Analysis of zz-www.sudokuoftheday.co.uk-20060429-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: 9.6.7..3..4...3...83.....9..8.5..2....2..4..87........6.438.9.....7.26.33...4..81 initial
Autosolve
position: 9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 1,5 => CTR => B5: 6,9 * DIS # B6: 1,5 => CTR => B6: 6,9 * PRF # B8: 1,5 => SOL * DIS # B8: 9 => CTR => B8: 1,5 * PRF # G1: 5,8 => SOL * PRF # F9: 5,6 => SOL * DIS # F9: 9 => CTR => F9: 5,6 * DIS # D1: 1,8 => CTR => D1: 2,4 * DIS # B5: 1,5 => CTR => B5: 6,9 * DIS # B6: 1,5 => CTR => B6: 6,9 * DIS # C6: 1,5 => CTR => C6: 3,9 * DIS # G5: 1,5 => CTR => G5: 3 * PRF # B8: 1,5 => SOL * DIS # B8: 9 => CTR => B8: 1,5 * DIS # B8: 1 => CTR => B8: 5,9 * DIS # F9: 6 => CTR => F9: 5,9 * DIS # C6: 5,9 => CTR => C6: 1,3 * DIS # F9: 6 => CTR => F9: 5,9 * DIS # B8: 1 => CTR => B8: 5,9 * DIS # F9: 6,9 => CTR => F9: 5 * PRF # F9: 5 => SOL * DIS # D5: 6,9 => CTR => D5: 1 * DIS # D6: 6,9 => CTR => D6: 1,2,8 * CNT 23 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 1,5 => CTR => B5: 6,9 * DIS B5: 6,9 # B6: 1,5 => CTR => B6: 6,9 * PRF B5: 6,9 + B6: 6,9 => SOL * STA B5: 6,9 + B6: 6,9 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.6.7..3..4...3...83.....9..8.5..2....2..4..87........6.438.9.....7.26.33...4..81 | initial |
| 9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781 | autosolve |
| 916478532247953816835216497481537269592164378763829154674381925158792643329645781 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B1: 1,5 F1: 5,8 F3: 5,6 I1: 2,4 I2: 6,7 A5: 1,5 H4: 1,6 I4: 6,9 A8: 1,5 C9: 5,9 E8: 5,9 D9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,B8: 1.. / A8 = 1 => 12 pairs (_) / B8 = 1 => 0 pairs (X) A5,A8: 1.. / A5 = 1 => 0 pairs (X) / A8 = 1 => 12 pairs (_) I1,I3: 2.. / I1 = 2 => 11 pairs (_) / I3 = 2 => 0 pairs (X) D6,E6: 2.. / D6 = 2 => 0 pairs (X) / E6 = 2 => 14 pairs (_) D1,I1: 2.. / D1 = 2 => 0 pairs (X) / I1 = 2 => 11 pairs (_) E3,E6: 2.. / E3 = 2 => 0 pairs (X) / E6 = 2 => 14 pairs (_) C4,C6: 3.. / C4 = 3 => 12 pairs (_) / C6 = 3 => 15 pairs (_) G5,G6: 3.. / G5 = 3 => 12 pairs (_) / G6 = 3 => 0 pairs (X) C4,E4: 3.. / C4 = 3 => 12 pairs (_) / E4 = 3 => 15 pairs (_) E5,G5: 3.. / E5 = 3 => 0 pairs (X) / G5 = 3 => 12 pairs (_) D1,D3: 4.. / D1 = 4 => 11 pairs (_) / D3 = 4 => 13 pairs (_) G6,I6: 4.. / G6 = 4 => 16 pairs (_) / I6 = 4 => 13 pairs (_) E8,F9: 5.. / E8 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) C9,F9: 5.. / C9 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) A5,A8: 5.. / A5 = 5 => 12 pairs (_) / A8 = 5 => 0 pairs (X) H2,H6: 5.. / H2 = 5 => 18 pairs (_) / H6 = 5 => 14 pairs (_) B5,B6: 6.. / B5 = 6 => 0 pairs (X) / B6 = 6 => 15 pairs (_) D9,F9: 6.. / D9 = 6 => 13 pairs (_) / F9 = 6 => 0 pairs (X) C2,C3: 7.. / C2 = 7 => 12 pairs (_) / C3 = 7 => 12 pairs (_) I2,I3: 7.. / I2 = 7 => 12 pairs (_) / I3 = 7 => 12 pairs (_) C2,I2: 7.. / C2 = 7 => 12 pairs (_) / I2 = 7 => 12 pairs (_) C3,I3: 7.. / C3 = 7 => 12 pairs (_) / I3 = 7 => 12 pairs (_) G1,G2: 8.. / G1 = 8 => 0 pairs (X) / G2 = 8 => 14 pairs (_) D6,F6: 8.. / D6 = 8 => 15 pairs (_) / F6 = 8 => 0 pairs (X) D2,G2: 8.. / D2 = 8 => 0 pairs (X) / G2 = 8 => 14 pairs (_) F1,F6: 8.. / F1 = 8 => 15 pairs (_) / F6 = 8 => 0 pairs (X) D2,E2: 9.. / D2 = 9 => 15 pairs (_) / E2 = 9 => 0 pairs (X) I4,I6: 9.. / I4 = 9 => 13 pairs (_) / I6 = 9 => 0 pairs (X) B8,C9: 9.. / B8 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) B8,E8: 9.. / B8 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) F6,F9: 9.. / F6 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) * DURATION: 0:00:31.814941 START: 22:45:03.184824 END: 22:45:34.999765 2019-04-30 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,D9,E8,F1,F3,H4,I1,I2,I4) * 9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781 * PAIR B1: 1,5 BLK 1 C2: 1,5,7 # reduction candidate for 1,5 C2: 1,5 # 12 pairs C3: 1,5,7 # reduction candidate for 1,5 C3: 1,5 # 12 pairs * PAIR B1: 1,5 ROW 1 G1: 1,5,4,8 # reduction candidate for 1,5 G1: 1,5 # 15 pairs G1: 4,8 # 13 pairs * PAIR B1: 1,5 COL B B5: 1,5,6,9 # reduction candidate for 1,5 B5: 1,5 => CTR * 956.78.3.24...385.83...5.9.48.5.7269512..4378769......674381925.98752643325.4.781 B5: 6,9 # 13 pairs B6: 1,5,6,9 # reduction candidate for 1,5 B6: 1,5 => CTR * 956.78.3224...385.83.2.549.48.567219562.34.7871.82.564674381925198752643325.46781 B6: 6,9 # 13 pairs B8: 1,5,9 # reduction candidate for 1,5 B8: 1,5 => SOLVED * 916478532247953816835216497481537269592164378763829154674381925158792643329645781 B8: 9 => CTR * 956.78.3224...385.83.2.549.48.5.72.95.2..43787..82.5.4674381925198752643325.4.781 * PAIR F1: 5,8 ROW 1 G1: 5,8,1,4 # reduction candidate for 5,8 G1: 5,8 => SOLVED * 916478532247953816835216497481537269592164378763829154674381925158792643329645781 G1: 1,4 # 15 pairs * PAIR F3: 5,6 BLK 2 E2: 5,6,1,9 # reduction candidate for 5,6 E2: 5,6 # 22 pairs E3: 5,6,1,2 # reduction candidate for 5,6 E3: 5,6 # 23 pairs * PAIR F3: 5,6 COL F F9: 5,6,9 # reduction candidate for 5,6 F9: 5,6 => SOLVED * 916478532247953816835216497481537269592164378763829154674381925158792643329645781 F9: 9 => CTR * 956.78.3.24...385.83...5.9.48.5.72..5.2..4.787..826514674381925198752643325649781 * PAIR I1: 2,4 BLK 3 I3: 2,4,6,7 # reduction candidate for 2,4 I3: 2,4 # 16 pairs I3: 6,7 # 13 pairs * PAIR I1: 2,4 ROW 1 D1: 2,4,1,8 # reduction candidate for 2,4 D1: 1,8 => CTR * 9.6.7543224...38..83.426.9748.5.72.9..2..4.787.92.8..4674381925.98752643325649781 D1: 2,4 # 13 pairs * PAIR I2: 6,7 BLK 3 I3: 6,7,2,4 # reduction candidate for 6,7 I3: 2,4 # 16 pairs I3: 6,7 # 13 pairs * PAIR A5: 1,5 BLK 4 B5: 1,5,6,9 # reduction candidate for 1,5 B5: 1,5 => CTR * 956.78.3.24...385.83...5.9.48.5.7269512..4378769......674381925.98752643325.4.781 B5: 6,9 # 13 pairs B6: 1,5,6,9 # reduction candidate for 1,5 B6: 1,5 => CTR * 956.78.3224...385.83.2.549.48.567219562.34.7871.82.564674381925198752643325.46781 B6: 6,9 # 13 pairs C6: 1,5,3,9 # reduction candidate for 1,5 C6: 1,5 => CTR * 9.6.78.3224.9.38..83.2.64974835.72.9.921.4.787..8293.4674381925..8792643329645781 C6: 3,9 # 13 pairs * PAIR A5: 1,5 ROW 5 G5: 1,5,3 # reduction candidate for 1,5 G5: 1,5 => CTR * 956.78.32247193856831..54974835.72.95629341787.....3.4674381925.98752643325.4.781 G5: 3 # 12 pairs * PAIR H4: 1,6 BLK 6 H6: 1,6,5 # reduction candidate for 1,6 H6: 1,6 # 18 pairs H6: 5 # 14 pairs * PAIR H4: 1,6 ROW 4 E4: 1,6,3,9 # reduction candidate for 1,6 E4: 3,9 # 15 pairs E4: 1,6 # 13 pairs * PAIR H4: 1,6 COL H H2: 1,6,5 # reduction candidate for 1,6 H2: 5 # 18 pairs H2: 1,6 # 14 pairs * PAIR I4: 6,9 BLK 6 I6: 6,9,4 # reduction candidate for 6,9 I6: 6,9 # 16 pairs I6: 4 # 13 pairs * PAIR I4: 6,9 ROW 4 E4: 6,9,1,3 # reduction candidate for 6,9 E4: 6,9 # 15 pairs E4: 1,3 # 15 pairs * PAIR A8: 1,5 BLK 7 B8: 1,5,9 # reduction candidate for 1,5 B8: 1,5 => SOLVED * 916478532247953816835216497481537269592164378763829154674381925158792643329645781 B8: 9 => CTR * 956.78.3224...385.83.2.549.48.5.72.95.2..43787..82.5.4674381925198752643325.4.781 * PAIR C9: 5,9 BLK 7 B8: 5,9,1 # reduction candidate for 5,9 B8: 1 => CTR * 956.78.3.24.9.38..83...6.9.48.5.72.91.2..4.787........674381925.18792643329645781 B8: 5,9 # 12 pairs * PAIR C9: 5,9 ROW 9 F9: 5,9,6 # reduction candidate for 5,9 F9: 6 => CTR * 956.78.3.24..9385.83...5.9.489537216..2..4.787....9...674381925..8752643325946781 F9: 5,9 # 13 pairs * PAIR C9: 5,9 COL C C6: 5,9,1,3 # reduction candidate for 5,9 C6: 5,9 => CTR * 95647813224.9.385.83.256497483567219..2.345787.582.3.4674381925518792643329645781 C6: 1,3 # 13 pairs * PAIR E8: 5,9 BLK 8 F9: 5,9,6 # reduction candidate for 5,9 F9: 6 => CTR * 956.78.3.24..9385.83...5.9.489537216..2..4.787....9...674381925..8752643325946781 F9: 5,9 # 13 pairs * PAIR E8: 5,9 ROW 8 B8: 5,9,1 # reduction candidate for 5,9 B8: 1 => CTR * 956.78.3.24.9.38..83...6.9.48.5.72.91.2..4.787........674381925.18792643329645781 B8: 5,9 # 12 pairs * PAIR E8: 5,9 COL E E2: 5,9,1,6 # reduction candidate for 5,9 E2: 1,6 # 16 pairs E2: 5,9 # 13 pairs * PAIR D9: 6,9 BLK 8 F9: 6,9,5 # reduction candidate for 6,9 F9: 6,9 => CTR * 956.78.3224...385.83.2.549.48.5.72.95.2..43787..82.5.4674381925198752643325.4.781 F9: 5 => SOLVED * 916478532247953816835216497481537269592164378763829154674381925158792643329645781 * PAIR D9: 6,9 COL D D2: 6,9,1,8 # reduction candidate for 6,9 D2: 6,9 # 16 pairs D5: 6,9,1 # reduction candidate for 6,9 D5: 6,9 => CTR * 956.78.3.24.193856831..549748.5.72.95.29.4.787.9826...674381925.98752643325.4.781 D5: 1 # 13 pairs D6: 6,9,1,2,8 # reduction candidate for 6,9 D6: 6,9 => CTR * 9.6.75.3.24...3...83...6.9.48.5.72....2..4.787...28...674381925.98752643325649781 D6: 1,2,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060429-absurd-base-pr-000.dot * REASONING * DIS # B5: 1,5 => CTR => B5: 6,9 * DIS # B6: 1,5 => CTR => B6: 6,9 * PRF # B8: 1,5 => SOL * DIS # B8: 9 => CTR => B8: 1,5 * PRF # G1: 5,8 => SOL * PRF # F9: 5,6 => SOL * DIS # F9: 9 => CTR => F9: 5,6 * DIS # D1: 1,8 => CTR => D1: 2,4 * DIS # B5: 1,5 => CTR => B5: 6,9 * DIS # B6: 1,5 => CTR => B6: 6,9 * DIS # C6: 1,5 => CTR => C6: 3,9 * DIS # G5: 1,5 => CTR => G5: 3 * PRF # B8: 1,5 => SOL * DIS # B8: 9 => CTR => B8: 1,5 * DIS # B8: 1 => CTR => B8: 5,9 * DIS # F9: 6 => CTR => F9: 5,9 * DIS # C6: 5,9 => CTR => C6: 1,3 * DIS # F9: 6 => CTR => F9: 5,9 * DIS # B8: 1 => CTR => B8: 5,9 * DIS # F9: 6,9 => CTR => F9: 5 * PRF # F9: 5 => SOL * DIS # D5: 6,9 => CTR => D5: 1 * DIS # D6: 6,9 => CTR => D6: 1,2,8 * CNT 23 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,D9,E8,F1,F3,H4,I1,I2,I4) * 9.6.7..3.24...3...83.....9.48.5.72....2..4.787........674381925..87.264332..4.781 * PAIR B1: 1,5 BLK 1 C2: 1,5,7 # reduction candidate for 1,5 C2: 1,5 # 12 pairs C3: 1,5,7 # reduction candidate for 1,5 C3: 1,5 # 12 pairs * PAIR B1: 1,5 ROW 1 G1: 1,5,4,8 # reduction candidate for 1,5 G1: 1,5 # 15 pairs G1: 4,8 # 13 pairs * PAIR B1: 1,5 COL B B5: 1,5,6,9 # reduction candidate for 1,5 B5: 1,5 => CTR * 956.78.3.24...385.83...5.9.48.5.7269512..4378769......674381925.98752643325.4.781 B6: 1,5,6,9 # reduction candidate for 1,5 B6: 1,5 => CTR * 956.78.3224...385.83.2.549.48.567219562.34.7871.82.564674381925198752643325.46781 B6: 6,9 => SOLVED * 916478532247953816835216497481537269592164378763829154674381925158792643329645781 * DURATION: 0:00:03.919539 START: 22:46:09.623771 END: 22:46:13.543310 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060429-absurd-base-pr-001.dot * REASONING * DIS # B5: 1,5 => CTR => B5: 6,9 * DIS B5: 6,9 # B6: 1,5 => CTR => B6: 6,9 * PRF B5: 6,9 + B6: 6,9 => SOL * STA B5: 6,9 + B6: 6,9 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060429, absurd
Solution
position: 916478532247953816835216497481537269592164378763829154674381925158792643329645781 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 # C2: 1,5 => UNS * INC # C3: 1,5 => UNS * INC # G1: 1,5 => UNS * INC # G1: 4,8 => UNS * DIS # B5: 1,5 => CTR => B5: 6,9 * INC # B5: 6,9 => UNS * DIS # B6: 1,5 => CTR => B6: 6,9 * INC # B6: 6,9 => UNS * PRF # B8: 1,5 => SOL * DIS # B8: 9 => CTR => B8: 1,5 * PRF # G1: 5,8 => SOL * INC # G1: 1,4 => UNS * INC # E2: 5,6 => UNS * INC # E3: 5,6 => UNS * PRF # F9: 5,6 => SOL * DIS # F9: 9 => CTR => F9: 5,6 * INC # I3: 2,4 => UNS * INC # I3: 6,7 => UNS * INC # D1: 2,4 => UNS * DIS # D1: 1,8 => CTR => D1: 2,4 * INC # I3: 6,7 => UNS * INC # I3: 2,4 => UNS * DIS # B5: 1,5 => CTR => B5: 6,9 * INC # B5: 6,9 => UNS * DIS # B6: 1,5 => CTR => B6: 6,9 * INC # B6: 6,9 => UNS * DIS # C6: 1,5 => CTR => C6: 3,9 * INC # C6: 3,9 => UNS * DIS # G5: 1,5 => CTR => G5: 3 * INC # G5: 3 => UNS * INC # H6: 1,6 => UNS * INC # H6: 5 => UNS * INC # E4: 1,6 => UNS * INC # E4: 3,9 => UNS * INC # H2: 1,6 => UNS * INC # H2: 5 => UNS * INC # I6: 6,9 => UNS * INC # I6: 4 => UNS * INC # E4: 6,9 => UNS * INC # E4: 1,3 => UNS * PRF # B8: 1,5 => SOL * DIS # B8: 9 => CTR => B8: 1,5 * INC # B8: 5,9 => UNS * DIS # B8: 1 => CTR => B8: 5,9 * INC # F9: 5,9 => UNS * DIS # F9: 6 => CTR => F9: 5,9 * DIS # C6: 5,9 => CTR => C6: 1,3 * INC # C6: 1,3 => UNS * INC # F9: 5,9 => UNS * DIS # F9: 6 => CTR => F9: 5,9 * INC # B8: 5,9 => UNS * DIS # B8: 1 => CTR => B8: 5,9 * INC # E2: 5,9 => UNS * INC # E2: 1,6 => UNS * DIS # F9: 6,9 => CTR => F9: 5 * PRF # F9: 5 => SOL * INC # D2: 6,9 => UNS * DIS # D5: 6,9 => CTR => D5: 1 * INC # D5: 1 => UNS * DIS # D6: 6,9 => CTR => D6: 1,2,8 * INC # D6: 1,2,8 => UNS * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 1,5 => UNS * INC # C3: 1,5 => UNS * INC # G1: 1,5 => UNS * INC # G1: 4,8 => UNS * DIS # B5: 1,5 => CTR => B5: 6,9 * DIS B5: 6,9 # B6: 1,5 => CTR => B6: 6,9 * PRF B5: 6,9 + B6: 6,9 => SOL * STA B5: 6,9 + B6: 6,9 * CNT 7 HDP CHAINS / 6 HYP OPENED