Analysis of zz-www.sudokuoftheday.co.uk-20190302-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: 8.7..26.3.5........31...8........7....9..6...7...48..2.7......9...6.1.451.2...... initial
Autosolve
position: 8.7..26.3.5........31...8........7....97.6...7...48..2.7....1.9...6712451.2...3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 1,5 => CTR => D1: 4,9 * PRF # A2: 4,6 => SOL * DIS # C4: 4,6 => CTR => C4: 3,5,8 * DIS # D2: 4,9 => CTR => D2: 1,3,8 * DIS # F2: 4,9 => CTR => F2: 3,7 * DIS # B4: 1,6 => CTR => B4: 2,4,8 * DIS # C4: 4,5,6 => CTR => C4: 3,8 * DIS # D7: 3,4 => CTR => D7: 2,8 * CNT 8 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 # D1: 1,5 => CTR => D1: 4,9 * PRF D1: 4,9 # A2: 4,6 => SOL * STA D1: 4,9 + A2: 4,6 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.7..26.3.5........31...8........7....9..6...7...48..2.7......9...6.1.451.2...... | initial |
| 8.7..26.3.5........31...8........7....97.6...7...48..2.7....1.9...6712451.2...3.. | autosolve |
| 897412653654837921231965874548129736329756418716348592475283169983671245162594387 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B1: 4,9 C2: 4,6 G2: 4,9 I3: 4,7 B6: 1,6 G5: 4,5 G6: 5,9 A8: 3,9 B8: 8,9 C8: 3,8 B9: 4,6 F7: 3,4 H7: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 2.. / A2 = 2 => 14 pairs (_) / A3 = 2 => 15 pairs (_) H2,H3: 2.. / H2 = 2 => 15 pairs (_) / H3 = 2 => 14 pairs (_) B4,B5: 2.. / B4 = 2 => 14 pairs (_) / B5 = 2 => 13 pairs (_) D7,E7: 2.. / D7 = 2 => 14 pairs (_) / E7 = 2 => 13 pairs (_) A2,H2: 2.. / A2 = 2 => 14 pairs (_) / H2 = 2 => 15 pairs (_) A3,H3: 2.. / A3 = 2 => 15 pairs (_) / H3 = 2 => 14 pairs (_) B5,E5: 2.. / B5 = 2 => 13 pairs (_) / E5 = 2 => 14 pairs (_) D4,D7: 2.. / D4 = 2 => 13 pairs (_) / D7 = 2 => 14 pairs (_) A8,C8: 3.. / A8 = 3 => 0 pairs (X) / C8 = 3 => 13 pairs (_) B1,D1: 4.. / B1 = 4 => 0 pairs (X) / D1 = 4 => 13 pairs (_) G2,G5: 4.. / G2 = 4 => 20 pairs (_) / G5 = 4 => 14 pairs (_) H1,H3: 5.. / H1 = 5 => 14 pairs (_) / H3 = 5 => 19 pairs (_) G5,G6: 5.. / G5 = 5 => 20 pairs (_) / G6 = 5 => 14 pairs (_) A7,C7: 5.. / A7 = 5 => 16 pairs (_) / C7 = 5 => 15 pairs (_) E2,E3: 6.. / E2 = 6 => 0 pairs (X) / E3 = 6 => 13 pairs (_) A3,E3: 6.. / A3 = 6 => 0 pairs (X) / E3 = 6 => 13 pairs (_) I4,I9: 6.. / I4 = 6 => 15 pairs (_) / I9 = 6 => 0 pairs (X) F2,F3: 7.. / F2 = 7 => 17 pairs (_) / F3 = 7 => 19 pairs (_) H9,I9: 7.. / H9 = 7 => 14 pairs (_) / I9 = 7 => 18 pairs (_) D2,E2: 8.. / D2 = 8 => 13 pairs (_) / E2 = 8 => 15 pairs (_) B8,C8: 8.. / B8 = 8 => 13 pairs (_) / C8 = 8 => 0 pairs (X) C4,C8: 8.. / C4 = 8 => 13 pairs (_) / C8 = 8 => 0 pairs (X) A8,B8: 9.. / A8 = 9 => 13 pairs (_) / B8 = 9 => 0 pairs (X) B1,B8: 9.. / B1 = 9 => 13 pairs (_) / B8 = 9 => 0 pairs (X) G2,G6: 9.. / G2 = 9 => 14 pairs (_) / G6 = 9 => 20 pairs (_) * DURATION: 0:00:28.845572 START: 04:09:54.945233 END: 04:10:23.790805 2019-05-01 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,B6,B8,B9,C2,C8,F7,G2,G5,G6,H7,I3) * 8.7..26.3.5........31...8........7....97.6...7...48..2.7....1.9...6712451.2...3.. * PAIR B1: 4,9 BLK 1 A2: 4,9,2,6 # reduction candidate for 4,9 A2: 4,9 # 17 pairs A3: 4,9,2,6 # reduction candidate for 4,9 A3: 4,9 # 17 pairs * PAIR B1: 4,9 ROW 1 D1: 4,9,1,5 # reduction candidate for 4,9 D1: 1,5 => CTR * 847..26.3.56.......31.6.8..6.....7....97.6...71..48.62.7....189398671245162...37. D1: 4,9 # 16 pairs * PAIR C2: 4,6 BLK 1 A2: 4,6,2,9 # reduction candidate for 4,6 A2: 4,6 => SOLVED * 897412653654837921231965874548129736329756418716348592475283169983671245162594387 A2: 2,9 # 14 pairs A3: 4,6,2,9 # reduction candidate for 4,6 A3: 4,6 # 14 pairs * PAIR C2: 4,6 COL C C4: 4,6,3,5,8 # reduction candidate for 4,6 C4: 4,6 => CTR * 847..26.3.56.......31.6.8....4...7..5.97.64..7.3.485.2475..3169398671245162...3.. C4: 3,5,8 # 13 pairs C7: 4,6,5 # reduction candidate for 4,6 C7: 4,6 # 16 pairs * PAIR G2: 4,9 ROW 2 A2: 4,9,2,6 # reduction candidate for 4,9 A2: 4,9 # 17 pairs D2: 4,9,1,3,8 # reduction candidate for 4,9 D2: 4,9 => CTR * 897412653.5.983....31.678.4......7....97.64..7...485.2.7...41.9...671245142...3.. D2: 1,3,8 # 13 pairs F2: 4,9,3,7 # reduction candidate for 4,9 F2: 4,9 => CTR * 847..2653256..49..9315678246.4...7..5.97.64..713948562475..318939867124516248.3.. F2: 3,7 # 14 pairs * PAIR I3: 4,7 BLK 3 I2: 4,7,1 # reduction candidate for 4,7 I2: 4,7 # 19 pairs I2: 1 # 15 pairs * PAIR I3: 4,7 ROW 3 F3: 4,7,5,9 # reduction candidate for 4,7 F3: 5,9 # 18 pairs F3: 4,7 # 15 pairs * PAIR B6: 1,6 BLK 4 B4: 1,6,2,4,8 # reduction candidate for 1,6 B4: 1,6 => CTR * 8974.26.3.54...9...31...8.44.8...7..3297.64..7.5.48..2.7....1.9983671245142...3.. B4: 2,4,8 # 13 pairs * PAIR B6: 1,6 ROW 6 H6: 1,6,3,9 # reduction candidate for 1,6 H6: 1,6 # 15 pairs H6: 3,9 # 14 pairs * PAIR G5: 4,5 ROW 5 A5: 4,5,3 # reduction candidate for 4,5 A5: 4,5 # 15 pairs A5: 3 # 14 pairs * PAIR G6: 5,9 ROW 6 D6: 5,9,1,3 # reduction candidate for 5,9 D6: 5,9 # 15 pairs D6: 1,3 # 14 pairs * PAIR C8: 3,8 COL C C4: 3,8,4,5,6 # reduction candidate for 3,8 C4: 4,5,6 => CTR * 847..26.3.56.......31.6.8..6.....7....97.6...713.48.62.7....189398671245162...37. C4: 3,8 # 15 pairs * PAIR B9: 4,6 BLK 7 A7: 4,6,5 # reduction candidate for 4,6 A7: 4,6 # 15 pairs C7: 4,6,5 # reduction candidate for 4,6 C7: 4,6 # 16 pairs * PAIR B9: 4,6 COL B B4: 4,6,1,2,8 # reduction candidate for 4,6 B4: 4,6 # 13 pairs B4: 1,2,8 # 13 pairs * PAIR F7: 3,4 BLK 8 D7: 3,4,2,8 # reduction candidate for 3,4 D7: 3,4 => CTR * 8974.26.3.5........31...8....82..7...297.6..87.5.48932576324189983671245142...3.. D7: 2,8 # 14 pairs * PAIR F7: 3,4 COL F F2: 3,4,7,9 # reduction candidate for 3,4 F2: 3,4 # 19 pairs F2: 7,9 # 17 pairs * PAIR H7: 6,8 BLK 9 H9: 6,8,7 # reduction candidate for 6,8 H9: 6,8 # 18 pairs I9: 6,8,7 # reduction candidate for 6,8 I9: 6,8 # 14 pairs * PAIR H7: 6,8 COL H H4: 6,8,1,3,9 # reduction candidate for 6,8 H4: 6,8 # 16 pairs H4: 1,3,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190302-absurd-base-pr-000.dot * REASONING * DIS # D1: 1,5 => CTR => D1: 4,9 * PRF # A2: 4,6 => SOL * DIS # C4: 4,6 => CTR => C4: 3,5,8 * DIS # D2: 4,9 => CTR => D2: 1,3,8 * DIS # F2: 4,9 => CTR => F2: 3,7 * DIS # B4: 1,6 => CTR => B4: 2,4,8 * DIS # C4: 4,5,6 => CTR => C4: 3,8 * DIS # D7: 3,4 => CTR => D7: 2,8 * CNT 8 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,B6,B8,B9,C2,C8,F7,G2,G5,G6,H7,I3) * 8.7..26.3.5........31...8........7....97.6...7...48..2.7....1.9...6712451.2...3.. * PAIR B1: 4,9 BLK 1 A2: 4,9,2,6 # reduction candidate for 4,9 A2: 4,9 # 17 pairs A3: 4,9,2,6 # reduction candidate for 4,9 A3: 4,9 # 17 pairs * PAIR B1: 4,9 ROW 1 D1: 4,9,1,5 # reduction candidate for 4,9 D1: 1,5 => CTR * 847..26.3.56.......31.6.8..6.....7....97.6...71..48.62.7....189398671245162...37. * PAIR RESTART * PAIR B1: 4,9 BLK 1 A2: 4,9,2,6 # reduction candidate for 4,9 A2: 4,9 # 20 pairs A3: 4,9,2,6 # reduction candidate for 4,9 A3: 4,9 # 17 pairs * PAIR C2: 4,6 BLK 1 A2: 4,6,2,9 # reduction candidate for 4,6 A2: 4,6 => SOLVED * 897412653654837921231965874548129736329756418716348592475283169983671245162594387 * DURATION: 0:00:06.497070 START: 04:10:51.289415 END: 04:10:57.786485 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190302-absurd-base-pr-001.dot * REASONING * DIS # D1: 1,5 => CTR => D1: 4,9 * PRF D1: 4,9 # A2: 4,6 => SOL * STA D1: 4,9 + A2: 4,6 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190302, absurd
Solution
position: 897412653654837921231965874548129736329756418716348592475283169983671245162594387 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 # A2: 4,9 => UNS * INC # A3: 4,9 => UNS * INC # D1: 4,9 => UNS * DIS # D1: 1,5 => CTR => D1: 4,9 * PRF # A2: 4,6 => SOL * INC # A2: 2,9 => UNS * INC # A3: 4,6 => UNS * DIS # C4: 4,6 => CTR => C4: 3,5,8 * INC # C4: 3,5,8 => UNS * INC # C7: 4,6 => UNS * INC # A2: 4,9 => UNS * DIS # D2: 4,9 => CTR => D2: 1,3,8 * INC # D2: 1,3,8 => UNS * DIS # F2: 4,9 => CTR => F2: 3,7 * INC # F2: 3,7 => UNS * INC # I2: 4,7 => UNS * INC # I2: 1 => UNS * INC # F3: 4,7 => UNS * INC # F3: 5,9 => UNS * DIS # B4: 1,6 => CTR => B4: 2,4,8 * INC # B4: 2,4,8 => UNS * INC # H6: 1,6 => UNS * INC # H6: 3,9 => UNS * INC # A5: 4,5 => UNS * INC # A5: 3 => UNS * INC # D6: 5,9 => UNS * INC # D6: 1,3 => UNS * INC # C4: 3,8 => UNS * DIS # C4: 4,5,6 => CTR => C4: 3,8 * INC # A7: 4,6 => UNS * INC # C7: 4,6 => UNS * INC # B4: 4,6 => UNS * INC # B4: 1,2,8 => UNS * DIS # D7: 3,4 => CTR => D7: 2,8 * INC # D7: 2,8 => UNS * INC # F2: 3,4 => UNS * INC # F2: 7,9 => UNS * INC # H9: 6,8 => UNS * INC # I9: 6,8 => UNS * INC # H4: 6,8 => UNS * INC # H4: 1,3,9 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 4,9 => UNS * INC # A3: 4,9 => UNS * INC # D1: 4,9 => UNS * DIS # D1: 1,5 => CTR => D1: 4,9 * INC D1: 4,9 # A2: 4,9 => UNS * INC D1: 4,9 # A3: 4,9 => UNS * PRF D1: 4,9 # A2: 4,6 => SOL * STA D1: 4,9 + A2: 4,6 * CNT 7 HDP CHAINS / 7 HYP OPENED