9.1.941236..84936.8...652391...8174259.. * PAIR RESTART * PAIR C3: 1,9 BLK 1 C2: 1,9,4 # reduction candidate for 1,9 C2: 1,9 => SOLVED * 378564129541932687269817345786159432924783516135246798493678251652391874817425963 * DURATION: 0:00:03.205375 START: 04:30:30.900278 END: 04:30:34.105653 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190313-absurd-base-pr-001.dot * REASONING * DIS # G1: 2,7 => CTR => G1: 1,3 * PRF G1: 1,3 # C2: 1,9 => SOL * STA G1: 1,3 + C2: 1,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190313, absurd
Solution
position: 378564129541932687269817345786159432924783516135246798493678251652391874817425963 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 # G1: 1,3 => UNS * DIS # G1: 2,7 => CTR => G1: 1,3 * PRF # C2: 1,9 => SOL * DIS # C2: 4 => CTR => C2: 1,9 * DIS # F1: 3,7 => CTR => F1: 4 * INC # F1: 4 => UNS * INC # E2: 3,7 => UNS * INC # E3: 3,7 => UNS * INC # B3: 3,7 => UNS * INC # G3: 3,7 => UNS * INC # F5: 3,9 => UNS * DIS # F5: 4,8 => CTR => F5: 3,9 * INC # G5: 4,5 => UNS * DIS # G5: 3,6 => CTR => G5: 4,5 * INC # B1: 3,4 => UNS * INC # B2: 3,4 => UNS * DIS # F4: 3,4 => CTR => F4: 9 * PRF # F4: 9 => SOL * DIS # E5: 3,4 => CTR => E5: 8 * INC # E5: 8 => UNS * PRF # F5: 3,4 => SOL * INC # F5: 8,9 => UNS * INC # E2: 3,4 => UNS * INC # E2: 1,7 => UNS * DIS # H6: 5,7 => CTR => H6: 9 * PRF # H6: 9 => SOL * INC # G7: 2,5 => UNS * DIS # G7: 1 => CTR => G7: 2,5 * INC # G7: 1,2 => UNS * DIS # G7: 5 => CTR => G7: 1,2 * INC # G8: 7,8 => UNS * INC # G8: 4 => UNS * INC # H2: 7,8 => UNS * INC # H2: 3,6 => UNS * INC # G8: 4,7 => UNS * INC # G8: 8 => UNS * INC # H2: 3,6 => UNS * INC # H2: 7,8 => UNS * DIS # I2: 3,6 => CTR => I2: 1,7 * INC # I2: 1,7 => UNS * INC # I5: 3,6 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 1,3 => UNS * DIS # G1: 2,7 => CTR => G1: 1,3 * PRF G1: 1,3 # C2: 1,9 => SOL * STA G1: 1,3 + C2: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED