Analysis of zz-www.sudokuoftheday.co.uk-20190104-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..3....8...4...7...8.1.3...3.24.5...9......648............7...3.4...2.1.1......9 initial
Autosolve
position: 2..3....8..34...7...8.1.3...3.249587.92..3..648...1923.2.1378..374...2.181..24739 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 1,9 => CTR => C1: 7 * PRF # C1: 7 => SOL * DIS # B1: 5,6 => CTR => B1: 4 * DIS # E2: 5,6 => CTR => E2: 8,9 * DIS # F2: 5,6 => CTR => F2: 2,8 * DIS # C1: 1 => CTR => C1: 7,9 * DIS # D3: 5,6 => CTR => D3: 7,9 * PRF # E1: 5,6 => SOL * DIS # E2: 5,6 => CTR => E2: 8,9 * DIS # F2: 5,6 => CTR => F2: 2,8 * DIS # D3: 5,6 => CTR => D3: 7,9 * DIS # F3: 5,6 => CTR => F3: 2 * DIS # B1: 5,6 => CTR => B1: 4 * DIS # F8: 8 => CTR => F8: 5,6 * DIS # G1: 4 => CTR => G1: 1,6 * DIS # I3: 4 => CTR => I3: 2,5 * DIS # F2: 2,5 => CTR => F2: 6,8 * DIS # D5: 5,7 => CTR => D5: 8 * PRF # E6: 5,7 => SOL * DIS # G1: 6 => CTR => G1: 1,4 * DIS # H1: 1,4 => CTR => H1: 5,9 * DIS # C7: 5,6 => CTR => C7: 9 * DIS # D8: 5,6 => CTR => D8: 8,9 * DIS # E8: 5,6 => CTR => E8: 8,9 * DIS # D3: 5,6 => CTR => D3: 7,9 * DIS # H7: 4,5 => CTR => H7: 6 * DIS # I3: 2 => CTR => I3: 4,5 * DIS # H7: 4 => CTR => H7: 5,6 * DIS # D8: 5,6 => CTR => D8: 8,9 * DIS # E8: 5,6 => CTR => E8: 8,9 * CNT 30 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 1,9 => CTR => C1: 7 * PRF C1: 7 => SOL * STA C1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2..3....8...4...7...8.1.3...3.24.5...9......648............7...3.4...2.1.1......9 | initial |
| 2..3....8..34...7...8.1.3...3.249587.92..3..648...1923.2.1378..374...2.181..24739 | autosolve |
| 247365198153498672968712345631249587792853416485671923529137864374986251816524739 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 1,9 B2: 5,6 A3: 7,9 F1: 5,6 G2: 1,6 I2: 2,5 A4: 1,6 C4: 1,6 A5: 5,7 C6: 5,7 G5: 1,4 H5: 1,4 C9: 5,6 D9: 5,6 I7: 4,5 H8: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,A2: 1.. / C1 = 1 => 0 pairs (X) / A2 = 1 => 18 pairs (_) A4,C4: 1.. / A4 = 1 => 0 pairs (X) / C4 = 1 => 18 pairs (_) G5,H5: 1.. / G5 = 1 => 0 pairs (X) / H5 = 1 => 15 pairs (_) A2,G2: 1.. / A2 = 1 => 18 pairs (_) / G2 = 1 => 0 pairs (X) A2,A4: 1.. / A2 = 1 => 18 pairs (_) / A4 = 1 => 0 pairs (X) C1,C4: 1.. / C1 = 1 => 0 pairs (X) / C4 = 1 => 18 pairs (_) H1,H5: 1.. / H1 = 1 => 0 pairs (X) / H5 = 1 => 15 pairs (_) F2,F3: 2.. / F2 = 2 => 0 pairs (X) / F3 = 2 => 16 pairs (_) I2,I3: 2.. / I2 = 2 => 16 pairs (_) / I3 = 2 => 0 pairs (X) F2,I2: 2.. / F2 = 2 => 0 pairs (X) / I2 = 2 => 16 pairs (_) F3,I3: 2.. / F3 = 2 => 16 pairs (_) / I3 = 2 => 0 pairs (X) B1,B3: 4.. / B1 = 4 => 17 pairs (_) / B3 = 4 => 0 pairs (X) G5,H5: 4.. / G5 = 4 => 15 pairs (_) / H5 = 4 => 0 pairs (X) H7,I7: 4.. / H7 = 4 => 0 pairs (X) / I7 = 4 => 18 pairs (_) G1,G5: 4.. / G1 = 4 => 0 pairs (X) / G5 = 4 => 15 pairs (_) I3,I7: 4.. / I3 = 4 => 0 pairs (X) / I7 = 4 => 18 pairs (_) A5,C6: 5.. / A5 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) C9,D9: 5.. / C9 = 5 => 0 pairs (X) / D9 = 5 => 16 pairs (_) A5,A7: 5.. / A5 = 5 => 0 pairs (X) / A7 = 5 => 0 pairs (_) G1,G2: 6.. / G1 = 6 => 0 pairs (X) / G2 = 6 => 18 pairs (_) A4,C4: 6.. / A4 = 6 => 18 pairs (_) / C4 = 6 => 0 pairs (X) D6,E6: 6.. / D6 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) H7,H8: 6.. / H7 = 6 => 16 pairs (_) / H8 = 6 => 0 pairs (X) C9,D9: 6.. / C9 = 6 => 16 pairs (_) / D9 = 6 => 0 pairs (X) A4,A7: 6.. / A4 = 6 => 18 pairs (_) / A7 = 6 => 0 pairs (X) C1,A3: 7.. / C1 = 7 => 0 pairs (*) / A3 = 7 => 0 pairs (X) E1,D3: 7.. / E1 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) A5,C6: 7.. / A5 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) C1,E1: 7.. / C1 = 7 => 0 pairs (*) / E1 = 7 => 0 pairs (X) A3,D3: 7.. / A3 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) A3,A5: 7.. / A3 = 7 => 0 pairs (X) / A5 = 7 => 0 pairs (_) C1,C6: 7.. / C1 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) E2,F2: 8.. / E2 = 8 => 0 pairs (X) / F2 = 8 => 19 pairs (_) D5,E5: 8.. / D5 = 8 => 17 pairs (_) / E5 = 8 => 0 pairs (X) D5,D8: 8.. / D5 = 8 => 17 pairs (_) / D8 = 8 => 0 pairs (X) F2,F8: 8.. / F2 = 8 => 19 pairs (_) / F8 = 8 => 0 pairs (X) H1,H3: 9.. / H1 = 9 => 21 pairs (_) / H3 = 9 => 0 pairs (X) A7,C7: 9.. / A7 = 9 => 0 pairs (X) / C7 = 9 => 18 pairs (_) D8,E8: 9.. / D8 = 9 => 17 pairs (_) / E8 = 9 => 0 pairs (X) A2,E2: 9.. / A2 = 9 => 0 pairs (X) / E2 = 9 => 18 pairs (_) C1,C7: 9.. / C1 = 9 => 0 pairs (X) / C7 = 9 => 18 pairs (_) D3,D8: 9.. / D3 = 9 => 0 pairs (X) / D8 = 9 => 17 pairs (_) * DURATION: 0:00:59.620107 START: 02:42:05.090853 END: 02:43:04.710960 2019-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A5,B2,C4,C6,C9,D9,F1,G2,G5,H5,H8,I2,I7) * 2..3....8..34...7...8.1.3...3.249587.92..3..648...1923.2.1378..374...2.181..24739 * PAIR A2: 1,9 BLK 1 C1: 1,9,7 # reduction candidate for 1,9 C1: 1,9 => CTR * 2.1376..89.34.81727.89123..136249587592783416487..19236291378..37489.261815624739 C1: 7 => SOLVED * 247365198153498672968712345631249587792853416485671923529137864374986251816524739 * PAIR B2: 5,6 BLK 1 B1: 5,6,4 # reduction candidate for 5,6 B1: 5,6 => CTR * 26.3.5..81534986727486123956312495875928.3..648...1923.2.1378.43749.6251816524739 B1: 4 # 17 pairs B3: 5,6,4 # reduction candidate for 5,6 B3: 5,6 # 17 pairs * PAIR B2: 5,6 ROW 2 E2: 5,6,8,9 # reduction candidate for 5,6 E2: 5,6 => CTR * 2.1376..89.34.81727.8.123..136249587592..3416487..19236291378..374...261815624739 E2: 8,9 # 17 pairs F2: 5,6,2,8 # reduction candidate for 5,6 F2: 5,6 => CTR * 2..3....89.348.1727.8.123..136249587592873416487..19236291378..374..8261815624739 F2: 2,8 # 17 pairs * PAIR A3: 7,9 BLK 1 C1: 7,9,1 # reduction candidate for 7,9 C1: 1 => CTR * 241375.989.34..17.7.891.3..136249587592783416487..19236291378..37489.261815624739 C1: 7,9 # 18 pairs * PAIR A3: 7,9 ROW 3 D3: 7,9,5,6 # reduction candidate for 7,9 D3: 5,6 => CTR * 2..37...8..3498.727.8.1239..3.249587592783..6487..192392.1378..374...2.181..24739 D3: 7,9 # 21 pairs * PAIR F1: 5,6 BLK 2 E1: 5,6,7,9 # reduction candidate for 5,6 E1: 5,6 => SOLVED * 247365198153498672968712345631249587792853416485671923529137864374986251816524739 E1: 7,9 # 17 pairs E2: 5,6,8,9 # reduction candidate for 5,6 E2: 5,6 => CTR * 2.1376..89.34.81727.8.123..136249587592..3416487..19236291378..374...261815624739 E2: 8,9 # 17 pairs F2: 5,6,2,8 # reduction candidate for 5,6 F2: 5,6 => CTR * 2..3....89.348.1727.8.123..136249587592873416487..19236291378..374..8261815624739 F2: 2,8 # 17 pairs D3: 5,6,7,9 # reduction candidate for 5,6 D3: 5,6 => CTR * 2..37...8..3498.727.8.1239..3.249587592783..6487..192392.1378..374...2.181..24739 D3: 7,9 # 21 pairs F3: 5,6,2 # reduction candidate for 5,6 F3: 5,6 => CTR * 2.137.698963482175..8.1.3.2136249587.928.341648...1923629137854374..8261815624739 F3: 2 # 16 pairs * PAIR F1: 5,6 ROW 1 B1: 5,6,4 # reduction candidate for 5,6 B1: 5,6 => CTR * 26.3.5..81534986727486123956312495875928.3..648...1923.2.1378.43749.6251816524739 B1: 4 # 17 pairs * PAIR F1: 5,6 COL F F8: 5,6,8 # reduction candidate for 5,6 F8: 8 => CTR * 2..3....89.348.17.7.8.1.3..136249587592873416487..19236291378..374..8261815624739 F8: 5,6 # 19 pairs * PAIR G2: 1,6 BLK 3 G1: 1,6,4 # reduction candidate for 1,6 G1: 4 => CTR * 269375418153498672748612395631249587.92..314648...192392.1378.4374986251816524739 G1: 1,6 # 15 pairs * PAIR I2: 2,5 BLK 3 I3: 2,5,4 # reduction candidate for 2,5 I3: 4 => CTR * 24.37...8.534...72768912354.3.249587592783416487561923.2.137845374...261815624739 I3: 2,5 # 18 pairs * PAIR I2: 2,5 ROW 2 F2: 2,5,6,8 # reduction candidate for 2,5 F2: 2,5 => CTR * 2..3....89.348.17.7.8.1.3..136249587592873416487..19236291378..374..8261815624739 F2: 6,8 # 17 pairs * PAIR A5: 5,7 ROW 5 D5: 5,7,8 # reduction candidate for 5,7 D5: 5,7 => CTR * 2.1376..89.34.81727.89123..136249587592783416487..19236291378..37489.261815624739 D5: 8 # 17 pairs E5: 5,7,8 # reduction candidate for 5,7 E5: 5,7 # 17 pairs * PAIR C6: 5,7 ROW 6 D6: 5,7,6 # reduction candidate for 5,7 D6: 5,7 # 17 pairs E6: 5,7,6 # reduction candidate for 5,7 E6: 5,7 => SOLVED * 247365198153498672968712345631249587792853416485671923529137864374986251816524739 E6: 6 # 17 pairs * PAIR G5: 1,4 COL G G1: 1,4,6 # reduction candidate for 1,4 G1: 6 => CTR * 2.13756989.34..17.7.891.3..1362495875927834164875619236291378..374...261815624739 G1: 1,4 # 18 pairs * PAIR H5: 1,4 COL H H1: 1,4,5,9 # reduction candidate for 1,4 H1: 1,4 => CTR * 2..3....8..34...7.7.8.1.39..3.249587592873..6487..1923.2.1378..3749..2.181..24739 H1: 5,9 # 17 pairs * PAIR C9: 5,6 BLK 7 A7: 5,6,9 # reduction candidate for 5,6 A7: 5,6 # 18 pairs C7: 5,6,9 # reduction candidate for 5,6 C7: 5,6 => CTR * 2.937...81.34986727.8.1239.631249587592783..6487..192392.1378..374...2.181..24739 C7: 9 # 18 pairs * PAIR D9: 5,6 BLK 8 D8: 5,6,8,9 # reduction candidate for 5,6 D8: 5,6 => CTR * 2.73....8..34...7...891.3...3.249587.928.3..648.761923.2.1378..374.982.181..24739 D8: 8,9 # 17 pairs E8: 5,6,8,9 # reduction candidate for 5,6 E8: 5,6 => CTR * 2..39...89.348.17.7.8.1.3...3.249587.928.3..648...1923.2.1378..3749.82.181..24739 E8: 8,9 # 17 pairs F8: 5,6,8 # reduction candidate for 5,6 F8: 5,6 # 19 pairs * PAIR D9: 5,6 COL D D3: 5,6,7,9 # reduction candidate for 5,6 D3: 5,6 => CTR * 2..37...8..3498.727.8.1239..3.249587592783..6487..192392.1378..374...2.181..24739 D3: 7,9 # 21 pairs D6: 5,6,7 # reduction candidate for 5,6 D6: 5,6 # 24 pairs * PAIR I7: 4,5 BLK 9 H7: 4,5,6 # reduction candidate for 4,5 H7: 4,5 => CTR * 2..376.989.345..7.7.891.3...3.249587592783..6487561923.2.1378..374895261815624739 H7: 6 # 16 pairs * PAIR I7: 4,5 COL I I3: 4,5,2 # reduction candidate for 4,5 I3: 2 => CTR * 2.137.698963482175..8.1.3.2136249587.928.341648...1923629137854374..8261815624739 I3: 4,5 # 16 pairs * PAIR H8: 5,6 BLK 9 H7: 5,6,4 # reduction candidate for 5,6 H7: 4 => CTR * 24.37...8..34...72768912354.3.249587592783416487561923.2.137845374895261815624739 H7: 5,6 # 18 pairs * PAIR H8: 5,6 ROW 8 D8: 5,6,8,9 # reduction candidate for 5,6 D8: 5,6 => CTR * 2.73....8..34...7...891.3...3.249587.928.3..648.761923.2.1378..374.982.181..24739 D8: 8,9 # 17 pairs E8: 5,6,8,9 # reduction candidate for 5,6 E8: 5,6 => CTR * 2..39...89.348.17.7.8.1.3...3.249587.928.3..648...1923.2.1378..3749.82.181..24739 E8: 8,9 # 17 pairs F8: 5,6,8 # reduction candidate for 5,6 F8: 5,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190104-absurd-base-pr-000.dot * REASONING * DIS # C1: 1,9 => CTR => C1: 7 * PRF # C1: 7 => SOL * DIS # B1: 5,6 => CTR => B1: 4 * DIS # E2: 5,6 => CTR => E2: 8,9 * DIS # F2: 5,6 => CTR => F2: 2,8 * DIS # C1: 1 => CTR => C1: 7,9 * DIS # D3: 5,6 => CTR => D3: 7,9 * PRF # E1: 5,6 => SOL * DIS # E2: 5,6 => CTR => E2: 8,9 * DIS # F2: 5,6 => CTR => F2: 2,8 * DIS # D3: 5,6 => CTR => D3: 7,9 * DIS # F3: 5,6 => CTR => F3: 2 * DIS # B1: 5,6 => CTR => B1: 4 * DIS # F8: 8 => CTR => F8: 5,6 * DIS # G1: 4 => CTR => G1: 1,6 * DIS # I3: 4 => CTR => I3: 2,5 * DIS # F2: 2,5 => CTR => F2: 6,8 * DIS # D5: 5,7 => CTR => D5: 8 * PRF # E6: 5,7 => SOL * DIS # G1: 6 => CTR => G1: 1,4 * DIS # H1: 1,4 => CTR => H1: 5,9 * DIS # C7: 5,6 => CTR => C7: 9 * DIS # D8: 5,6 => CTR => D8: 8,9 * DIS # E8: 5,6 => CTR => E8: 8,9 * DIS # D3: 5,6 => CTR => D3: 7,9 * DIS # H7: 4,5 => CTR => H7: 6 * DIS # I3: 2 => CTR => I3: 4,5 * DIS # H7: 4 => CTR => H7: 5,6 * DIS # D8: 5,6 => CTR => D8: 8,9 * DIS # E8: 5,6 => CTR => E8: 8,9 * CNT 30 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A5,B2,C4,C6,C9,D9,F1,G2,G5,H5,H8,I2,I7) * 2..3....8..34...7...8.1.3...3.249587.92..3..648...1923.2.1378..374...2.181..24739 * PAIR A2: 1,9 BLK 1 C1: 1,9,7 # reduction candidate for 1,9 C1: 1,9 => CTR * 2.1376..89.34.81727.89123..136249587592783416487..19236291378..37489.261815624739 C1: 7 => SOLVED * 247365198153498672968712345631249587792853416485671923529137864374986251816524739 * DURATION: 0:00:02.614287 START: 02:43:51.936403 END: 02:43:54.550690 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190104-absurd-base-pr-001.dot * REASONING * DIS # C1: 1,9 => CTR => C1: 7 * PRF C1: 7 => SOL * STA C1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190104, absurd
Solution
position: 247365198153498672968712345631249587792853416485671923529137864374986251816524739 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:
* DIS # C1: 1,9 => CTR => C1: 7 * PRF # C1: 7 => SOL * DIS # B1: 5,6 => CTR => B1: 4 * INC # B1: 4 => UNS * INC # B3: 5,6 => UNS * DIS # E2: 5,6 => CTR => E2: 8,9 * INC # E2: 8,9 => UNS * DIS # F2: 5,6 => CTR => F2: 2,8 * INC # F2: 2,8 => UNS * INC # C1: 7,9 => UNS * DIS # C1: 1 => CTR => C1: 7,9 * INC # D3: 7,9 => UNS * DIS # D3: 5,6 => CTR => D3: 7,9 * PRF # E1: 5,6 => SOL * INC # E1: 7,9 => UNS * DIS # E2: 5,6 => CTR => E2: 8,9 * INC # E2: 8,9 => UNS * DIS # F2: 5,6 => CTR => F2: 2,8 * INC # F2: 2,8 => UNS * DIS # D3: 5,6 => CTR => D3: 7,9 * INC # D3: 7,9 => UNS * DIS # F3: 5,6 => CTR => F3: 2 * INC # F3: 2 => UNS * DIS # B1: 5,6 => CTR => B1: 4 * INC # B1: 4 => UNS * INC # F8: 5,6 => UNS * DIS # F8: 8 => CTR => F8: 5,6 * INC # G1: 1,6 => UNS * DIS # G1: 4 => CTR => G1: 1,6 * INC # I3: 2,5 => UNS * DIS # I3: 4 => CTR => I3: 2,5 * DIS # F2: 2,5 => CTR => F2: 6,8 * INC # F2: 6,8 => UNS * DIS # D5: 5,7 => CTR => D5: 8 * INC # D5: 8 => UNS * INC # E5: 5,7 => UNS * INC # D6: 5,7 => UNS * PRF # E6: 5,7 => SOL * INC # E6: 6 => UNS * INC # G1: 1,4 => UNS * DIS # G1: 6 => CTR => G1: 1,4 * DIS # H1: 1,4 => CTR => H1: 5,9 * INC # H1: 5,9 => UNS * INC # A7: 5,6 => UNS * DIS # C7: 5,6 => CTR => C7: 9 * INC # C7: 9 => UNS * DIS # D8: 5,6 => CTR => D8: 8,9 * INC # D8: 8,9 => UNS * DIS # E8: 5,6 => CTR => E8: 8,9 * INC # E8: 8,9 => UNS * INC # F8: 5,6 => UNS * DIS # D3: 5,6 => CTR => D3: 7,9 * INC # D3: 7,9 => UNS * INC # D6: 5,6 => UNS * DIS # H7: 4,5 => CTR => H7: 6 * INC # H7: 6 => UNS * INC # I3: 4,5 => UNS * DIS # I3: 2 => CTR => I3: 4,5 * INC # H7: 5,6 => UNS * DIS # H7: 4 => CTR => H7: 5,6 * DIS # D8: 5,6 => CTR => D8: 8,9 * INC # D8: 8,9 => UNS * DIS # E8: 5,6 => CTR => E8: 8,9 * INC # E8: 8,9 => UNS * INC # F8: 5,6 => UNS * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 1,9 => CTR => C1: 7 * PRF C1: 7 => SOL * STA C1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED