Analysis of zz-www.sudokuoftheday.co.uk-20060625-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: ..3..9.........8.9..8........4....1.....73.8..3.14...539741.6..4...2..7...56....4 initial
Autosolve
position: ..3..9.........8.99.8........4....1.....7348.83.14.7.539741.6..4...2..7.2856.71.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H1: 2,5 => SOL * DIS # H2: 2,5 => CTR => H2: 3,4,6 * DIS # G3: 2,5 => CTR => G3: 3 * PRF # G3: 3 => SOL * DIS # H3: 2,5 => CTR => H3: 3,4,6 * DIS # B4: 2,6 => CTR => B4: 5,7 * DIS # I4: 2,6 => CTR => I4: 3 * PRF # D4: 5,9 => SOL * PRF # C6: 2,6 => SOL * DIS # C6: 9 => CTR => C6: 2,6 * DIS # I4: 2,6 => CTR => I4: 3 * DIS # C5: 2,6 => CTR => C5: 1,9 * DIS # G4: 3 => CTR => G4: 2,9 * PRF # C6: 6 => SOL * DIS # C5: 1,6 => CTR => C5: 2,9 * DIS # G8: 5 => CTR => G8: 3,9 * PRF # H1: 2,5 => SOL * DIS # H2: 2,5 => CTR => H2: 3,4,6 * DIS # H3: 2,5 => CTR => H3: 3,4,6 * DIS # G8: 5 => CTR => G8: 3,9 * CNT 20 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H1: 2,5 => SOL * STA H1: 2,5 * CNT 1 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3..9.........8.9..8........4....1.....73.8..3.14...539741.6..4...2..7...56....4 | initial |
| ..3..9.........8.99.8........4....1.....7348.83.14.7.539741.6..4...2..7.2856.71.4 | autosolve |
| 743869521652731849918254367574986213129573486836142795397418652461325978285697134 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) F2: 1,4 F3: 1,4 G1: 2,5 I1: 1,7 I3: 1,7 F4: 2,6 D5: 5,9 F6: 2,6 I5: 2,6 H6: 2,9 B8: 1,6 C8: 1,6 F7: 5,8 D8: 3,9 F8: 5,8 E9: 3,9 H7: 2,5 I7: 2,8 I8: 3,8 H9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 1.. / F2 = 1 => 19 pairs (_) / F3 = 1 => 16 pairs (_) I1,I3: 1.. / I1 = 1 => 18 pairs (_) / I3 = 1 => 17 pairs (_) B8,C8: 1.. / B8 = 1 => 20 pairs (_) / C8 = 1 => 19 pairs (_) F4,F6: 2.. / F4 = 2 => 21 pairs (_) / F6 = 2 => 0 pairs (*) H7,I7: 2.. / H7 = 2 => 0 pairs (X) / I7 = 2 => 18 pairs (_) G4,I4: 3.. / G4 = 3 => 0 pairs (X) / I4 = 3 => 18 pairs (_) D8,E9: 3.. / D8 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) E9,H9: 3.. / E9 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) I4,I8: 3.. / I4 = 3 => 18 pairs (_) / I8 = 3 => 0 pairs (X) F2,F3: 4.. / F2 = 4 => 16 pairs (_) / F3 = 4 => 19 pairs (_) B1,H1: 4.. / B1 = 4 => 20 pairs (_) / H1 = 4 => 20 pairs (_) F7,F8: 5.. / F7 = 5 => 0 pairs (X) / F8 = 5 => 18 pairs (_) H7,G8: 5.. / H7 = 5 => 18 pairs (_) / G8 = 5 => 0 pairs (X) F7,H7: 5.. / F7 = 5 => 0 pairs (X) / H7 = 5 => 18 pairs (_) F8,G8: 5.. / F8 = 5 => 18 pairs (_) / G8 = 5 => 0 pairs (X) F4,F6: 6.. / F4 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) I4,I5: 6.. / I4 = 6 => 0 pairs (X) / I5 = 6 => 22 pairs (_) B8,C8: 6.. / B8 = 6 => 19 pairs (_) / C8 = 6 => 20 pairs (_) C6,F6: 6.. / C6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) I1,I3: 7.. / I1 = 7 => 17 pairs (_) / I3 = 7 => 18 pairs (_) A4,B4: 7.. / A4 = 7 => 20 pairs (_) / B4 = 7 => 21 pairs (_) D1,E1: 8.. / D1 = 8 => 0 pairs (*) / E1 = 8 => 0 pairs (X) D4,E4: 8.. / D4 = 8 => 21 pairs (_) / E4 = 8 => 0 pairs (*) F7,F8: 8.. / F7 = 8 => 18 pairs (_) / F8 = 8 => 0 pairs (X) I7,I8: 8.. / I7 = 8 => 0 pairs (X) / I8 = 8 => 18 pairs (_) F7,I7: 8.. / F7 = 8 => 18 pairs (_) / I7 = 8 => 0 pairs (X) F8,I8: 8.. / F8 = 8 => 0 pairs (X) / I8 = 8 => 18 pairs (_) D1,D4: 8.. / D1 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) E1,E4: 8.. / E1 = 8 => 21 pairs (_) / E4 = 8 => 0 pairs (*) C5,C6: 9.. / C5 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) G4,H6: 9.. / G4 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) D8,E9: 9.. / D8 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) G8,H9: 9.. / G8 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) C5,D5: 9.. / C5 = 9 => 0 pairs (*) / D5 = 9 => 0 pairs (X) C6,H6: 9.. / C6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) D8,G8: 9.. / D8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) E9,H9: 9.. / E9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) E4,E9: 9.. / E4 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) G4,G8: 9.. / G4 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) H6,H9: 9.. / H6 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) * DURATION: 0:00:52.278030 START: 00:05:16.489673 END: 00:06:08.767703 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C8,D5,D8,E9,F2,F3,F4,F6,F7,F8,G1,H6,H7,H9,I1,I3,I5,I7,I8) * ..3..9.........8.99.8........4....1.....7348.83.14.7.539741.6..4...2..7.2856.71.4 * PAIR F2: 1,4 ROW 2 B2: 1,4,2,5,6,7 # reduction candidate for 1,4 B2: 1,4 # 22 pairs B2: 2,5,6,7 # 20 pairs * PAIR F3: 1,4 ROW 3 B3: 1,4,2,5,6,7 # reduction candidate for 1,4 B3: 2,5,6,7 # 20 pairs B3: 1,4 # 19 pairs * PAIR G1: 2,5 BLK 3 H1: 2,5,4,6 # reduction candidate for 2,5 H1: 2,5 => SOLVED * 743869521652731849918254367574986213129573486836142795397418652461325978285697134 H1: 4,6 # 21 pairs H2: 2,5,3,4,6 # reduction candidate for 2,5 H2: 2,5 => CTR * ..3..95......3.8299.8...3....498.213..957348683214679539741.6.24..32.978285697134 H2: 3,4,6 # 20 pairs G3: 2,5,3 # reduction candidate for 2,5 G3: 2,5 => CTR * ..3..9.........8.99.8........4.9..1...957348.83.14.72539741.6524..92537.285637194 G3: 3 => SOLVED * 743869521652731849918254367574986213129573486836142795397418652461325978285697134 H3: 2,5,3,4,6 # reduction candidate for 2,5 H3: 2,5 => CTR * ..386954...273.8.99.8...32...498.213..957348683.1427953974186524..325978285697134 H3: 3,4,6 # 20 pairs * PAIR G1: 2,5 ROW 1 B1: 2,5,1,4,6,7 # reduction candidate for 2,5 B1: 2,5 # 23 pairs D1: 2,5,7,8 # reduction candidate for 2,5 D1: 2,5 # 23 pairs * PAIR I1: 1,7 ROW 1 A1: 1,7,5,6 # reduction candidate for 1,7 A1: 1,7 # 21 pairs B1: 1,7,2,4,5,6 # reduction candidate for 1,7 B1: 1,7 # 22 pairs * PAIR I3: 1,7 ROW 3 B3: 1,7,2,4,5,6 # reduction candidate for 1,7 B3: 2,4,5,6 # 20 pairs B3: 1,7 # 20 pairs * PAIR F4: 2,6 ROW 4 B4: 2,6,5,7 # reduction candidate for 2,6 B4: 2,6 => CTR * ..3..9.........8.99.8......7.4....1....97348.83914672539741.6524..32597.2856.71.4 B4: 5,7 # 21 pairs I4: 2,6,3 # reduction candidate for 2,6 I4: 2,6 => CTR * ..3..9.........8.99.8........4...31.....7348.83.14.79539741.6..4...2.9732856.71.4 I4: 3 # 18 pairs * PAIR D5: 5,9 BLK 5 D4: 5,9,8 # reduction candidate for 5,9 D4: 5,9 => SOLVED * 743869521652731849918254367574986213129573486836142795397418652461325978285697134 D4: 8 # 21 pairs E4: 5,9,8 # reduction candidate for 5,9 E4: 5,9 # 21 pairs * PAIR F6: 2,6 ROW 6 C6: 2,6,9 # reduction candidate for 2,6 C6: 2,6 => SOLVED * 743869521652731849918254367574986213129573486836142795397418652461325978285697134 C6: 9 => CTR * ..3..9.........8.99.8........4.9231.....7348.83914672539741.6524...25.782856.7194 * PAIR I5: 2,6 BLK 6 I4: 2,6,3 # reduction candidate for 2,6 I4: 2,6 => CTR * ..3..9.........8.99.8........4...31.....7348.83.14.79539741.6..4...2.9732856.71.4 I4: 3 # 18 pairs * PAIR I5: 2,6 ROW 5 B5: 2,6,1,5 # reduction candidate for 2,6 B5: 2,6 # 23 pairs C5: 2,6,1,9 # reduction candidate for 2,6 C5: 2,6 => CTR * ..3..9.........8.99.8........4....1....97348.83914672539741.6524..32597.2856.71.4 C5: 1,9 # 21 pairs * PAIR H6: 2,9 BLK 6 G4: 2,9,3 # reduction candidate for 2,9 G4: 3 => CTR * ..3..9.........8.99.8........4...31.....7348.83.14.79539741.6..4...2.9732856.71.4 G4: 2,9 # 18 pairs * PAIR H6: 2,9 ROW 6 C6: 2,9,6 # reduction candidate for 2,9 C6: 6 => SOLVED * 743869521652731849918254367574986213129573486836142795397418652461325978285697134 C6: 2,9 # 21 pairs * PAIR B8: 1,6 COL B B1: 1,6,2,4,5,7 # reduction candidate for 1,6 B1: 1,6 # 22 pairs B2: 1,6,2,4,5,7 # reduction candidate for 1,6 B2: 1,6 # 22 pairs B3: 1,6,2,4,5,7 # reduction candidate for 1,6 B3: 1,6 # 22 pairs B5: 1,6,2,5 # reduction candidate for 1,6 B5: 1,6 # 21 pairs * PAIR C8: 1,6 COL C C2: 1,6,2 # reduction candidate for 1,6 C2: 1,6 # 23 pairs C5: 1,6,2,9 # reduction candidate for 1,6 C5: 1,6 => CTR * ..3..9.........8.99.8........4....1....97348.83914672539741.6524..32597.2856.71.4 C5: 2,9 # 21 pairs * PAIR D8: 3,9 ROW 8 G8: 3,9,5 # reduction candidate for 3,9 G8: 5 => CTR * ..3..9.........8.99.8........4...913...97348.83.14.7.539741.6..4...2..7.2856.71.4 G8: 3,9 # 18 pairs * PAIR H7: 2,5 COL H H1: 2,5,4,6 # reduction candidate for 2,5 H1: 2,5 => SOLVED * 743869521652731849918254367574986213129573486836142795397418652461325978285697134 H1: 4,6 # 21 pairs H2: 2,5,3,4,6 # reduction candidate for 2,5 H2: 2,5 => CTR * ..3..95......3.8299.8...3....498.213..957348683214679539741.6.24..32.978285697134 H2: 3,4,6 # 20 pairs H3: 2,5,3,4,6 # reduction candidate for 2,5 H3: 2,5 => CTR * ..386954...273.8.99.8...32...498.213..957348683.1427953974186524..325978285697134 H3: 3,4,6 # 20 pairs * PAIR H9: 3,9 BLK 9 G8: 3,9,5 # reduction candidate for 3,9 G8: 5 => CTR * ..3..9.........8.99.8........4...913...97348.83.14.7.539741.6..4...2..7.2856.71.4 G8: 3,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060625-absurd-base-pr-000.dot * REASONING * PRF # H1: 2,5 => SOL * DIS # H2: 2,5 => CTR => H2: 3,4,6 * DIS # G3: 2,5 => CTR => G3: 3 * PRF # G3: 3 => SOL * DIS # H3: 2,5 => CTR => H3: 3,4,6 * DIS # B4: 2,6 => CTR => B4: 5,7 * DIS # I4: 2,6 => CTR => I4: 3 * PRF # D4: 5,9 => SOL * PRF # C6: 2,6 => SOL * DIS # C6: 9 => CTR => C6: 2,6 * DIS # I4: 2,6 => CTR => I4: 3 * DIS # C5: 2,6 => CTR => C5: 1,9 * DIS # G4: 3 => CTR => G4: 2,9 * PRF # C6: 6 => SOL * DIS # C5: 1,6 => CTR => C5: 2,9 * DIS # G8: 5 => CTR => G8: 3,9 * PRF # H1: 2,5 => SOL * DIS # H2: 2,5 => CTR => H2: 3,4,6 * DIS # H3: 2,5 => CTR => H3: 3,4,6 * DIS # G8: 5 => CTR => G8: 3,9 * CNT 20 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C8,D5,D8,E9,F2,F3,F4,F6,F7,F8,G1,H6,H7,H9,I1,I3,I5,I7,I8) * ..3..9.........8.99.8........4....1.....7348.83.14.7.539741.6..4...2..7.2856.71.4 * PAIR F2: 1,4 ROW 2 B2: 1,4,2,5,6,7 # reduction candidate for 1,4 B2: 1,4 # 22 pairs B2: 2,5,6,7 # 20 pairs * PAIR F3: 1,4 ROW 3 B3: 1,4,2,5,6,7 # reduction candidate for 1,4 B3: 2,5,6,7 # 20 pairs B3: 1,4 # 19 pairs * PAIR G1: 2,5 BLK 3 H1: 2,5,4,6 # reduction candidate for 2,5 H1: 2,5 => SOLVED * 743869521652731849918254367574986213129573486836142795397418652461325978285697134 * DURATION: 0:00:04.380317 START: 00:06:46.043541 END: 00:06:50.423858 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060625-absurd-base-pr-001.dot * REASONING * PRF # H1: 2,5 => SOL * STA H1: 2,5 * CNT 1 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060625, absurd
Solution
position: 743869521652731849918254367574986213129573486836142795397418652461325978285697134 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 # B2: 1,4 => UNS * INC # B2: 2,5,6,7 => UNS * INC # B3: 1,4 => UNS * INC # B3: 2,5,6,7 => UNS * PRF # H1: 2,5 => SOL * INC # H1: 4,6 => UNS * DIS # H2: 2,5 => CTR => H2: 3,4,6 * INC # H2: 3,4,6 => UNS * DIS # G3: 2,5 => CTR => G3: 3 * PRF # G3: 3 => SOL * DIS # H3: 2,5 => CTR => H3: 3,4,6 * INC # H3: 3,4,6 => UNS * INC # B1: 2,5 => UNS * INC # D1: 2,5 => UNS * INC # A1: 1,7 => UNS * INC # B1: 1,7 => UNS * INC # B3: 1,7 => UNS * INC # B3: 2,4,5,6 => UNS * DIS # B4: 2,6 => CTR => B4: 5,7 * INC # B4: 5,7 => UNS * DIS # I4: 2,6 => CTR => I4: 3 * INC # I4: 3 => UNS * PRF # D4: 5,9 => SOL * INC # D4: 8 => UNS * INC # E4: 5,9 => UNS * PRF # C6: 2,6 => SOL * DIS # C6: 9 => CTR => C6: 2,6 * DIS # I4: 2,6 => CTR => I4: 3 * INC # I4: 3 => UNS * INC # B5: 2,6 => UNS * DIS # C5: 2,6 => CTR => C5: 1,9 * INC # C5: 1,9 => UNS * INC # G4: 2,9 => UNS * DIS # G4: 3 => CTR => G4: 2,9 * INC # C6: 2,9 => UNS * PRF # C6: 6 => SOL * INC # B1: 1,6 => UNS * INC # B2: 1,6 => UNS * INC # B3: 1,6 => UNS * INC # B5: 1,6 => UNS * INC # C2: 1,6 => UNS * DIS # C5: 1,6 => CTR => C5: 2,9 * INC # C5: 2,9 => UNS * INC # G8: 3,9 => UNS * DIS # G8: 5 => CTR => G8: 3,9 * PRF # H1: 2,5 => SOL * INC # H1: 4,6 => UNS * DIS # H2: 2,5 => CTR => H2: 3,4,6 * INC # H2: 3,4,6 => UNS * DIS # H3: 2,5 => CTR => H3: 3,4,6 * INC # H3: 3,4,6 => UNS * INC # G8: 3,9 => UNS * DIS # G8: 5 => CTR => G8: 3,9 * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,4 => UNS * INC # B2: 2,5,6,7 => UNS * INC # B3: 1,4 => UNS * INC # B3: 2,5,6,7 => UNS * PRF # H1: 2,5 => SOL * STA H1: 2,5 * CNT 5 HDP CHAINS / 5 HYP OPENED