Analysis of zz-www.sudokuoftheday.co.uk-20190127-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: .2........38.7.6.914.8........1.....6.....1.34...95.7......8.91.81.2.7.5.....9..2 initial
Autosolve
position: 7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 1 => CTR => F2: 2,4 * DIS # H2: 2,4 => CTR => H2: 1 * PRF # G1: 4,8 => SOL * DIS # H1: 4,8 => CTR => H1: 1,3 * PRF # H1: 1,3 => SOL * PRF # G3: 5 => SOL * DIS # F3: 2,3 => CTR => F3: 6 * DIS # C4: 5,7 => CTR => C4: 2,3 * PRF # B7: 5,7 => SOL * DIS # B7: 6 => CTR => B7: 5,7 * DIS # B9: 5,7 => CTR => B9: 6 * PRF # B9: 6 => SOL * DIS # C4: 5,7 => CTR => C4: 2,3 * PRF # F4: 3,6 => SOL * DIS # F4: 4,6 => CTR => F4: 2,3,7 * PRF # B7: 5,7 => SOL * DIS # B7: 6 => CTR => B7: 5,7 * DIS # C7: 5,7 => CTR => C7: 4 * PRF # C7: 4 => SOL * DIS # F8: 3,6 => CTR => F8: 4 * DIS # H8: 4 => CTR => H8: 3,6 * DIS # B9: 5,7 => CTR => B9: 6 * PRF # B9: 6 => SOL * PRF # C9: 5,7 => SOL * DIS # C9: 4 => CTR => C9: 5,7 * DIS # H8: 3,4 => CTR => H8: 6 * PRF # H8: 6 => SOL * DIS # E7: 3,4 => CTR => E7: 6 * PRF # E7: 6 => SOL * DIS # G1: 3,4 => CTR => G1: 5,8 * PRF # H9: 4,8 => SOL * DIS # H9: 6 => CTR => H9: 4,8 * PRF # G1: 4,8 => SOL * CNT 33 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 1 => CTR => F2: 2,4 * PRF F2: 2,4 # G1: 4,8 => SOL * STA F2: 2,4 + G1: 4,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2........38.7.6.914.8........1.....6.....1.34...95.7......8.91.81.2.7.5.....9..2 | initial |
| 7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2 | autosolve |
| 726951834538472619149836527872143956695287143413695278254768391981324765367519482 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) D2: 2,4 I1: 4,8 H3: 2,3 B4: 5,7 C6: 2,3 D5: 2,4 D6: 3,6 I4: 4,6 G6: 2,8 I6: 6,8 D7: 5,7 D8: 3,6 D9: 5,7 G7: 3,4 G9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F2: 1.. / F1 = 1 => 18 pairs (_) / F2 = 1 => 0 pairs (X) H1,H2: 1.. / H1 = 1 => 0 pairs (X) / H2 = 1 => 18 pairs (_) F1,H1: 1.. / F1 = 1 => 18 pairs (_) / H1 = 1 => 0 pairs (X) F2,H2: 1.. / F2 = 1 => 0 pairs (X) / H2 = 1 => 18 pairs (_) C6,G6: 2.. / C6 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) D2,D5: 2.. / D2 = 2 => 20 pairs (_) / D5 = 2 => 21 pairs (_) G3,G6: 2.. / G3 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) C4,C6: 3.. / C4 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) G7,H8: 3.. / G7 = 3 => 17 pairs (_) / H8 = 3 => 0 pairs (X) C6,D6: 3.. / C6 = 3 => 0 pairs (*) / D6 = 3 => 0 pairs (X) E7,G7: 3.. / E7 = 3 => 0 pairs (X) / G7 = 3 => 17 pairs (_) D6,D8: 3.. / D6 = 3 => 0 pairs (X) / D8 = 3 => 0 pairs (_) C7,C9: 4.. / C7 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) E7,F8: 4.. / E7 = 4 => 0 pairs (X) / F8 = 4 => 20 pairs (_) F8,H8: 4.. / F8 = 4 => 20 pairs (_) / H8 = 4 => 0 pairs (X) D2,D5: 4.. / D2 = 4 => 21 pairs (_) / D5 = 4 => 20 pairs (_) I1,I4: 4.. / I1 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) E1,E3: 5.. / E1 = 5 => 0 pairs (*) / E3 = 5 => 0 pairs (X) G1,G3: 5.. / G1 = 5 => 24 pairs (_) / G3 = 5 => 0 pairs (*) H4,H5: 5.. / H4 = 5 => 20 pairs (_) / H5 = 5 => 19 pairs (_) D7,D9: 5.. / D7 = 5 => 17 pairs (_) / D9 = 5 => 17 pairs (_) E1,G1: 5.. / E1 = 5 => 0 pairs (*) / G1 = 5 => 0 pairs (X) E3,G3: 5.. / E3 = 5 => 24 pairs (_) / G3 = 5 => 0 pairs (*) C5,H5: 5.. / C5 = 5 => 20 pairs (_) / H5 = 5 => 19 pairs (_) E3,F3: 6.. / E3 = 6 => 0 pairs (X) / F3 = 6 => 18 pairs (_) I4,I6: 6.. / I4 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) B7,B9: 6.. / B7 = 6 => 0 pairs (X) / B9 = 6 => 0 pairs (_) H8,H9: 6.. / H8 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) D6,I6: 6.. / D6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) B7,E7: 6.. / B7 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) B9,H9: 6.. / B9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) D6,D8: 6.. / D6 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) F4,F5: 7.. / F4 = 7 => 22 pairs (_) / F5 = 7 => 16 pairs (_) D7,D9: 7.. / D7 = 7 => 17 pairs (_) / D9 = 7 => 17 pairs (_) C5,F5: 7.. / C5 = 7 => 22 pairs (_) / F5 = 7 => 16 pairs (_) G6,I6: 8.. / G6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) G9,H9: 8.. / G9 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) H1,H9: 8.. / H1 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) I1,I6: 8.. / I1 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) * DURATION: 0:00:48.549606 START: 03:15:00.188119 END: 03:15:48.737725 2019-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D2,D5,D6,D7,D8,D9,G6,G7,G9,H3,I1,I4,I6) * 7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2 * PAIR D2: 2,4 BLK 2 F2: 2,4,1 # reduction candidate for 2,4 F2: 1 => CTR * 7269.381453847162914985..378..1..9..69..8.1.341.695.782.4.6839198132476536..19482 F2: 2,4 # 18 pairs * PAIR D2: 2,4 ROW 2 H2: 2,4,1 # reduction candidate for 2,4 H2: 2,4 => CTR * 7269.381453847162914985..378..1..9..69..8.1.341.695.782.4.6839198132476536..19482 H2: 1 # 18 pairs * PAIR I1: 4,8 BLK 3 G1: 4,8,3,5 # reduction candidate for 4,8 G1: 4,8 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 G1: 3,5 # 24 pairs H1: 4,8,1,3 # reduction candidate for 4,8 H1: 4,8 => CTR * 7269.1...5384726191498....78..14.9.669.28714341.695.782...683919813247653...19..2 H1: 1,3 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 * PAIR H3: 2,3 BLK 3 G3: 2,3,5 # reduction candidate for 2,3 G3: 5 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 G3: 2,3 # 24 pairs * PAIR H3: 2,3 ROW 3 F3: 2,3,6 # reduction candidate for 2,3 F3: 2,3 => CTR * 72695..84538.7.61914986.5278..1..9.669..8.1.341369527826...8.919813267453.4.19862 F3: 6 # 18 pairs * PAIR B4: 5,7 BLK 4 C4: 5,7,2,3 # reduction candidate for 5,7 C4: 5,7 => CTR * 7269....4538.7.6.91498....78..1.29.66924871534136952782...483919813267453...19..2 C4: 2,3 # 17 pairs C5: 5,7,2 # reduction candidate for 5,7 C5: 5,7 # 17 pairs * PAIR B4: 5,7 COL B B7: 5,7,6 # reduction candidate for 5,7 B7: 5,7 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 B7: 6 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862 B9: 5,7,6 # reduction candidate for 5,7 B9: 5,7 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862 B9: 6 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 * PAIR C6: 2,3 BLK 4 C4: 2,3,5,7 # reduction candidate for 2,3 C4: 5,7 => CTR * 7269....4538.7.6.91498....78..1.29.66924871534136952782...483919813267453...19..2 C4: 2,3 # 17 pairs * PAIR D5: 2,4 BLK 5 F4: 2,4,3,6,7 # reduction candidate for 2,4 F4: 2,4 # 18 pairs F5: 2,4,7 # reduction candidate for 2,4 F5: 2,4 # 22 pairs * PAIR D5: 2,4 ROW 5 H5: 2,4,5 # reduction candidate for 2,4 H5: 2,4 # 20 pairs H5: 5 # 19 pairs * PAIR D6: 3,6 BLK 5 E4: 3,6,4 # reduction candidate for 3,6 E4: 3,6 # 16 pairs F4: 3,6,2,4,7 # reduction candidate for 3,6 F4: 3,6 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 F4: 2,4,7 # 16 pairs * PAIR I4: 4,6 ROW 4 E4: 4,6,3 # reduction candidate for 4,6 E4: 4,6 # 17 pairs F4: 4,6,2,3,7 # reduction candidate for 4,6 F4: 4,6 => CTR * 7269.....538.7.6.91498....78..1..9..69.28714341..95.7.2....8.91981.247.53...19..2 F4: 2,3,7 # 15 pairs * PAIR D7: 5,7 ROW 7 B7: 5,7,6 # reduction candidate for 5,7 B7: 5,7 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 B7: 6 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862 C7: 5,7,4 # reduction candidate for 5,7 C7: 5,7 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.69527826...849198132.7.53.4.19862 C7: 4 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 * PAIR D8: 3,6 BLK 8 E7: 3,6,4 # reduction candidate for 3,6 E7: 3,6 # 20 pairs F8: 3,6,4 # reduction candidate for 3,6 F8: 3,6 => CTR * 7269..48.538.7.6.91498....78..1..9..69..8.1.341..95.7.2...48391981.2.7453.4.19862 F8: 4 # 20 pairs * PAIR D8: 3,6 ROW 8 H8: 3,6,4 # reduction candidate for 3,6 H8: 4 => CTR * 7269..48.538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8391981.2.7453.4.19862 H8: 3,6 # 20 pairs * PAIR D9: 5,7 ROW 9 B9: 5,7,6 # reduction candidate for 5,7 B9: 5,7 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862 B9: 6 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 C9: 5,7,4 # reduction candidate for 5,7 C9: 5,7 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 C9: 4 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.69527826...849198132.7.53.4.19862 * PAIR G7: 3,4 BLK 9 H8: 3,4,6 # reduction candidate for 3,4 H8: 3,4 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862 H8: 6 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 * PAIR G7: 3,4 ROW 7 E7: 3,4,6 # reduction candidate for 3,4 E7: 3,4 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862 E7: 6 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 * PAIR G7: 3,4 COL G G1: 3,4,5,8 # reduction candidate for 3,4 G1: 3,4 => CTR * 72695..84538.7.6191498..5278..1..9.669..8.1.34136952782....84919813247653...198.2 G1: 5,8 # 22 pairs * PAIR G9: 4,8 BLK 9 H9: 4,8,6 # reduction candidate for 4,8 H9: 4,8 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 H9: 6 => CTR * 7269...84538.7.6191498....78..1..9.669..8.1.341.695.782....8.9198132.7.53...19862 * PAIR G9: 4,8 COL G G1: 4,8,3,5 # reduction candidate for 4,8 G1: 4,8 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 G1: 3,5 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190127-absurd-base-pr-000.dot * REASONING * DIS # F2: 1 => CTR => F2: 2,4 * DIS # H2: 2,4 => CTR => H2: 1 * PRF # G1: 4,8 => SOL * DIS # H1: 4,8 => CTR => H1: 1,3 * PRF # H1: 1,3 => SOL * PRF # G3: 5 => SOL * DIS # F3: 2,3 => CTR => F3: 6 * DIS # C4: 5,7 => CTR => C4: 2,3 * PRF # B7: 5,7 => SOL * DIS # B7: 6 => CTR => B7: 5,7 * DIS # B9: 5,7 => CTR => B9: 6 * PRF # B9: 6 => SOL * DIS # C4: 5,7 => CTR => C4: 2,3 * PRF # F4: 3,6 => SOL * DIS # F4: 4,6 => CTR => F4: 2,3,7 * PRF # B7: 5,7 => SOL * DIS # B7: 6 => CTR => B7: 5,7 * DIS # C7: 5,7 => CTR => C7: 4 * PRF # C7: 4 => SOL * DIS # F8: 3,6 => CTR => F8: 4 * DIS # H8: 4 => CTR => H8: 3,6 * DIS # B9: 5,7 => CTR => B9: 6 * PRF # B9: 6 => SOL * PRF # C9: 5,7 => SOL * DIS # C9: 4 => CTR => C9: 5,7 * DIS # H8: 3,4 => CTR => H8: 6 * PRF # H8: 6 => SOL * DIS # E7: 3,4 => CTR => E7: 6 * PRF # E7: 6 => SOL * DIS # G1: 3,4 => CTR => G1: 5,8 * PRF # H9: 4,8 => SOL * DIS # H9: 6 => CTR => H9: 4,8 * PRF # G1: 4,8 => SOL * CNT 33 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D2,D5,D6,D7,D8,D9,G6,G7,G9,H3,I1,I4,I6) * 7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2 * PAIR D2: 2,4 BLK 2 F2: 2,4,1 # reduction candidate for 2,4 F2: 1 => CTR * 7269.381453847162914985..378..1..9..69..8.1.341.695.782.4.6839198132476536..19482 * PAIR I1: 4,8 BLK 3 G1: 4,8,3,5 # reduction candidate for 4,8 G1: 4,8 => SOLVED * 726951834538472619149836527872143956695287143413695278254768391981324765367519482 * DURATION: 0:00:03.198857 START: 03:16:29.977772 END: 03:16:33.176629 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190127-absurd-base-pr-001.dot * REASONING * DIS # F2: 1 => CTR => F2: 2,4 * PRF F2: 2,4 # G1: 4,8 => SOL * STA F2: 2,4 + G1: 4,8 * 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, 20190127, absurd
Solution
position: 726951834538472619149836527872143956695287143413695278254768391981324765367519482 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 # F2: 2,4 => UNS * DIS # F2: 1 => CTR => F2: 2,4 * DIS # H2: 2,4 => CTR => H2: 1 * INC # H2: 1 => UNS * PRF # G1: 4,8 => SOL * INC # G1: 3,5 => UNS * DIS # H1: 4,8 => CTR => H1: 1,3 * PRF # H1: 1,3 => SOL * INC # G3: 2,3 => UNS * PRF # G3: 5 => SOL * DIS # F3: 2,3 => CTR => F3: 6 * INC # F3: 6 => UNS * DIS # C4: 5,7 => CTR => C4: 2,3 * INC # C4: 2,3 => UNS * INC # C5: 5,7 => UNS * PRF # B7: 5,7 => SOL * DIS # B7: 6 => CTR => B7: 5,7 * DIS # B9: 5,7 => CTR => B9: 6 * PRF # B9: 6 => SOL * INC # C4: 2,3 => UNS * DIS # C4: 5,7 => CTR => C4: 2,3 * INC # F4: 2,4 => UNS * INC # F5: 2,4 => UNS * INC # H5: 2,4 => UNS * INC # H5: 5 => UNS * INC # E4: 3,6 => UNS * PRF # F4: 3,6 => SOL * INC # F4: 2,4,7 => UNS * INC # E4: 4,6 => UNS * DIS # F4: 4,6 => CTR => F4: 2,3,7 * INC # F4: 2,3,7 => UNS * PRF # B7: 5,7 => SOL * DIS # B7: 6 => CTR => B7: 5,7 * DIS # C7: 5,7 => CTR => C7: 4 * PRF # C7: 4 => SOL * INC # E7: 3,6 => UNS * DIS # F8: 3,6 => CTR => F8: 4 * INC # F8: 4 => UNS * INC # H8: 3,6 => UNS * DIS # H8: 4 => CTR => H8: 3,6 * DIS # B9: 5,7 => CTR => B9: 6 * PRF # B9: 6 => SOL * PRF # C9: 5,7 => SOL * DIS # C9: 4 => CTR => C9: 5,7 * DIS # H8: 3,4 => CTR => H8: 6 * PRF # H8: 6 => SOL * DIS # E7: 3,4 => CTR => E7: 6 * PRF # E7: 6 => SOL * DIS # G1: 3,4 => CTR => G1: 5,8 * INC # G1: 5,8 => UNS * PRF # H9: 4,8 => SOL * DIS # H9: 6 => CTR => H9: 4,8 * PRF # G1: 4,8 => SOL * INC # G1: 3,5 => UNS * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 2,4 => UNS * DIS # F2: 1 => CTR => F2: 2,4 * PRF F2: 2,4 # G1: 4,8 => SOL * STA F2: 2,4 + G1: 4,8 * CNT 3 HDP CHAINS / 3 HYP OPENED