Analysis of zz-www.sudokuoftheday.co.uk-20060628-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: 152.6...........68...........1.54..2.34..9...9.......34....5...2.81..3.5....7.29. initial
Autosolve
position: 152.6..3......2.68.......2...13549.2.34..9...92......34....5...2.81.63.5....7.29. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 7,8 => CTR => D1: 4,9 * DIS # I1: 4,7 => CTR => I1: 9 * DIS # G2: 4,7 => CTR => G2: 1,5 * PRF # G3: 4,7 => SOL * DIS # A5: 5,7 => CTR => A5: 8 * DIS # H6: 5,7 => CTR => H6: 1,4,8 * DIS # D5: 2 => CTR => D5: 6,7 * PRF # G6: 6,7 => SOL * DIS # E5: 1,8 => CTR => E5: 2 * DIS # G6: 1,8 => CTR => G6: 4,6,7 * DIS # H6: 1,8 => CTR => H6: 4,5,7 * DIS # H6: 1,7 => CTR => H6: 4,5,8 * DIS # F3: 3 => CTR => F3: 1,7 * DIS # H5: 7,8 => CTR => H5: 1,5 * DIS # G6: 7,8 => CTR => G6: 1,4,6 * DIS # H6: 7,8 => CTR => H6: 1,4,5 * DIS # H7: 7,8 => CTR => H7: 1 * DIS # C7: 7,9 => CTR => C7: 3,6 * DIS # B2: 7,9 => CTR => B2: 4 * DIS # B3: 7,9 => CTR => B3: 4,6,8 * DIS # B7: 1,6 => CTR => B7: 7,9 * DIS # I9: 1,6 => CTR => I9: 4 * DIS # E7: 3 => CTR => E7: 2,9 * DIS # H6: 1,5,8 => CTR => H6: 4,7 * CNT 24 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 # D1: 7,8 => CTR => D1: 4,9 * PRF D1: 4,9 # D5: 6,7 => SOL * STA D1: 4,9 + D5: 6,7 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 152.6...........68...........1.54..2.34..9...9.......34....5...2.81..3.5....7.29. | initial |
| 152.6..3......2.68.......2...13549.2.34..9...92......34....5...2.81.63.5....7.29. | autosolve |
| 152468739347912568689537421761354982834629157925781643473295816298146375516873294 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 3,7 F1: 7,8 G1: 4,7 C6: 5,7 D6: 6,7 E6: 1,8 F6: 1,7 H4: 7,8 B8: 7,9 B9: 1,6 D7: 2,9 E8: 4,9 D9: 4,8 F9: 3,8 H8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,B9: 1.. / B7 = 1 => 0 pairs (X) / B9 = 1 => 15 pairs (_) E2,G2: 1.. / E2 = 1 => 16 pairs (_) / G2 = 1 => 15 pairs (_) B9,I9: 1.. / B9 = 1 => 15 pairs (_) / I9 = 1 => 0 pairs (X) F3,F6: 1.. / F3 = 1 => 0 pairs (X) / F6 = 1 => 15 pairs (_) D5,E5: 2.. / D5 = 2 => 0 pairs (X) / E5 = 2 => 15 pairs (_) D7,E7: 2.. / D7 = 2 => 15 pairs (_) / E7 = 2 => 0 pairs (X) D5,D7: 2.. / D5 = 2 => 0 pairs (X) / D7 = 2 => 15 pairs (_) E5,E7: 2.. / E5 = 2 => 15 pairs (_) / E7 = 2 => 0 pairs (X) E7,F9: 3.. / E7 = 3 => 0 pairs (X) / F9 = 3 => 14 pairs (_) C7,E7: 3.. / C7 = 3 => 14 pairs (_) / E7 = 3 => 0 pairs (X) F3,F9: 3.. / F3 = 3 => 0 pairs (X) / F9 = 3 => 14 pairs (_) B2,B3: 4.. / B2 = 4 => 15 pairs (_) / B3 = 4 => 0 pairs (X) G6,H6: 4.. / G6 = 4 => 0 pairs (X) / H6 = 4 => 14 pairs (_) E8,D9: 4.. / E8 = 4 => 14 pairs (_) / D9 = 4 => 0 pairs (X) H8,I9: 4.. / H8 = 4 => 0 pairs (X) / I9 = 4 => 14 pairs (_) E8,H8: 4.. / E8 = 4 => 14 pairs (_) / H8 = 4 => 0 pairs (X) D9,I9: 4.. / D9 = 4 => 0 pairs (X) / I9 = 4 => 14 pairs (_) H6,H8: 4.. / H6 = 4 => 14 pairs (_) / H8 = 4 => 0 pairs (X) D2,D3: 5.. / D2 = 5 => 15 pairs (_) / D3 = 5 => 19 pairs (_) G2,G3: 5.. / G2 = 5 => 19 pairs (_) / G3 = 5 => 15 pairs (_) A5,C6: 5.. / A5 = 5 => 0 pairs (X) / C6 = 5 => 17 pairs (_) H5,H6: 5.. / H5 = 5 => 17 pairs (_) / H6 = 5 => 0 pairs (X) A9,C9: 5.. / A9 = 5 => 17 pairs (_) / C9 = 5 => 0 pairs (X) D2,G2: 5.. / D2 = 5 => 15 pairs (_) / G2 = 5 => 19 pairs (_) D3,G3: 5.. / D3 = 5 => 19 pairs (_) / G3 = 5 => 15 pairs (_) A5,H5: 5.. / A5 = 5 => 0 pairs (X) / H5 = 5 => 17 pairs (_) C6,H6: 5.. / C6 = 5 => 17 pairs (_) / H6 = 5 => 0 pairs (X) A5,A9: 5.. / A5 = 5 => 0 pairs (X) / A9 = 5 => 17 pairs (_) C6,C9: 5.. / C6 = 5 => 17 pairs (_) / C9 = 5 => 0 pairs (X) A4,B4: 6.. / A4 = 6 => 17 pairs (_) / B4 = 6 => 18 pairs (_) D5,D6: 6.. / D5 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) D6,G6: 6.. / D6 = 6 => 15 pairs (_) / G6 = 6 => 0 pairs (*) B8,H8: 7.. / B8 = 7 => 0 pairs (X) / H8 = 7 => 14 pairs (_) A3,B3: 8.. / A3 = 8 => 0 pairs (X) / B3 = 8 => 16 pairs (_) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 14 pairs (_) E5,E6: 8.. / E5 = 8 => 0 pairs (X) / E6 = 8 => 15 pairs (_) D9,F9: 8.. / D9 = 8 => 14 pairs (_) / F9 = 8 => 0 pairs (X) G7,H7: 8.. / G7 = 8 => 17 pairs (_) / H7 = 8 => 0 pairs (X) B3,B4: 8.. / B3 = 8 => 16 pairs (_) / B4 = 8 => 0 pairs (X) D1,D9: 8.. / D1 = 8 => 0 pairs (X) / D9 = 8 => 14 pairs (_) F1,F9: 8.. / F1 = 8 => 14 pairs (_) / F9 = 8 => 0 pairs (X) I1,I3: 9.. / I1 = 9 => 15 pairs (_) / I3 = 9 => 0 pairs (X) D1,I1: 9.. / D1 = 9 => 0 pairs (X) / I1 = 9 => 15 pairs (_) B8,E8: 9.. / B8 = 9 => 14 pairs (_) / E8 = 9 => 0 pairs (X) * DURATION: 0:00:49.138641 START: 00:09:36.873905 END: 00:10:26.012546 2019-05-01 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B8,B9,C6,D6,D7,D9,E6,E8,F1,F6,F9,G1,H4,H8) * 152.6..3......2.68.......2...13549.2.34..9...92......34....5...2.81.63.5....7.29. * PAIR A2: 3,7 BLK 1 C2: 3,7,9 # reduction candidate for 3,7 C2: 3,7 # 19 pairs A3: 3,7,6,8 # reduction candidate for 3,7 A3: 3,7 # 24 pairs C3: 3,7,6,9 # reduction candidate for 3,7 C3: 3,7 # 24 pairs * PAIR F1: 7,8 BLK 2 D1: 7,8,4,9 # reduction candidate for 7,8 D1: 7,8 => CTR * 152768439.....2.68.....1.27..1354982834..975.9256871434....5...2.8146375...873294 D1: 4,9 # 17 pairs * PAIR G1: 4,7 BLK 3 I1: 4,7,9 # reduction candidate for 4,7 I1: 4,7 => CTR * 152968437..9..2.68.....7.29..1354982834.29...92..81.434.3295...298146375.1.873294 I1: 9 # 15 pairs G2: 4,7,1,5 # reduction candidate for 4,7 G2: 4,7 => CTR * 152468739...512468.4.937521.813549.2.34.29...92..81.434..2.5...2.8146375.1.873294 G2: 1,5 # 16 pairs G3: 4,7,1,5 # reduction candidate for 4,7 G3: 4,7 => SOLVED * 152468739347912568689537421761354982834629157925781643473295816298146375516873294 G3: 1,5 # 16 pairs I3: 4,7,1,9 # reduction candidate for 4,7 I3: 4,7 # 18 pairs * PAIR G1: 4,7 ROW 1 D1: 4,7,8,9 # reduction candidate for 4,7 D1: 8,9 # 16 pairs D1: 4,7 # 15 pairs * PAIR G1: 4,7 COL G G6: 4,7,1,6,8 # reduction candidate for 4,7 G6: 4,7 # 20 pairs G6: 1,6,8 # 16 pairs * PAIR C6: 5,7 BLK 4 A5: 5,7,8 # reduction candidate for 5,7 A5: 5,7 => CTR * 152867439.....2.68.....3.2...1354972.34..9...92...1..34..235...278196345...47829. A5: 8 # 19 pairs * PAIR C6: 5,7 ROW 6 H6: 5,7,1,4,8 # reduction candidate for 5,7 H6: 5,7 => CTR * 152.6..3......2.68.......2...13549.2.34..9...92....4.34....5...2.81.6345...47829. H6: 1,4,8 # 17 pairs * PAIR D6: 6,7 BLK 5 D5: 6,7,2 # reduction candidate for 6,7 D5: 2 => CTR * 152.68.39.....2.68.....1.27..1354982834219756925687.434.3925...298146375...873294 D5: 6,7 # 15 pairs * PAIR D6: 6,7 ROW 6 G6: 6,7,1,4,8 # reduction candidate for 6,7 G6: 6,7 => SOLVED * 152468739347912568689537421761354982834629157925781643473295816298146375516873294 G6: 1,4,8 # 15 pairs * PAIR E6: 1,8 BLK 5 E5: 1,8,2 # reduction candidate for 1,8 E5: 1,8 => CTR * 152.68.39.....2.68.....1.27..1354982834219756925687.434.3925...298146375...873294 E5: 2 # 15 pairs * PAIR E6: 1,8 ROW 6 G6: 1,8,4,6,7 # reduction candidate for 1,8 G6: 1,8 => CTR * 152.68.3.....12.68.......2...1354982834..9.5.9256871434.3..5816298146375516873294 G6: 4,6,7 # 15 pairs H6: 1,8,4,5,7 # reduction candidate for 1,8 H6: 1,8 => CTR * 152.6..3......2.68.......2...13549.2.34..9.5.925...4.34....5...2.81.63455..47829. H6: 4,5,7 # 15 pairs * PAIR F6: 1,7 ROW 6 G6: 1,7,4,6,8 # reduction candidate for 1,7 G6: 1,7 # 15 pairs H6: 1,7,4,5,8 # reduction candidate for 1,7 H6: 1,7 => CTR * 152.6..3......2.68.......2...13549.2.34..9.5.925...4.34....5...2.81.63455..47829. H6: 4,5,8 # 15 pairs * PAIR F6: 1,7 COL F F3: 1,7,3 # reduction candidate for 1,7 F3: 3 => CTR * 152867439.....2.68.....3.2...13549.2.34.29...92..81.434..235...2.81.63.5....7829. F3: 1,7 # 14 pairs * PAIR H4: 7,8 BLK 6 G5: 7,8,1,6 # reduction candidate for 7,8 G5: 7,8 # 18 pairs H5: 7,8,1,5 # reduction candidate for 7,8 H5: 7,8 => CTR * 152867439.....2.68.....3.2...135497253472968.9276.1.534....5.1.2.81.6345.15478296 H5: 1,5 # 16 pairs G6: 7,8,1,4,6 # reduction candidate for 7,8 G6: 7,8 => CTR * 152.6843......2.68.8.4.752..61354982834729651925681743473295816298146375516873294 G6: 1,4,6 # 15 pairs H6: 7,8,1,4,5 # reduction candidate for 7,8 H6: 7,8 => CTR * 152.6..3......2.68.......2...13549.2.34..9.5.925...4.34....5.1.2.81.634551.478296 H6: 1,4,5 # 15 pairs * PAIR H4: 7,8 ROW 4 A4: 7,8,6 # reduction candidate for 7,8 A4: 7,8 # 18 pairs B4: 7,8,6 # reduction candidate for 7,8 B4: 7,8 # 17 pairs * PAIR H4: 7,8 COL H H7: 7,8,1 # reduction candidate for 7,8 H7: 7,8 => CTR * 152.6.73......2.68.......2...13549.2.34..9...92.68.4.34....5...278196345...47829. H7: 1 # 17 pairs * PAIR B8: 7,9 BLK 7 B7: 7,9,1,6 # reduction candidate for 7,9 B7: 7,9 # 19 pairs C7: 7,9,3,6 # reduction candidate for 7,9 C7: 7,9 => CTR * 152867439.....2.68.....3.2...13549.2.34.29...92..81.434..235...2.81.63.5....7829. C7: 3,6 # 19 pairs * PAIR B8: 7,9 COL B B2: 7,9,4 # reduction candidate for 7,9 B2: 7,9 => CTR * 152867.3......2.68.4.....2..81354972.34..9...92......34....5...278196345...47829. B2: 4 # 15 pairs B3: 7,9,4,6,8 # reduction candidate for 7,9 B3: 7,9 => CTR * 152867439.4...2.68896543.2.681354972.34..9...92...1..34.9235...278196345...47829. B3: 4,6,8 # 15 pairs * PAIR B9: 1,6 BLK 7 B7: 1,6,7,9 # reduction candidate for 1,6 B7: 1,6 => CTR * 152867439.....2.68..6..3.2.6.13549.2.34..9...92...1..34...35...2.81.6345...47829. B7: 7,9 # 19 pairs * PAIR B9: 1,6 ROW 9 I9: 1,6,4 # reduction candidate for 1,6 I9: 1,6 => CTR * 152867439.....2.68.....3.2...13549.2.34..9...92...1..34...35...278196345...47829. I9: 4 # 14 pairs * PAIR D7: 2,9 BLK 8 E7: 2,9,3 # reduction candidate for 2,9 E7: 3 => CTR * 152867439.....2.68.....3.2...13549.2.34.29...92..81..34..235...278196345...47829. E7: 2,9 # 14 pairs * PAIR E8: 4,9 COL E E2: 4,9,1,3 # reduction candidate for 4,9 E2: 4,9 # 21 pairs E3: 4,9,1,3 # reduction candidate for 4,9 E3: 4,9 # 19 pairs * PAIR D9: 4,8 COL D D1: 4,8,7,9 # reduction candidate for 4,8 D1: 4,8 # 16 pairs D1: 7,9 # 13 pairs * PAIR H8: 4,7 COL H H6: 4,7,1,5,8 # reduction candidate for 4,7 H6: 1,5,8 => CTR * 152.6..3......2.68.......2...13549.2.34..9...92....4.34....5...2.81.6345...47829. H6: 4,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060628-absurd-base-pr-000.dot * REASONING * DIS # D1: 7,8 => CTR => D1: 4,9 * DIS # I1: 4,7 => CTR => I1: 9 * DIS # G2: 4,7 => CTR => G2: 1,5 * PRF # G3: 4,7 => SOL * DIS # A5: 5,7 => CTR => A5: 8 * DIS # H6: 5,7 => CTR => H6: 1,4,8 * DIS # D5: 2 => CTR => D5: 6,7 * PRF # G6: 6,7 => SOL * DIS # E5: 1,8 => CTR => E5: 2 * DIS # G6: 1,8 => CTR => G6: 4,6,7 * DIS # H6: 1,8 => CTR => H6: 4,5,7 * DIS # H6: 1,7 => CTR => H6: 4,5,8 * DIS # F3: 3 => CTR => F3: 1,7 * DIS # H5: 7,8 => CTR => H5: 1,5 * DIS # G6: 7,8 => CTR => G6: 1,4,6 * DIS # H6: 7,8 => CTR => H6: 1,4,5 * DIS # H7: 7,8 => CTR => H7: 1 * DIS # C7: 7,9 => CTR => C7: 3,6 * DIS # B2: 7,9 => CTR => B2: 4 * DIS # B3: 7,9 => CTR => B3: 4,6,8 * DIS # B7: 1,6 => CTR => B7: 7,9 * DIS # I9: 1,6 => CTR => I9: 4 * DIS # E7: 3 => CTR => E7: 2,9 * DIS # H6: 1,5,8 => CTR => H6: 4,7 * CNT 24 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B8,B9,C6,D6,D7,D9,E6,E8,F1,F6,F9,G1,H4,H8) * 152.6..3......2.68.......2...13549.2.34..9...92......34....5...2.81.63.5....7.29. * PAIR A2: 3,7 BLK 1 C2: 3,7,9 # reduction candidate for 3,7 C2: 3,7 # 19 pairs A3: 3,7,6,8 # reduction candidate for 3,7 A3: 3,7 # 24 pairs C3: 3,7,6,9 # reduction candidate for 3,7 C3: 3,7 # 24 pairs * PAIR F1: 7,8 BLK 2 D1: 7,8,4,9 # reduction candidate for 7,8 D1: 7,8 => CTR * 152768439.....2.68.....1.27..1354982834..975.9256871434....5...2.8146375...873294 * PAIR D6: 6,7 BLK 5 D5: 6,7,2 # reduction candidate for 6,7 D5: 6,7 => SOLVED * 152468739347912568689537421761354982834629157925781643473295816298146375516873294 * DURATION: 0:00:05.280924 START: 00:11:04.873115 END: 00:11:10.154039 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060628-absurd-base-pr-001.dot * REASONING * DIS # D1: 7,8 => CTR => D1: 4,9 * PRF D1: 4,9 # D5: 6,7 => SOL * STA D1: 4,9 + D5: 6,7 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060628, absurd
Solution
position: 152468739347912568689537421761354982834629157925781643473295816298146375516873294 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: 3,7 => UNS * INC # A3: 3,7 => UNS * INC # C3: 3,7 => UNS * DIS # D1: 7,8 => CTR => D1: 4,9 * INC # D1: 4,9 => UNS * DIS # I1: 4,7 => CTR => I1: 9 * INC # I1: 9 => UNS * DIS # G2: 4,7 => CTR => G2: 1,5 * INC # G2: 1,5 => UNS * PRF # G3: 4,7 => SOL * INC # G3: 1,5 => UNS * INC # I3: 4,7 => UNS * INC # D1: 4,7 => UNS * INC # D1: 8,9 => UNS * INC # G6: 4,7 => UNS * INC # G6: 1,6,8 => UNS * DIS # A5: 5,7 => CTR => A5: 8 * INC # A5: 8 => UNS * DIS # H6: 5,7 => CTR => H6: 1,4,8 * INC # H6: 1,4,8 => UNS * INC # D5: 6,7 => UNS * DIS # D5: 2 => CTR => D5: 6,7 * PRF # G6: 6,7 => SOL * INC # G6: 1,4,8 => UNS * DIS # E5: 1,8 => CTR => E5: 2 * INC # E5: 2 => UNS * DIS # G6: 1,8 => CTR => G6: 4,6,7 * INC # G6: 4,6,7 => UNS * DIS # H6: 1,8 => CTR => H6: 4,5,7 * INC # H6: 4,5,7 => UNS * INC # G6: 1,7 => UNS * DIS # H6: 1,7 => CTR => H6: 4,5,8 * INC # H6: 4,5,8 => UNS * INC # F3: 1,7 => UNS * DIS # F3: 3 => CTR => F3: 1,7 * INC # G5: 7,8 => UNS * DIS # H5: 7,8 => CTR => H5: 1,5 * INC # H5: 1,5 => UNS * DIS # G6: 7,8 => CTR => G6: 1,4,6 * INC # G6: 1,4,6 => UNS * DIS # H6: 7,8 => CTR => H6: 1,4,5 * INC # H6: 1,4,5 => UNS * INC # A4: 7,8 => UNS * INC # B4: 7,8 => UNS * DIS # H7: 7,8 => CTR => H7: 1 * INC # H7: 1 => UNS * INC # B7: 7,9 => UNS * DIS # C7: 7,9 => CTR => C7: 3,6 * INC # C7: 3,6 => UNS * DIS # B2: 7,9 => CTR => B2: 4 * INC # B2: 4 => UNS * DIS # B3: 7,9 => CTR => B3: 4,6,8 * INC # B3: 4,6,8 => UNS * DIS # B7: 1,6 => CTR => B7: 7,9 * INC # B7: 7,9 => UNS * DIS # I9: 1,6 => CTR => I9: 4 * INC # I9: 4 => UNS * INC # E7: 2,9 => UNS * DIS # E7: 3 => CTR => E7: 2,9 * INC # E2: 4,9 => UNS * INC # E3: 4,9 => UNS * INC # D1: 4,8 => UNS * INC # D1: 7,9 => UNS * INC # H6: 4,7 => UNS * DIS # H6: 1,5,8 => CTR => H6: 4,7 * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 3,7 => UNS * INC # A3: 3,7 => UNS * INC # C3: 3,7 => UNS * DIS # D1: 7,8 => CTR => D1: 4,9 * PRF D1: 4,9 # D5: 6,7 => SOL * STA D1: 4,9 + D5: 6,7 * CNT 5 HDP CHAINS / 5 HYP OPENED