Analysis of zz-www.sudokuoftheday.co.uk-20190421-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: ..7.8.6.....12...86........4.28....7....6..93.63....2.8...71.5.....9.3...4.2.3... initial
Autosolve
position: ..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 1,2 => SOL * DIS # B8: 1,2 => CTR => B8: 7 * DIS # A2: 5,9 => CTR => A2: 3 * PRF # C3: 5,9 => SOL * DIS # G2: 7 => CTR => G2: 5,9 * DIS # G3: 2,9 => CTR => G3: 5 * DIS # G2: 5 => CTR => G2: 7,9 * CNT 7 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 1,2 => SOL * STA A1: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7.8.6.....12...86........4.28....7....6..93.63....2.8...71.5.....9.3...4.2.3... | initial |
| ..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8. | autosolve |
| 127589634354126978689347512492835167518762493763914825836471259275698341941253786 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 1,2 B2: 5,9 F1: 5,9 H2: 3,7 H3: 1,3 B4: 5,9 A6: 7,9 F4: 5,9 D5: 5,7 D6: 7,9 C7: 6,9 D7: 4,6 D8: 4,6 G7: 2,9 G9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,B8: 2.. / A8 = 2 => 17 pairs (_) / B8 = 2 => 0 pairs (X) G7,I7: 2.. / G7 = 2 => 15 pairs (_) / I7 = 2 => 0 pairs (X) A1,A8: 2.. / A1 = 2 => 0 pairs (X) / A8 = 2 => 17 pairs (_) G3,G7: 2.. / G3 = 2 => 0 pairs (X) / G7 = 2 => 15 pairs (_) A1,A2: 3.. / A1 = 3 => 0 pairs (X) / A2 = 3 => 20 pairs (_) D1,D3: 3.. / D1 = 3 => 21 pairs (_) / D3 = 3 => 20 pairs (_) A2,H2: 3.. / A2 = 3 => 20 pairs (_) / H2 = 3 => 0 pairs (X) D3,H3: 3.. / D3 = 3 => 20 pairs (_) / H3 = 3 => 21 pairs (_) H1,I1: 4.. / H1 = 4 => 16 pairs (_) / I1 = 4 => 20 pairs (_) D7,D8: 4.. / D7 = 4 => 15 pairs (_) / D8 = 4 => 16 pairs (_) D7,I7: 4.. / D7 = 4 => 15 pairs (_) / I7 = 4 => 16 pairs (_) H1,H8: 4.. / H1 = 4 => 16 pairs (_) / H8 = 4 => 20 pairs (_) G2,G3: 5.. / G2 = 5 => 0 pairs (X) / G3 = 5 => 16 pairs (_) F4,D5: 5.. / F4 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) A8,C8: 5.. / A8 = 5 => 0 pairs (X) / C8 = 5 => 16 pairs (_) B4,F4: 5.. / B4 = 5 => 17 pairs (_) / F4 = 5 => 0 pairs (*) B2,B4: 5.. / B2 = 5 => 0 pairs (*) / B4 = 5 => 0 pairs (X) F1,F4: 5.. / F1 = 5 => 17 pairs (_) / F4 = 5 => 0 pairs (*) D7,D8: 6.. / D7 = 6 => 16 pairs (_) / D8 = 6 => 15 pairs (_) C9,I9: 6.. / C9 = 6 => 18 pairs (_) / I9 = 6 => 19 pairs (_) G2,H2: 7.. / G2 = 7 => 0 pairs (X) / H2 = 7 => 20 pairs (_) D5,D6: 7.. / D5 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) H8,G9: 7.. / H8 = 7 => 0 pairs (X) / G9 = 7 => 20 pairs (_) A6,D6: 7.. / A6 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) A9,G9: 7.. / A9 = 7 => 0 pairs (X) / G9 = 7 => 20 pairs (_) B5,B8: 7.. / B5 = 7 => 0 pairs (X) / B8 = 7 => 20 pairs (_) G2,G9: 7.. / G2 = 7 => 0 pairs (X) / G9 = 7 => 20 pairs (_) H2,H8: 7.. / H2 = 7 => 20 pairs (_) / H8 = 7 => 0 pairs (X) B3,C3: 8.. / B3 = 8 => 16 pairs (_) / C3 = 8 => 21 pairs (_) B5,C5: 8.. / B5 = 8 => 21 pairs (_) / C5 = 8 => 16 pairs (_) B3,B5: 8.. / B3 = 8 => 16 pairs (_) / B5 = 8 => 21 pairs (_) C3,C5: 8.. / C3 = 8 => 21 pairs (_) / C5 = 8 => 16 pairs (_) B4,A6: 9.. / B4 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) F4,D6: 9.. / F4 = 9 => 17 pairs (_) / D6 = 9 => 0 pairs (*) B4,F4: 9.. / B4 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) A6,D6: 9.. / A6 = 9 => 17 pairs (_) / D6 = 9 => 0 pairs (*) B2,B4: 9.. / B2 = 9 => 17 pairs (_) / B4 = 9 => 0 pairs (*) F1,F4: 9.. / F1 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) * DURATION: 0:00:42.898480 START: 05:29:49.659457 END: 05:30:32.557937 2019-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,B2,B4,C7,D5,D6,D7,D8,F1,F4,G7,G9,H2,H3) * ..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8. * PAIR B1: 1,2 BLK 1 A1: 1,2,3,5,9 # reduction candidate for 1,2 A1: 1,2 => SOLVED * 127589634354126978689347512492835167518762493763914825836471259275698341941253786 A1: 3,5,9 # 21 pairs B3: 1,2,8 # reduction candidate for 1,2 B3: 1,2 # 21 pairs * PAIR B1: 1,2 ROW 1 I1: 1,2,4,9 # reduction candidate for 1,2 I1: 1,2 # 23 pairs I1: 4,9 # 17 pairs * PAIR B1: 1,2 COL B B8: 1,2,7 # reduction candidate for 1,2 B8: 1,2 => CTR * ..7.856...9412673868.34751.45283916717856249396371482583..71.5.....983..74.25398. B8: 7 # 20 pairs * PAIR B2: 5,9 BLK 1 A1: 5,9,1,2,3 # reduction candidate for 5,9 A1: 5,9 # 23 pairs A2: 5,9,3 # reduction candidate for 5,9 A2: 5,9 => CTR * 317.8.6....4126.386..347.1.4.283.167....62493.63.1482583..71.5.2.5.9837.74.25398. A2: 3 # 20 pairs C3: 5,9,1,8 # reduction candidate for 5,9 C3: 5,9 => SOLVED * 127589634354126978689347512492835167518762493763914825836471259275698341941253786 C3: 1,8 # 21 pairs * PAIR B2: 5,9 ROW 2 G2: 5,9,7 # reduction candidate for 5,9 G2: 7 => CTR * 317.8.642..412673862.34751.4.283.167....62493.63.1482583..7125.....9837.74.25398. G2: 5,9 # 20 pairs * PAIR F1: 5,9 BLK 2 D1: 5,9,3 # reduction candidate for 5,9 D1: 5,9 # 20 pairs D3: 5,9,3 # reduction candidate for 5,9 D3: 5,9 # 21 pairs * PAIR F1: 5,9 ROW 1 A1: 5,9,1,2,3 # reduction candidate for 5,9 A1: 5,9 # 23 pairs A1: 1,2,3 # 16 pairs * PAIR H3: 1,3 BLK 3 H1: 1,3,4 # reduction candidate for 1,3 H1: 1,3 # 20 pairs H1: 4 # 16 pairs * PAIR A6: 7,9 COL A A9: 7,9,1 # reduction candidate for 7,9 A9: 1 # 23 pairs A9: 7,9 # 20 pairs * PAIR D5: 5,7 ROW 5 A5: 5,7,1 # reduction candidate for 5,7 A5: 1 # 22 pairs A5: 5,7 # 20 pairs * PAIR C7: 6,9 BLK 7 C9: 6,9,1 # reduction candidate for 6,9 C9: 1 # 23 pairs C9: 6,9 # 18 pairs * PAIR C7: 6,9 ROW 7 I7: 6,9,2,4 # reduction candidate for 6,9 I7: 6,9 # 16 pairs I7: 2,4 # 16 pairs * PAIR D7: 4,6 ROW 7 I7: 4,6,2,9 # reduction candidate for 4,6 I7: 2,9 # 19 pairs I7: 4,6 # 17 pairs * PAIR D8: 4,6 ROW 8 I8: 4,6,1 # reduction candidate for 4,6 I8: 1 # 20 pairs I8: 4,6 # 18 pairs * PAIR G7: 2,9 BLK 9 I7: 2,9,4,6 # reduction candidate for 2,9 I7: 2,9 # 19 pairs I7: 4,6 # 17 pairs * PAIR G7: 2,9 COL G G3: 2,9,5 # reduction candidate for 2,9 G3: 2,9 => CTR * ..7.856..3941265786.5.47...452839167..856249396371482583..71.5.5...983...4.25378. G3: 5 # 16 pairs * PAIR G9: 7,9 ROW 9 A9: 7,9,1 # reduction candidate for 7,9 A9: 1 # 23 pairs A9: 7,9 # 20 pairs * PAIR G9: 7,9 COL G G2: 7,9,5 # reduction candidate for 7,9 G2: 5 => CTR * ..7.856..3941265786.5.47...452839167..856249396371482583..71.5.5...983...4.25378. G2: 7,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190421-absurd-base-pr-000.dot * REASONING * PRF # A1: 1,2 => SOL * DIS # B8: 1,2 => CTR => B8: 7 * DIS # A2: 5,9 => CTR => A2: 3 * PRF # C3: 5,9 => SOL * DIS # G2: 7 => CTR => G2: 5,9 * DIS # G3: 2,9 => CTR => G3: 5 * DIS # G2: 5 => CTR => G2: 7,9 * CNT 7 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,B2,B4,C7,D5,D6,D7,D8,F1,F4,G7,G9,H2,H3) * ..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8. * PAIR B1: 1,2 BLK 1 A1: 1,2,3,5,9 # reduction candidate for 1,2 A1: 1,2 => SOLVED * 127589634354126978689347512492835167518762493763914825836471259275698341941253786 * DURATION: 0:00:01.820717 START: 05:30:57.868098 END: 05:30:59.688815 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190421-absurd-base-pr-001.dot * REASONING * PRF # A1: 1,2 => SOL * STA A1: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190421, absurd
Solution
position: 127589634354126978689347512492835167518762493763914825836471259275698341941253786 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:
* PRF # A1: 1,2 => SOL * INC # A1: 3,5,9 => UNS * INC # B3: 1,2 => UNS * INC # I1: 1,2 => UNS * INC # I1: 4,9 => UNS * DIS # B8: 1,2 => CTR => B8: 7 * INC # B8: 7 => UNS * INC # A1: 5,9 => UNS * DIS # A2: 5,9 => CTR => A2: 3 * INC # A2: 3 => UNS * PRF # C3: 5,9 => SOL * INC # C3: 1,8 => UNS * INC # G2: 5,9 => UNS * DIS # G2: 7 => CTR => G2: 5,9 * INC # D1: 5,9 => UNS * INC # D3: 5,9 => UNS * INC # A1: 5,9 => UNS * INC # A1: 1,2,3 => UNS * INC # H1: 1,3 => UNS * INC # H1: 4 => UNS * INC # A9: 7,9 => UNS * INC # A9: 1 => UNS * INC # A5: 5,7 => UNS * INC # A5: 1 => UNS * INC # C9: 6,9 => UNS * INC # C9: 1 => UNS * INC # I7: 6,9 => UNS * INC # I7: 2,4 => UNS * INC # I7: 4,6 => UNS * INC # I7: 2,9 => UNS * INC # I8: 4,6 => UNS * INC # I8: 1 => UNS * INC # I7: 2,9 => UNS * INC # I7: 4,6 => UNS * DIS # G3: 2,9 => CTR => G3: 5 * INC # G3: 5 => UNS * INC # A9: 7,9 => UNS * INC # A9: 1 => UNS * INC # G2: 7,9 => UNS * DIS # G2: 5 => CTR => G2: 7,9 * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 1,2 => SOL * STA A1: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED