Analysis of zz-www.sudokuoftheday.co.uk-20060803-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: 415...3......9..8.9..7.....6....5718..71..6..3.....2....427....5....1.6......94.. initial
Autosolve
position: 415...3.....59.18.9..71.5..64...5718..714.6..3.1..72....427....5..4.1.6.....594.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A9: 2,7 => CTR => A9: 1,8 * PRF # A9: 1,8 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 2 => CTR => E1: 6,8 * DIS # F1: 6,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # D6: 6,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # D9: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * DIS # C8: 3,8 => CTR => C8: 2,9 * DIS # B6: 5,9 => CTR => B6: 8 * PRF # B6: 8 => SOL * DIS # F1: 6 => CTR => F1: 2,8 * DIS # D6: 6,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 2 => CTR => E1: 6,8 * PRF # A9: 1,8 => SOL * DIS # A9: 2,7 => CTR => A9: 1,8 * PRF # D9: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * DIS # B7: 6,8 => CTR => B7: 3,9 * DIS # F1: 6,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # D9: 6 => CTR => D9: 3,8 * DIS # B8: 3,8 => CTR => B8: 2,7,9 * DIS # C8: 3,8 => CTR => C8: 2,9 * PRF # B7: 3,6 => SOL * PRF # I7: 1 => SOL * PRF # B8: 8,9 => SOL * DIS # C8: 8,9 => CTR => C8: 2,3 * PRF # C8: 2,3 => SOL * CNT 33 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A9: 2,7 => CTR => A9: 1,8 * PRF A9: 1,8 => SOL * STA A9: 1,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 415...3......9..8.9..7.....6....5718..71..6..3.....2....427....5....1.6......94.. | initial |
| 415...3.....59.18.9..71.5..64...5718..714.6..3.1..72....427....5..4.1.6.....594.. | autosolve |
| 415682379723594186968713524649325718257148693381967245834276951592431867176859432 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A2: 2,7 D1: 6,8 F2: 3,4 F3: 3,4 H1: 7,9 I1: 7,9 H3: 2,4 C4: 2,9 A5: 2,8 B5: 5,9 D4: 3,9 E4: 2,3 F5: 2,8 E6: 6,8 A7: 1,8 F7: 6,8 E8: 3,8 G7: 8,9 H7: 3,5 G8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,A9: 1.. / A7 = 1 => 22 pairs (_) / A9 = 1 => 0 pairs (*) I7,I9: 1.. / I7 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) A7,I7: 1.. / A7 = 1 => 22 pairs (_) / I7 = 1 => 0 pairs (*) A9,I9: 1.. / A9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) E1,F1: 2.. / E1 = 2 => 0 pairs (X) / F1 = 2 => 0 pairs (_) C4,A5: 2.. / C4 = 2 => 0 pairs (X) / A5 = 2 => 0 pairs (_) E4,F5: 2.. / E4 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) C4,E4: 2.. / C4 = 2 => 0 pairs (X) / E4 = 2 => 0 pairs (_) A5,F5: 2.. / A5 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) E1,E4: 2.. / E1 = 2 => 0 pairs (X) / E4 = 2 => 0 pairs (_) F1,F5: 2.. / F1 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) H3,H9: 2.. / H3 = 2 => 23 pairs (_) / H9 = 2 => 20 pairs (_) F2,F3: 3.. / F2 = 3 => 22 pairs (_) / F3 = 3 => 19 pairs (_) D4,E4: 3.. / D4 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) H5,I5: 3.. / H5 = 3 => 23 pairs (_) / I5 = 3 => 23 pairs (_) E8,D9: 3.. / E8 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) D4,D9: 3.. / D4 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) E4,E8: 3.. / E4 = 3 => 0 pairs (X) / E8 = 3 => 0 pairs (_) F2,F3: 4.. / F2 = 4 => 19 pairs (_) / F3 = 4 => 22 pairs (_) H6,I6: 4.. / H6 = 4 => 23 pairs (_) / I6 = 4 => 20 pairs (_) F2,I2: 4.. / F2 = 4 => 19 pairs (_) / I2 = 4 => 22 pairs (_) H3,H6: 4.. / H3 = 4 => 20 pairs (_) / H6 = 4 => 23 pairs (_) B5,B6: 5.. / B5 = 5 => 24 pairs (_) / B6 = 5 => 0 pairs (X) H7,I7: 5.. / H7 = 5 => 22 pairs (_) / I7 = 5 => 22 pairs (_) I2,I3: 6.. / I2 = 6 => 22 pairs (_) / I3 = 6 => 21 pairs (_) D6,E6: 6.. / D6 = 6 => 0 pairs (X) / E6 = 6 => 21 pairs (_) F7,D9: 6.. / F7 = 6 => 21 pairs (_) / D9 = 6 => 0 pairs (X) B7,F7: 6.. / B7 = 6 => 0 pairs (X) / F7 = 6 => 21 pairs (_) E1,E6: 6.. / E1 = 6 => 0 pairs (X) / E6 = 6 => 21 pairs (_) F1,F7: 6.. / F1 = 6 => 0 pairs (X) / F7 = 6 => 21 pairs (_) A2,B2: 7.. / A2 = 7 => 19 pairs (_) / B2 = 7 => 0 pairs (X) H1,I1: 7.. / H1 = 7 => 21 pairs (_) / I1 = 7 => 21 pairs (_) B8,I8: 7.. / B8 = 7 => 20 pairs (_) / I8 = 7 => 21 pairs (_) A2,A9: 7.. / A2 = 7 => 19 pairs (_) / A9 = 7 => 0 pairs (X) H1,H9: 7.. / H1 = 7 => 21 pairs (_) / H9 = 7 => 21 pairs (_) B3,C3: 8.. / B3 = 8 => 0 pairs (X) / C3 = 8 => 20 pairs (_) A5,B6: 8.. / A5 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) G7,G8: 8.. / G7 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) A5,F5: 8.. / A5 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) H1,I1: 9.. / H1 = 9 => 21 pairs (_) / I1 = 9 => 21 pairs (_) D4,D6: 9.. / D4 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) G7,G8: 9.. / G7 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) C4,D4: 9.. / C4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) B7,G7: 9.. / B7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) C4,C8: 9.. / C4 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) * DURATION: 0:00:56.819744 START: 01:31:31.569128 END: 01:32:28.388872 2019-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A7,B5,C4,D1,D4,E4,E6,E8,F2,F3,F5,F7,G7,G8,H1,H3,H7,I1) * 415...3.....59.18.9..71.5..64...5718..714.6..3.1..72....427....5..4.1.6.....594.. * PAIR A2: 2,7 BLK 1 B2: 2,7,3,6 # reduction candidate for 2,7 B2: 2,7 # 23 pairs B2: 3,6 # 20 pairs * PAIR A2: 2,7 COL A A9: 2,7,1,8 # reduction candidate for 2,7 A9: 2,7 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.1 A9: 1,8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 * PAIR D1: 6,8 BLK 2 E1: 6,8,2 # reduction candidate for 6,8 E1: 6,8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 E1: 2 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.. F1: 6,8,2 # reduction candidate for 6,8 F1: 6,8 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.. F1: 2 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 * PAIR D1: 6,8 COL D D6: 6,8,9 # reduction candidate for 6,8 D6: 6,8 => CTR * 415...3.....59.18.9..71.5..64.935718..71426..3.1..72....427....5.9481.6.....594.. D6: 9 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 D9: 6,8,3 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 D9: 3 => CTR * 415...3.....59.18.9..71.5..649..5718..714.6..3.1..72....4276...5..48196....3594.. * PAIR H3: 2,4 BLK 3 I2: 2,4,6 # reduction candidate for 2,4 I2: 2,4 # 21 pairs I3: 2,4,6 # reduction candidate for 2,4 I3: 2,4 # 22 pairs * PAIR C4: 2,9 COL C C8: 2,9,3,8 # reduction candidate for 2,9 C8: 3,8 => CTR * 4156823..7..59.18.9.871.5..6493257182571486..3819672....4276...5..431.6....8594.. C8: 2,9 # 22 pairs * PAIR A5: 2,8 COL A A9: 2,8,1,7 # reduction candidate for 2,8 A9: 2,8 # 22 pairs A9: 1,7 # 21 pairs * PAIR B5: 5,9 BLK 4 B6: 5,9,8 # reduction candidate for 5,9 B6: 5,9 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.1 B6: 8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 * PAIR B5: 5,9 ROW 5 H5: 5,9,3 # reduction candidate for 5,9 H5: 5,9 # 23 pairs I5: 5,9,3 # reduction candidate for 5,9 I5: 5,9 # 23 pairs * PAIR F5: 2,8 COL F F1: 2,8,6 # reduction candidate for 2,8 F1: 6 => CTR * 415.263.....59.18.9..71.5..6429357188.71426..3.1.672..164278...5..4.1.6.....594.. F1: 2,8 # 21 pairs * PAIR E6: 6,8 BLK 5 D6: 6,8,9 # reduction candidate for 6,8 D6: 6,8 => CTR * 415...3.....59.18.9..71.5..64.935718..71426..3.1..72....427....5.9481.6.....594.. D6: 9 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 * PAIR E6: 6,8 COL E E1: 6,8,2 # reduction candidate for 6,8 E1: 6,8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 E1: 2 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.. * PAIR A7: 1,8 BLK 7 A9: 1,8,2,7 # reduction candidate for 1,8 A9: 1,8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 A9: 2,7 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.1 * PAIR F7: 6,8 BLK 8 D9: 6,8,3 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 D9: 3 => CTR * 415...3.....59.18.9..71.5..649..5718..714.6..3.1..72....4276...5..48196....3594.. * PAIR F7: 6,8 ROW 7 B7: 6,8,3,9 # reduction candidate for 6,8 B7: 6,8 => CTR * 415...3.....59.18.9..71.5..64.3257182.71486..3819672..86427.9..5..43186.....594.. B7: 3,9 # 22 pairs * PAIR F7: 6,8 COL F F1: 6,8,2 # reduction candidate for 6,8 F1: 6,8 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.. F1: 2 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 * PAIR E8: 3,8 BLK 8 D9: 3,8,6 # reduction candidate for 3,8 D9: 6 => CTR * 415...3.....59.18.9..71.5..64.3257182.71486..3819672....427....5..4.1.6.....594.. D9: 3,8 # 21 pairs * PAIR E8: 3,8 ROW 8 B8: 3,8,2,7,9 # reduction candidate for 3,8 B8: 3,8 => CTR * 415...379...59.18.9..71.5..6493257182571486933819672....427....5.24.1967....594.. B8: 2,7,9 # 20 pairs C8: 3,8,2,9 # reduction candidate for 3,8 C8: 3,8 => CTR * 4156823..7..59.18.9.871.5..6493257182571486..3819672....4276...5..431.6....8594.. C8: 2,9 # 22 pairs * PAIR G7: 8,9 ROW 7 B7: 8,9,3,6 # reduction candidate for 8,9 B7: 3,6 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 B7: 8,9 # 24 pairs * PAIR H7: 3,5 BLK 9 I7: 3,5,1 # reduction candidate for 3,5 I7: 1 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 I7: 3,5 # 22 pairs * PAIR H7: 3,5 COL H H5: 3,5,9 # reduction candidate for 3,5 H5: 9 # 23 pairs H5: 3,5 # 23 pairs * PAIR G8: 8,9 ROW 8 B8: 8,9,2,3,7 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 B8: 2,3,7 # 20 pairs C8: 8,9,2,3 # reduction candidate for 8,9 C8: 8,9 => CTR * 4156823..7..59.18.9.871.5..6493257182.71486..3819672....4276...5..431.6....8594.. C8: 2,3 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060803-absurd-base-pr-000.dot * REASONING * DIS # A9: 2,7 => CTR => A9: 1,8 * PRF # A9: 1,8 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 2 => CTR => E1: 6,8 * DIS # F1: 6,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # D6: 6,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # D9: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * DIS # C8: 3,8 => CTR => C8: 2,9 * DIS # B6: 5,9 => CTR => B6: 8 * PRF # B6: 8 => SOL * DIS # F1: 6 => CTR => F1: 2,8 * DIS # D6: 6,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 2 => CTR => E1: 6,8 * PRF # A9: 1,8 => SOL * DIS # A9: 2,7 => CTR => A9: 1,8 * PRF # D9: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * DIS # B7: 6,8 => CTR => B7: 3,9 * DIS # F1: 6,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # D9: 6 => CTR => D9: 3,8 * DIS # B8: 3,8 => CTR => B8: 2,7,9 * DIS # C8: 3,8 => CTR => C8: 2,9 * PRF # B7: 3,6 => SOL * PRF # I7: 1 => SOL * PRF # B8: 8,9 => SOL * DIS # C8: 8,9 => CTR => C8: 2,3 * PRF # C8: 2,3 => SOL * CNT 33 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A7,B5,C4,D1,D4,E4,E6,E8,F2,F3,F5,F7,G7,G8,H1,H3,H7,I1) * 415...3.....59.18.9..71.5..64...5718..714.6..3.1..72....427....5..4.1.6.....594.. * PAIR A2: 2,7 BLK 1 B2: 2,7,3,6 # reduction candidate for 2,7 B2: 2,7 # 23 pairs B2: 3,6 # 20 pairs * PAIR A2: 2,7 COL A A9: 2,7,1,8 # reduction candidate for 2,7 A9: 2,7 => CTR * 415.2.3.....59.18.9..71.5..6429357188.71426..3.1.672..1.427....5.9481.6.....594.1 A9: 1,8 => SOLVED * 415682379723594186968713524649325718257148693381967245834276951592431867176859432 * DURATION: 0:00:03.662279 START: 01:33:08.194500 END: 01:33:11.856779 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060803-absurd-base-pr-001.dot * REASONING * DIS # A9: 2,7 => CTR => A9: 1,8 * PRF A9: 1,8 => SOL * STA A9: 1,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060803, absurd
Solution
position: 415682379723594186968713524649325718257148693381967245834276951592431867176859432 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: 2,7 => UNS * INC # B2: 3,6 => UNS * DIS # A9: 2,7 => CTR => A9: 1,8 * PRF # A9: 1,8 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 2 => CTR => E1: 6,8 * DIS # F1: 6,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # D6: 6,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # D9: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * INC # I2: 2,4 => UNS * INC # I3: 2,4 => UNS * INC # C8: 2,9 => UNS * DIS # C8: 3,8 => CTR => C8: 2,9 * INC # A9: 2,8 => UNS * INC # A9: 1,7 => UNS * DIS # B6: 5,9 => CTR => B6: 8 * PRF # B6: 8 => SOL * INC # H5: 5,9 => UNS * INC # I5: 5,9 => UNS * INC # F1: 2,8 => UNS * DIS # F1: 6 => CTR => F1: 2,8 * DIS # D6: 6,8 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 2 => CTR => E1: 6,8 * PRF # A9: 1,8 => SOL * DIS # A9: 2,7 => CTR => A9: 1,8 * PRF # D9: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * DIS # B7: 6,8 => CTR => B7: 3,9 * INC # B7: 3,9 => UNS * DIS # F1: 6,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * INC # D9: 3,8 => UNS * DIS # D9: 6 => CTR => D9: 3,8 * DIS # B8: 3,8 => CTR => B8: 2,7,9 * INC # B8: 2,7,9 => UNS * DIS # C8: 3,8 => CTR => C8: 2,9 * INC # C8: 2,9 => UNS * INC # B7: 8,9 => UNS * PRF # B7: 3,6 => SOL * INC # I7: 3,5 => UNS * PRF # I7: 1 => SOL * INC # H5: 3,5 => UNS * INC # H5: 9 => UNS * PRF # B8: 8,9 => SOL * INC # B8: 2,3,7 => UNS * DIS # C8: 8,9 => CTR => C8: 2,3 * PRF # C8: 2,3 => SOL * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 2,7 => UNS * INC # B2: 3,6 => UNS * DIS # A9: 2,7 => CTR => A9: 1,8 * PRF A9: 1,8 => SOL * STA A9: 1,8 * CNT 4 HDP CHAINS / 3 HYP OPENED