Analysis of zz-www.sudokuoftheday.co.uk-20060908-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: 2....9..4.5.27...........1.......167....18.5...4.....2...1..38..3.78...16..3..... initial
Autosolve
position: 2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 5,6 => CTR => I3: 3,8,9 * DIS # D1: 5,6 => CTR => D1: 8 * PRF # E1: 5,6 => SOL * DIS # E1: 3 => CTR => E1: 5,6 * DIS # G8: 5,6 => CTR => G8: 9 * DIS # I2: 6,9 => CTR => I2: 3,8 * DIS # I3: 6,9 => CTR => I3: 3,5,8 * DIS # C2: 6,9 => CTR => C2: 3,8 * DIS # G8: 5 => CTR => G8: 6,9 * PRF # I2: 3,9 => SOL * PRF # C5: 3,7 => SOL * DIS # C5: 6 => CTR => C5: 3,7 * PRF # D6: 6,9 => SOL * PRF # D6: 6,9 => SOL * PRF # I2: 3,9 => SOL * PRF # C7: 5,9 => SOL * DIS # C8: 5,9 => CTR => C8: 2 * DIS # G8: 6 => CTR => G8: 5,9 * PRF # B1: 1,8 => SOL * DIS # B1: 6 => CTR => B1: 1,8 * DIS # C1: 1,8 => CTR => C1: 3,6 * PRF # C1: 3,6 => SOL * DIS # F8: 2,4 => CTR => F8: 5,6 * DIS # E9: 2,4 => CTR => E9: 5,9 * DIS # I7: 5,9 => CTR => I7: 6 * DIS # E9: 2,4 => CTR => E9: 5,9 * DIS # I3: 5,9 => CTR => I3: 3,6,8 * CNT 27 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:
* DIS # I3: 5,6 => CTR => I3: 3,8,9 * DIS I3: 3,8,9 # I2: 6,9 => CTR => I2: 3,8 * PRF I3: 3,8,9 + I2: 3,8 # I3: 8 => SOL * STA I3: 3,8,9 + I2: 3,8 + I3: 8 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2....9..4.5.27...........1.......167....18.5...4.....2...1..38..3.78...16..3..... | initial |
| 2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7.. | autosolve |
| 213869574458271693976543218895432167327618459164957832749125386532786941681394725 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) G1: 5,6 G2: 6,9 H2: 3,9 B4: 8,9 A5: 3,7 B6: 6,9 D4: 4,9 D5: 6,9 I5: 3,9 H6: 3,9 A8: 5,9 B9: 1,8 C9: 1,8 H8: 2,4 H9: 2,4 I9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 0 pairs (*) / C1 = 1 => 0 pairs (X) B9,C9: 1.. / B9 = 1 => 0 pairs (X) / C9 = 1 => 0 pairs (_) B1,B9: 1.. / B1 = 1 => 0 pairs (*) / B9 = 1 => 0 pairs (X) C1,C9: 1.. / C1 = 1 => 0 pairs (X) / C9 = 1 => 0 pairs (_) E4,F4: 2.. / E4 = 2 => 17 pairs (_) / F4 = 2 => 0 pairs (*) C7,C8: 2.. / C7 = 2 => 0 pairs (X) / C8 = 2 => 16 pairs (_) H8,H9: 2.. / H8 = 2 => 0 pairs (X) / H9 = 2 => 15 pairs (_) I5,H6: 3.. / I5 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) C1,E1: 3.. / C1 = 3 => 0 pairs (*) / E1 = 3 => 0 pairs (X) E6,H6: 3.. / E6 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) F3,F4: 3.. / F3 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) H2,H6: 3.. / H2 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) H8,H9: 4.. / H8 = 4 => 15 pairs (_) / H9 = 4 => 0 pairs (X) F8,H8: 4.. / F8 = 4 => 0 pairs (X) / H8 = 4 => 15 pairs (_) D3,D4: 4.. / D3 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) G1,I3: 5.. / G1 = 5 => 18 pairs (_) / I3 = 5 => 0 pairs (X) A4,C4: 5.. / A4 = 5 => 0 pairs (X) / C4 = 5 => 18 pairs (_) D6,E6: 5.. / D6 = 5 => 18 pairs (_) / E6 = 5 => 0 pairs (*) G1,G8: 5.. / G1 = 5 => 18 pairs (_) / G8 = 5 => 0 pairs (X) C5,B6: 6.. / C5 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) I7,G8: 6.. / I7 = 6 => 17 pairs (_) / G8 = 6 => 0 pairs (X) C5,D5: 6.. / C5 = 6 => 0 pairs (X) / D5 = 6 => 0 pairs (_) F8,G8: 6.. / F8 = 6 => 17 pairs (_) / G8 = 6 => 0 pairs (X) B1,B6: 6.. / B1 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) A5,C5: 7.. / A5 = 7 => 19 pairs (_) / C5 = 7 => 0 pairs (*) A7,C7: 7.. / A7 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) A5,A7: 7.. / A5 = 7 => 19 pairs (_) / A7 = 7 => 0 pairs (*) C5,C7: 7.. / C5 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) D1,D3: 8.. / D1 = 8 => 17 pairs (_) / D3 = 8 => 0 pairs (X) I2,I3: 8.. / I2 = 8 => 16 pairs (_) / I3 = 8 => 0 pairs (*) B9,C9: 8.. / B9 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) C2,I2: 8.. / C2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) A3,A4: 8.. / A3 = 8 => 21 pairs (_) / A4 = 8 => 0 pairs (*) B4,B6: 9.. / B4 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) I5,H6: 9.. / I5 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) E7,E9: 9.. / E7 = 9 => 0 pairs (X) / E9 = 9 => 20 pairs (_) B4,D4: 9.. / B4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) D5,I5: 9.. / D5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) E9,I9: 9.. / E9 = 9 => 20 pairs (_) / I9 = 9 => 0 pairs (X) G2,G8: 9.. / G2 = 9 => 0 pairs (X) / G8 = 9 => 19 pairs (_) H2,H6: 9.. / H2 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) * DURATION: 0:00:57.203435 START: 02:28:28.148505 END: 02:29:25.351940 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B4,B6,B9,C9,D4,D5,G1,G2,H2,H6,H8,H9,I5,I9) * 2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7.. * PAIR G1: 5,6 BLK 3 I3: 5,6,3,8,9 # reduction candidate for 5,6 I3: 5,6 => CTR * 2.3..9.7445.271938.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7.. I3: 3,8,9 # 18 pairs * PAIR G1: 5,6 ROW 1 D1: 5,6,8 # reduction candidate for 5,6 D1: 5,6 => CTR * 2..5.967445.271..8.7.8..21.8954..167.2.618459164957832.4.1..38..3.78.9.16..39.7.5 D1: 8 # 17 pairs E1: 5,6,3 # reduction candidate for 5,6 E1: 5,6 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 E1: 3 => CTR * 2...3957445.27169..7..4.21....423167.2.618459164957832.4.16.38..3.78.9.16..39.7.5 * PAIR G1: 5,6 COL G G8: 5,6,9 # reduction candidate for 5,6 G8: 5,6 => CTR * 2.3..9.7445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7.. G8: 9 # 19 pairs * PAIR G2: 6,9 BLK 3 I2: 6,9,3,8 # reduction candidate for 6,9 I2: 6,9 => CTR * 2....9.74458271.3..7....2188954..167.2..18453164.378.2.4.1..38..3.78...16..3..7.. I2: 3,8 # 17 pairs I3: 6,9,3,5,8 # reduction candidate for 6,9 I3: 6,9 => CTR * 2.3.6957445.271.38.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7.. I3: 3,5,8 # 16 pairs * PAIR G2: 6,9 ROW 2 C2: 6,9,3,8 # reduction candidate for 6,9 C2: 6,9 => CTR * 2.3..9.7445.271.38.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7.. C2: 3,8 # 20 pairs * PAIR G2: 6,9 COL G G8: 6,9,5 # reduction candidate for 6,9 G8: 5 => CTR * 2.3..9674456271938.7..6321539....167.2..184531.4.37892.4.1..386.3.7865416..3..729 G8: 6,9 # 18 pairs * PAIR H2: 3,9 BLK 3 I2: 3,9,6,8 # reduction candidate for 3,9 I2: 3,9 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 I2: 6,8 # 17 pairs I3: 3,9,5,6,8 # reduction candidate for 3,9 I3: 3,9 # 21 pairs * PAIR H2: 3,9 ROW 2 C2: 3,9,6,8 # reduction candidate for 3,9 C2: 3,9 # 21 pairs C2: 6,8 # 17 pairs * PAIR A5: 3,7 BLK 4 C5: 3,7,6 # reduction candidate for 3,7 C5: 3,7 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 C5: 6 => CTR * 2....9.7445.271....7....21.......167726918453194..78.2.4.1..38..3.78...16..3..7.. * PAIR B6: 6,9 ROW 6 D6: 6,9,5 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 D6: 5 # 18 pairs * PAIR D5: 6,9 BLK 5 D6: 6,9,5 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 D6: 5 # 18 pairs * PAIR I5: 3,9 COL I I2: 3,9,6,8 # reduction candidate for 3,9 I2: 3,9 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 I2: 6,8 # 17 pairs I3: 3,9,5,6,8 # reduction candidate for 3,9 I3: 3,9 # 21 pairs * PAIR A8: 5,9 BLK 7 A7: 5,9,7 # reduction candidate for 5,9 A7: 5,9 # 19 pairs C7: 5,9,2,7 # reduction candidate for 5,9 C7: 5,9 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 C7: 2,7 # 17 pairs C8: 5,9,2 # reduction candidate for 5,9 C8: 5,9 => CTR * 2....9.7445.271....7....21.......167.2761845916495783274219.38..3.78.9.16..3..7.5 C8: 2 # 16 pairs * PAIR A8: 5,9 ROW 8 G8: 5,9,6 # reduction candidate for 5,9 G8: 6 => CTR * 2.3.6957445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78.6.16..3..7.. G8: 5,9 # 17 pairs * PAIR B9: 1,8 COL B B1: 1,8,6 # reduction candidate for 1,8 B1: 1,8 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 B1: 6 => CTR * 26183957445.271....7....21......3167.2691845.1.4..78.2.4.1..38..3.78...16..3..7.. * PAIR C9: 1,8 COL C C1: 1,8,3,6 # reduction candidate for 1,8 C1: 1,8 => CTR * 2...3957445.27169..7..4.21....423167.2.618459164957832.4.16.38..3.78.9.16..39.7.5 C1: 3,6 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 * PAIR H8: 2,4 ROW 8 F8: 2,4,5,6 # reduction candidate for 2,4 F8: 2,4 => CTR * 2.3.6957445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78.6.16..3..7.. F8: 5,6 # 16 pairs * PAIR H9: 2,4 ROW 9 E9: 2,4,5,9 # reduction candidate for 2,4 E9: 2,4 => CTR * 2....9.7445.27193..7....21.......167.2.9184531.4.37892.4.19.38..3.78...16..3..7.9 E9: 5,9 # 19 pairs F9: 2,4,5 # reduction candidate for 2,4 F9: 2,4 # 19 pairs * PAIR I9: 5,9 BLK 9 I7: 5,9,6 # reduction candidate for 5,9 I7: 5,9 => CTR * 2.3.6957445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78.6.16..3..7.. I7: 6 # 17 pairs G8: 5,9,6 # reduction candidate for 5,9 G8: 5,9 # 17 pairs * PAIR I9: 5,9 ROW 9 E9: 5,9,2,4 # reduction candidate for 5,9 E9: 2,4 => CTR * 2....9.7445.27193..7....21.......167.2.9184531.4.37892.4.19.38..3.78...16..3..7.9 E9: 5,9 # 19 pairs * PAIR I9: 5,9 COL I I3: 5,9,3,6,8 # reduction candidate for 5,9 I3: 5,9 => CTR * 2.3..9.7445.271.38.7...321.39....167.2..184531.4.37892.4.1..386.3.786.416..3..72. I3: 3,6,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060908-absurd-base-pr-000.dot * REASONING * DIS # I3: 5,6 => CTR => I3: 3,8,9 * DIS # D1: 5,6 => CTR => D1: 8 * PRF # E1: 5,6 => SOL * DIS # E1: 3 => CTR => E1: 5,6 * DIS # G8: 5,6 => CTR => G8: 9 * DIS # I2: 6,9 => CTR => I2: 3,8 * DIS # I3: 6,9 => CTR => I3: 3,5,8 * DIS # C2: 6,9 => CTR => C2: 3,8 * DIS # G8: 5 => CTR => G8: 6,9 * PRF # I2: 3,9 => SOL * PRF # C5: 3,7 => SOL * DIS # C5: 6 => CTR => C5: 3,7 * PRF # D6: 6,9 => SOL * PRF # D6: 6,9 => SOL * PRF # I2: 3,9 => SOL * PRF # C7: 5,9 => SOL * DIS # C8: 5,9 => CTR => C8: 2 * DIS # G8: 6 => CTR => G8: 5,9 * PRF # B1: 1,8 => SOL * DIS # B1: 6 => CTR => B1: 1,8 * DIS # C1: 1,8 => CTR => C1: 3,6 * PRF # C1: 3,6 => SOL * DIS # F8: 2,4 => CTR => F8: 5,6 * DIS # E9: 2,4 => CTR => E9: 5,9 * DIS # I7: 5,9 => CTR => I7: 6 * DIS # E9: 2,4 => CTR => E9: 5,9 * DIS # I3: 5,9 => CTR => I3: 3,6,8 * CNT 27 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B4,B6,B9,C9,D4,D5,G1,G2,H2,H6,H8,H9,I5,I9) * 2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7.. * PAIR G1: 5,6 BLK 3 I3: 5,6,3,8,9 # reduction candidate for 5,6 I3: 5,6 => CTR * 2.3..9.7445.271938.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7.. * PAIR G2: 6,9 BLK 3 I2: 6,9,3,8 # reduction candidate for 6,9 I2: 6,9 => CTR * 2....9574458271.3..7....2188954..167.2..18453164.378.2.4.1..38..3.78...16..3..7.. * PAIR H2: 3,9 BLK 3 I3: 3,9,8 # reduction candidate for 3,9 I3: 8 => SOLVED * 213869574458271693976543218895432167327618459164957832749125386532786941681394725 * DURATION: 0:00:05.797407 START: 02:30:05.939861 END: 02:30:11.737268 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060908-absurd-base-pr-001.dot * REASONING * DIS # I3: 5,6 => CTR => I3: 3,8,9 * DIS I3: 3,8,9 # I2: 6,9 => CTR => I2: 3,8 * PRF I3: 3,8,9 + I2: 3,8 # I3: 8 => SOL * STA I3: 3,8,9 + I2: 3,8 + I3: 8 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060908, absurd
Solution
position: 213869574458271693976543218895432167327618459164957832749125386532786941681394725 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 # I3: 5,6 => CTR => I3: 3,8,9 * INC # I3: 3,8,9 => UNS * DIS # D1: 5,6 => CTR => D1: 8 * INC # D1: 8 => UNS * PRF # E1: 5,6 => SOL * DIS # E1: 3 => CTR => E1: 5,6 * DIS # G8: 5,6 => CTR => G8: 9 * INC # G8: 9 => UNS * DIS # I2: 6,9 => CTR => I2: 3,8 * INC # I2: 3,8 => UNS * DIS # I3: 6,9 => CTR => I3: 3,5,8 * INC # I3: 3,5,8 => UNS * DIS # C2: 6,9 => CTR => C2: 3,8 * INC # C2: 3,8 => UNS * INC # G8: 6,9 => UNS * DIS # G8: 5 => CTR => G8: 6,9 * PRF # I2: 3,9 => SOL * INC # I2: 6,8 => UNS * INC # I3: 3,9 => UNS * INC # C2: 3,9 => UNS * INC # C2: 6,8 => UNS * PRF # C5: 3,7 => SOL * DIS # C5: 6 => CTR => C5: 3,7 * PRF # D6: 6,9 => SOL * INC # D6: 5 => UNS * PRF # D6: 6,9 => SOL * INC # D6: 5 => UNS * PRF # I2: 3,9 => SOL * INC # I2: 6,8 => UNS * INC # I3: 3,9 => UNS * INC # A7: 5,9 => UNS * PRF # C7: 5,9 => SOL * INC # C7: 2,7 => UNS * DIS # C8: 5,9 => CTR => C8: 2 * INC # C8: 2 => UNS * INC # G8: 5,9 => UNS * DIS # G8: 6 => CTR => G8: 5,9 * PRF # B1: 1,8 => SOL * DIS # B1: 6 => CTR => B1: 1,8 * DIS # C1: 1,8 => CTR => C1: 3,6 * PRF # C1: 3,6 => SOL * DIS # F8: 2,4 => CTR => F8: 5,6 * INC # F8: 5,6 => UNS * DIS # E9: 2,4 => CTR => E9: 5,9 * INC # E9: 5,9 => UNS * INC # F9: 2,4 => UNS * DIS # I7: 5,9 => CTR => I7: 6 * INC # I7: 6 => UNS * INC # G8: 5,9 => UNS * INC # E9: 5,9 => UNS * DIS # E9: 2,4 => CTR => E9: 5,9 * DIS # I3: 5,9 => CTR => I3: 3,6,8 * INC # I3: 3,6,8 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I3: 5,6 => CTR => I3: 3,8,9 * DIS I3: 3,8,9 # I2: 6,9 => CTR => I2: 3,8 * INC I3: 3,8,9 + I2: 3,8 # I3: 3,9 => UNS * PRF I3: 3,8,9 + I2: 3,8 # I3: 8 => SOL * STA I3: 3,8,9 + I2: 3,8 + I3: 8 * CNT 4 HDP CHAINS / 4 HYP OPENED