Analysis of zz-www.sudokuoftheday.co.uk-20060330-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: ...6........8..7.14...12..58....62.7..4..7.5..3....9...6......2.734.1..99.1.6.... initial
Autosolve
position: ...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D4: 3,9 => CTR => D4: 1,5 * DIS # E6: 4,8 => CTR => E6: 2 * DIS # I6: 4,8 => CTR => I6: 6 * DIS # G8: 6 => CTR => G8: 5,8 * DIS # G9: 3 => CTR => G9: 5,8 * DIS # H4: 1,4 => CTR => H4: 3 * PRF # H4: 3 => SOL * PRF # H6: 1,4 => SOL * DIS # H6: 8 => CTR => H6: 1,4 * DIS # G8: 6,8 => CTR => G8: 5 * PRF # G8: 5 => SOL * DIS # H3: 6,8 => CTR => H3: 3,9 * PRF # G9: 3,8 => SOL * DIS # G9: 5 => CTR => G9: 3,8 * DIS # I1: 3,8 => CTR => I1: 4 * CNT 15 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D4: 3,9 => CTR => D4: 1,5 * DIS D4: 1,5 # E6: 4,8 => CTR => E6: 2 * DIS D4: 1,5 + E6: 2 # I6: 4,8 => CTR => I6: 6 * DIS D4: 1,5 + E6: 2 + I6: 6 # F1: 5 => CTR => F1: 3,9 * DIS D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 6 => CTR => G8: 5,8 * PRF D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 # G9: 5,8 => SOL * STA D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 + G9: 5,8 * CNT 6 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6........8..7.14...12..58....62.7..4..7.5..3....9...6......2.734.1..99.1.6.... | initial |
| ...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7. | autosolve |
| 152679384396854721487312695819546237624937158735128946568793412273481569941265873 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 3,6 B3: 8,9 C4: 5,9 A5: 1,6 D6: 1,5 F6: 4,8 F7: 3,9 E8: 5,8 F9: 5,8 G7: 1,4 H7: 1,4 H8: 6,8 I9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 18 pairs (_) / B1 = 1 => 18 pairs (_) G7,H7: 1.. / G7 = 1 => 0 pairs (X) / H7 = 1 => 22 pairs (_) G5,G7: 1.. / G5 = 1 => 22 pairs (_) / G7 = 1 => 0 pairs (X) H1,H2: 2.. / H1 = 2 => 13 pairs (_) / H2 = 2 => 15 pairs (_) B5,C6: 2.. / B5 = 2 => 15 pairs (_) / C6 = 2 => 0 pairs (X) E5,E6: 2.. / E5 = 2 => 0 pairs (X) / E6 = 2 => 15 pairs (_) B5,E5: 2.. / B5 = 2 => 15 pairs (_) / E5 = 2 => 0 pairs (X) C6,E6: 2.. / C6 = 2 => 0 pairs (X) / E6 = 2 => 15 pairs (_) A1,A2: 3.. / A1 = 3 => 0 pairs (X) / A2 = 3 => 13 pairs (_) G9,I9: 3.. / G9 = 3 => 0 pairs (X) / I9 = 3 => 15 pairs (_) G7,H7: 4.. / G7 = 4 => 22 pairs (_) / H7 = 4 => 0 pairs (X) E4,H4: 4.. / E4 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) G1,G7: 4.. / G1 = 4 => 0 pairs (X) / G7 = 4 => 22 pairs (_) I1,I6: 4.. / I1 = 4 => 22 pairs (_) / I6 = 4 => 0 pairs (X) D4,D6: 5.. / D4 = 5 => 18 pairs (_) / D6 = 5 => 12 pairs (_) E8,F9: 5.. / E8 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) G8,G9: 5.. / G8 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) C6,D6: 5.. / C6 = 5 => 18 pairs (_) / D6 = 5 => 12 pairs (_) E8,G8: 5.. / E8 = 5 => 0 pairs (X) / G8 = 5 => 0 pairs (_) F9,G9: 5.. / F9 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) I5,I6: 6.. / I5 = 6 => 0 pairs (X) / I6 = 6 => 22 pairs (_) G8,H8: 6.. / G8 = 6 => 0 pairs (X) / H8 = 6 => 14 pairs (_) A5,I5: 6.. / A5 = 6 => 22 pairs (_) / I5 = 6 => 0 pairs (X) G3,G8: 6.. / G3 = 6 => 14 pairs (_) / G8 = 6 => 0 pairs (X) E1,D3: 7.. / E1 = 7 => 16 pairs (_) / D3 = 7 => 18 pairs (_) A6,C6: 7.. / A6 = 7 => 14 pairs (_) / C6 = 7 => 23 pairs (_) D7,E7: 7.. / D7 = 7 => 16 pairs (_) / E7 = 7 => 18 pairs (_) C3,D3: 7.. / C3 = 7 => 16 pairs (_) / D3 = 7 => 18 pairs (_) A1,A6: 7.. / A1 = 7 => 23 pairs (_) / A6 = 7 => 14 pairs (_) D3,D7: 7.. / D3 = 7 => 18 pairs (_) / D7 = 7 => 16 pairs (_) E1,E7: 7.. / E1 = 7 => 16 pairs (_) / E7 = 7 => 18 pairs (_) B1,B3: 8.. / B1 = 8 => 0 pairs (X) / B3 = 8 => 13 pairs (_) E8,F9: 8.. / E8 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) F6,F9: 8.. / F6 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) * DURATION: 0:00:36.184592 START: 22:00:51.097376 END: 22:01:27.281968 2019-04-30 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,C4,D6,E8,F6,F7,F9,G7,H7,H8,I9) * ...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7. * PAIR A2: 3,6 ROW 2 H2: 3,6,2,4,9 # reduction candidate for 3,6 H2: 3,6 # 18 pairs H2: 2,4,9 # 14 pairs * PAIR B3: 8,9 BLK 1 B1: 8,9,1,2,5 # reduction candidate for 8,9 B1: 8,9 # 22 pairs B1: 1,2,5 # 13 pairs * PAIR B3: 8,9 ROW 3 H3: 8,9,3,6 # reduction candidate for 8,9 H3: 8,9 # 17 pairs H3: 3,6 # 17 pairs * PAIR C4: 5,9 BLK 4 B4: 5,9,1 # reduction candidate for 5,9 B4: 1 # 18 pairs B4: 5,9 # 16 pairs * PAIR C4: 5,9 ROW 4 D4: 5,9,1,3 # reduction candidate for 5,9 D4: 5,9 # 18 pairs D4: 1,3 # 13 pairs * PAIR C4: 5,9 COL C C1: 5,9,2,7 # reduction candidate for 5,9 C1: 5,9 # 15 pairs C2: 5,9,2,6 # reduction candidate for 5,9 C2: 5,9 # 15 pairs * PAIR A5: 1,6 BLK 4 A6: 1,6,7 # reduction candidate for 1,6 A6: 1,6 # 23 pairs A6: 7 # 14 pairs * PAIR D6: 1,5 BLK 5 D4: 1,5,3,9 # reduction candidate for 1,5 D4: 3,9 => CTR * ...6..4.....8..7.14...12..58...462.76.41.7.5..3.5.89..568...1422734.1..994126..7. D4: 1,5 # 18 pairs * PAIR F6: 4,8 BLK 5 E6: 4,8,2 # reduction candidate for 4,8 E6: 4,8 => CTR * ...6........8..7.14...12..58....62.7..4.27.5.7325..916568...1422734.1..994126..7. E6: 2 # 15 pairs * PAIR F6: 4,8 ROW 6 H6: 4,8,1 # reduction candidate for 4,8 H6: 4,8 # 22 pairs I6: 4,8,6 # reduction candidate for 4,8 I6: 4,8 => CTR * .1.6..4833.68.472148.3126958..146237124937856637..8914568...142273481569941265.7. I6: 6 # 22 pairs * PAIR F7: 3,9 BLK 8 D7: 3,9,7 # reduction candidate for 3,9 D7: 3,9 # 18 pairs E7: 3,9,7 # reduction candidate for 3,9 E7: 3,9 # 16 pairs * PAIR F7: 3,9 COL F F1: 3,9,4,5 # reduction candidate for 3,9 F1: 3,9 # 15 pairs F2: 3,9,4,5 # reduction candidate for 3,9 F2: 3,9 # 15 pairs * PAIR E8: 5,8 ROW 8 G8: 5,8,6 # reduction candidate for 5,8 G8: 6 => CTR * ...6........8..7.14...12..58....62.7..4..7.5..3...491.568...142273451689941268573 G8: 5,8 # 14 pairs * PAIR F9: 5,8 ROW 9 G9: 5,8,3 # reduction candidate for 5,8 G9: 3 => CTR * ...6..4.33.68.47.14..3126.58...46237..4.37856637528914568793142273481569941265378 G9: 5,8 # 15 pairs * PAIR H7: 1,4 COL H H4: 1,4,3 # reduction candidate for 1,4 H4: 1,4 => CTR * ...6....8...8..7.148..126.58....62.7..4.87356.3..2498.568.....22734.1.69941268573 H4: 3 => SOLVED * 152679384396854721487312695819546237624937158735128946568793412273481569941265873 H6: 1,4,8 # reduction candidate for 1,4 H6: 1,4 => SOLVED * 152679384396854721487312695819546237624937158735128946568793412273481569941265873 H6: 8 => CTR * ...6....8...8..7.148..126.58....62.7..4.87.56.3..2498.568.....22734.1.69941268573 * PAIR H8: 6,8 BLK 9 G8: 6,8,5 # reduction candidate for 6,8 G8: 6,8 => CTR * ...6....4...84.7.14...12..58....6247..4..735..3...491.568.....2273451..9941268573 G8: 5 => SOLVED * 152679384396854721487312695819546237624937158735128946568793412273481569941265873 * PAIR H8: 6,8 COL H H3: 6,8,3,9 # reduction candidate for 6,8 H3: 6,8 => CTR * .8.6........8.47.14973126858.9.46237.24.37.5.73..289..568793..2273481569941265.7. H3: 3,9 # 14 pairs * PAIR I9: 3,8 BLK 9 G9: 3,8,5 # reduction candidate for 3,8 G9: 3,8 => SOLVED * 152679384396854721487312695819546237624937158735128946568793412273481569941265873 G9: 5 => CTR * ...6....4...84.7.14...12..58....6247..4..735..3...491.568.....2273451..9941268573 * PAIR I9: 3,8 COL I I1: 3,8,4 # reduction candidate for 3,8 I1: 3,8 => CTR * .1.6..4833.68.472148.3126958..146237124937856637528914568...142273481569941265378 I1: 4 # 22 pairs I5: 3,8,6 # reduction candidate for 3,8 I5: 3,8 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060330-absurd-base-pr-000.dot * REASONING * DIS # D4: 3,9 => CTR => D4: 1,5 * DIS # E6: 4,8 => CTR => E6: 2 * DIS # I6: 4,8 => CTR => I6: 6 * DIS # G8: 6 => CTR => G8: 5,8 * DIS # G9: 3 => CTR => G9: 5,8 * DIS # H4: 1,4 => CTR => H4: 3 * PRF # H4: 3 => SOL * PRF # H6: 1,4 => SOL * DIS # H6: 8 => CTR => H6: 1,4 * DIS # G8: 6,8 => CTR => G8: 5 * PRF # G8: 5 => SOL * DIS # H3: 6,8 => CTR => H3: 3,9 * PRF # G9: 3,8 => SOL * DIS # G9: 5 => CTR => G9: 3,8 * DIS # I1: 3,8 => CTR => I1: 4 * CNT 15 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,C4,D6,E8,F6,F7,F9,G7,H7,H8,I9) * ...6........8..7.14...12..58....62.7..4..7.5..3....9..568.....22734.1..994126..7. * PAIR A2: 3,6 ROW 2 H2: 3,6,2,4,9 # reduction candidate for 3,6 H2: 3,6 # 18 pairs H2: 2,4,9 # 14 pairs * PAIR B3: 8,9 BLK 1 B1: 8,9,1,2,5 # reduction candidate for 8,9 B1: 8,9 # 22 pairs B1: 1,2,5 # 13 pairs * PAIR B3: 8,9 ROW 3 H3: 8,9,3,6 # reduction candidate for 8,9 H3: 8,9 # 17 pairs H3: 3,6 # 17 pairs * PAIR C4: 5,9 BLK 4 B4: 5,9,1 # reduction candidate for 5,9 B4: 1 # 18 pairs B4: 5,9 # 16 pairs * PAIR C4: 5,9 ROW 4 D4: 5,9,1,3 # reduction candidate for 5,9 D4: 5,9 # 18 pairs D4: 1,3 # 13 pairs * PAIR C4: 5,9 COL C C1: 5,9,2,7 # reduction candidate for 5,9 C1: 5,9 # 15 pairs C2: 5,9,2,6 # reduction candidate for 5,9 C2: 5,9 # 15 pairs * PAIR A5: 1,6 BLK 4 A6: 1,6,7 # reduction candidate for 1,6 A6: 1,6 # 23 pairs A6: 7 # 14 pairs * PAIR D6: 1,5 BLK 5 D4: 1,5,3,9 # reduction candidate for 1,5 D4: 3,9 => CTR * ...6..4.....8..7.14...12..58...462.76.41.7.5..3.5.89..568...1422734.1..994126..7. * PAIR F6: 4,8 BLK 5 E6: 4,8,2 # reduction candidate for 4,8 E6: 4,8 => CTR * ...6........8..7.14...12..58..1.62.7.14927.5.7325..916568...1422734.1..994126..7. * PAIR F6: 4,8 ROW 6 H6: 4,8,1 # reduction candidate for 4,8 H6: 4,8 # 22 pairs I6: 4,8,6 # reduction candidate for 4,8 I6: 4,8 => CTR * .1.6..4833.68.472148.3126958..146237124937856637528914568...142273481569941265378 * RESTART * PAIR RESTART * PAIR F7: 3,9 BLK 8 D7: 3,9,7 # reduction candidate for 3,9 D7: 3,9 # 26 pairs E7: 3,9,7 # reduction candidate for 3,9 E7: 3,9 # 16 pairs * PAIR F7: 3,9 COL F F1: 3,9,5 # reduction candidate for 3,9 F1: 5 => CTR * ...6.5..435.8.97.14...12..58....6237624.8715..3..2.9.6568..3412273451..9941268573 * PAIR RESTART * PAIR F7: 3,9 BLK 8 D7: 3,9,7 # reduction candidate for 3,9 D7: 3,9 # 28 pairs E7: 3,9,7 # reduction candidate for 3,9 E7: 3,9 # 18 pairs * PAIR E8: 5,8 ROW 8 G8: 5,8,6 # reduction candidate for 5,8 G8: 6 => CTR * ...6....43..8..7.14...12..58....62.7624..715..3..2.9.6568...412273451689941268573 * PAIR RESTART * PAIR F9: 5,8 ROW 9 G9: 5,8,3 # reduction candidate for 5,8 G9: 5,8 => SOLVED * 152679384396854721487312695819546237624937158735128946568793412273481569941265873 * DURATION: 0:00:18.843075 START: 22:01:52.481927 END: 22:02:11.325002 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060330-absurd-base-pr-001.dot * REASONING * DIS # D4: 3,9 => CTR => D4: 1,5 * DIS D4: 1,5 # E6: 4,8 => CTR => E6: 2 * DIS D4: 1,5 + E6: 2 # I6: 4,8 => CTR => I6: 6 * DIS D4: 1,5 + E6: 2 + I6: 6 # F1: 5 => CTR => F1: 3,9 * DIS D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 6 => CTR => G8: 5,8 * PRF D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 # G9: 5,8 => SOL * STA D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 + G9: 5,8 * CNT 6 HDP CHAINS / 28 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060330, absurd
Solution
position: 152679384396854721487312695819546237624937158735128946568793412273481569941265873 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 # H2: 3,6 => UNS * INC # H2: 2,4,9 => UNS * INC # B1: 8,9 => UNS * INC # B1: 1,2,5 => UNS * INC # H3: 8,9 => UNS * INC # H3: 3,6 => UNS * INC # B4: 5,9 => UNS * INC # B4: 1 => UNS * INC # D4: 5,9 => UNS * INC # D4: 1,3 => UNS * INC # C1: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # A6: 1,6 => UNS * INC # A6: 7 => UNS * INC # D4: 1,5 => UNS * DIS # D4: 3,9 => CTR => D4: 1,5 * DIS # E6: 4,8 => CTR => E6: 2 * INC # E6: 2 => UNS * INC # H6: 4,8 => UNS * DIS # I6: 4,8 => CTR => I6: 6 * INC # I6: 6 => UNS * INC # D7: 3,9 => UNS * INC # E7: 3,9 => UNS * INC # F1: 3,9 => UNS * INC # F2: 3,9 => UNS * INC # G8: 5,8 => UNS * DIS # G8: 6 => CTR => G8: 5,8 * INC # G9: 5,8 => UNS * DIS # G9: 3 => CTR => G9: 5,8 * DIS # H4: 1,4 => CTR => H4: 3 * PRF # H4: 3 => SOL * PRF # H6: 1,4 => SOL * DIS # H6: 8 => CTR => H6: 1,4 * DIS # G8: 6,8 => CTR => G8: 5 * PRF # G8: 5 => SOL * DIS # H3: 6,8 => CTR => H3: 3,9 * INC # H3: 3,9 => UNS * PRF # G9: 3,8 => SOL * DIS # G9: 5 => CTR => G9: 3,8 * DIS # I1: 3,8 => CTR => I1: 4 * INC # I1: 4 => UNS * INC # I5: 3,8 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 3,6 => UNS * INC # H2: 2,4,9 => UNS * INC # B1: 8,9 => UNS * INC # B1: 1,2,5 => UNS * INC # H3: 8,9 => UNS * INC # H3: 3,6 => UNS * INC # B4: 5,9 => UNS * INC # B4: 1 => UNS * INC # D4: 5,9 => UNS * INC # D4: 1,3 => UNS * INC # C1: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # A6: 1,6 => UNS * INC # A6: 7 => UNS * INC # D4: 1,5 => UNS * DIS # D4: 3,9 => CTR => D4: 1,5 * DIS D4: 1,5 # E6: 4,8 => CTR => E6: 2 * INC D4: 1,5 + E6: 2 # H6: 4,8 => UNS * DIS D4: 1,5 + E6: 2 # I6: 4,8 => CTR => I6: 6 * INC D4: 1,5 + E6: 2 + I6: 6 # D7: 3,9 => UNS * INC D4: 1,5 + E6: 2 + I6: 6 # E7: 3,9 => UNS * INC D4: 1,5 + E6: 2 + I6: 6 # F1: 3,9 => UNS * DIS D4: 1,5 + E6: 2 + I6: 6 # F1: 5 => CTR => F1: 3,9 * INC D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # D7: 3,9 => UNS * INC D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # E7: 3,9 => UNS * INC D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 5,8 => UNS * DIS D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 # G8: 6 => CTR => G8: 5,8 * PRF D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 # G9: 5,8 => SOL * STA D4: 1,5 + E6: 2 + I6: 6 + F1: 3,9 + G8: 5,8 + G9: 5,8 * CNT 28 HDP CHAINS / 28 HYP OPENED