Analysis of zz-www.sudokuoftheday.co.uk-20190320-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: .396..8...57.......2..1.......15...6.....8.1.9.5.2.3....2.37.....1294.6.........7 initial
Autosolve
position: .396..8...57.8.....2..1.......15...6.....8.15915.263....2.37.....129456.....61..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 6 => SOL * DIS # A5: 4,7 => CTR => A5: 2,3,6 * DIS # G5: 4,7 => CTR => G5: 2,9 * DIS # H6: 7 => CTR => H6: 4,8 * DIS # A8: 3 => CTR => A8: 7,8 * CNT 5 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 6 => SOL * STA A2: 6 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .396..8...57.......2..1.......15...6.....8.1.9.5.2.3....2.37.....1294.6.........7 | initial |
| .396..8...57.8.....2..1.......15...6.....8.15915.263....2.37.....129456.....61..7 | autosolve |
| 139672854657489132824315679248153796376948215915726348462537981781294563593861427 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 1,4 E1: 4,7 F1: 2,5 F4: 3,9 D5: 3,9 E5: 4,7 D6: 4,7 I6: 4,8 B8: 7,8 D7: 5,8 D9: 5,8 I8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 13 pairs (_) / A2 = 1 => 13 pairs (_) G7,I7: 1.. / G7 = 1 => 14 pairs (_) / I7 = 1 => 0 pairs (*) A1,I1: 1.. / A1 = 1 => 13 pairs (_) / I1 = 1 => 13 pairs (_) G2,G7: 1.. / G2 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) F1,F2: 2.. / F1 = 2 => 15 pairs (_) / F2 = 2 => 13 pairs (_) I1,I2: 2.. / I1 = 2 => 13 pairs (_) / I2 = 2 => 15 pairs (_) A4,A5: 2.. / A4 = 2 => 16 pairs (_) / A5 = 2 => 12 pairs (_) G9,H9: 2.. / G9 = 2 => 13 pairs (_) / H9 = 2 => 18 pairs (_) F1,I1: 2.. / F1 = 2 => 15 pairs (_) / I1 = 2 => 13 pairs (_) F2,I2: 2.. / F2 = 2 => 13 pairs (_) / I2 = 2 => 15 pairs (_) A5,G5: 2.. / A5 = 2 => 12 pairs (_) / G5 = 2 => 16 pairs (_) H4,H9: 2.. / H4 = 2 => 13 pairs (_) / H9 = 2 => 18 pairs (_) F4,D5: 3.. / F4 = 3 => 14 pairs (_) / D5 = 3 => 16 pairs (_) I8,H9: 3.. / I8 = 3 => 15 pairs (_) / H9 = 3 => 0 pairs (X) A8,I8: 3.. / A8 = 3 => 0 pairs (X) / I8 = 3 => 15 pairs (_) E5,D6: 4.. / E5 = 4 => 13 pairs (_) / D6 = 4 => 0 pairs (X) E1,E5: 4.. / E1 = 4 => 0 pairs (X) / E5 = 4 => 13 pairs (_) F1,F3: 5.. / F1 = 5 => 13 pairs (_) / F3 = 5 => 15 pairs (_) H1,H3: 5.. / H1 = 5 => 15 pairs (_) / H3 = 5 => 13 pairs (_) A7,A9: 5.. / A7 = 5 => 18 pairs (_) / A9 = 5 => 13 pairs (_) D7,D9: 5.. / D7 = 5 => 13 pairs (_) / D9 = 5 => 18 pairs (_) F1,H1: 5.. / F1 = 5 => 13 pairs (_) / H1 = 5 => 15 pairs (_) F3,H3: 5.. / F3 = 5 => 15 pairs (_) / H3 = 5 => 13 pairs (_) A7,D7: 5.. / A7 = 5 => 18 pairs (_) / D7 = 5 => 13 pairs (_) A9,D9: 5.. / A9 = 5 => 13 pairs (_) / D9 = 5 => 18 pairs (_) G2,G3: 6.. / G2 = 6 => 17 pairs (_) / G3 = 6 => 0 pairs (*) A7,B7: 6.. / A7 = 6 => 18 pairs (_) / B7 = 6 => 17 pairs (_) A2,G2: 6.. / A2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) B5,B7: 6.. / B5 = 6 => 18 pairs (_) / B7 = 6 => 17 pairs (_) C3,C5: 6.. / C3 = 6 => 19 pairs (_) / C5 = 6 => 18 pairs (_) E1,D3: 7.. / E1 = 7 => 13 pairs (_) / D3 = 7 => 0 pairs (X) E5,D6: 7.. / E5 = 7 => 0 pairs (X) / D6 = 7 => 13 pairs (_) A8,B8: 7.. / A8 = 7 => 14 pairs (_) / B8 = 7 => 17 pairs (_) E1,H1: 7.. / E1 = 7 => 13 pairs (_) / H1 = 7 => 0 pairs (X) D6,H6: 7.. / D6 = 7 => 13 pairs (_) / H6 = 7 => 0 pairs (X) D3,D6: 7.. / D3 = 7 => 0 pairs (X) / D6 = 7 => 13 pairs (_) E1,E5: 7.. / E1 = 7 => 13 pairs (_) / E5 = 7 => 0 pairs (X) A3,C3: 8.. / A3 = 8 => 14 pairs (_) / C3 = 8 => 21 pairs (_) H6,I6: 8.. / H6 = 8 => 14 pairs (_) / I6 = 8 => 15 pairs (_) D7,D9: 8.. / D7 = 8 => 18 pairs (_) / D9 = 8 => 13 pairs (_) F4,D5: 9.. / F4 = 9 => 16 pairs (_) / D5 = 9 => 14 pairs (_) B7,B9: 9.. / B7 = 9 => 0 pairs (X) / B9 = 9 => 13 pairs (_) D5,G5: 9.. / D5 = 9 => 14 pairs (_) / G5 = 9 => 16 pairs (_) * DURATION: 0:00:42.171714 START: 04:40:04.986594 END: 04:40:47.158308 2019-05-01 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,D5,D6,D7,D9,E1,E5,F1,F4,I6,I8) * .396..8...57.8.....2..1.......15...6.....8.15915.263....2.37.....129456.....61..7 * PAIR A1: 1,4 BLK 1 A2: 1,4,6 # reduction candidate for 1,4 A2: 6 => SOLVED * 139672854657489132824315679248153796376948215915726348462537981781294563593861427 A2: 1,4 # 17 pairs * PAIR A1: 1,4 ROW 1 I1: 1,4,2 # reduction candidate for 1,4 I1: 1,4 # 15 pairs I1: 2 # 13 pairs * PAIR E1: 4,7 BLK 2 D3: 4,7,3,9 # reduction candidate for 4,7 D3: 3,9 # 16 pairs D3: 4,7 # 14 pairs * PAIR E1: 4,7 ROW 1 H1: 4,7,5 # reduction candidate for 4,7 H1: 5 # 15 pairs H1: 4,7 # 13 pairs * PAIR F4: 3,9 COL F F2: 3,9,2 # reduction candidate for 3,9 F2: 3,9 # 15 pairs F3: 3,9,5 # reduction candidate for 3,9 F3: 3,9 # 13 pairs * PAIR D5: 3,9 COL D D2: 3,9,4 # reduction candidate for 3,9 D2: 3,9 # 14 pairs D3: 3,9,4,7 # reduction candidate for 3,9 D3: 3,9 # 16 pairs * PAIR E5: 4,7 ROW 5 A5: 4,7,2,3,6 # reduction candidate for 4,7 A5: 4,7 => CTR * .396..8...57.8.....2..1....2..153..6..39.8215915.263..562837.....129456339.561.27 A5: 2,3,6 # 12 pairs B5: 4,7,6 # reduction candidate for 4,7 B5: 4,7 # 17 pairs G5: 4,7,2,9 # reduction candidate for 4,7 G5: 4,7 => CTR * .396..8...57.8.69.826.19453748153926263948715915726384682537149371294568594861237 G5: 2,9 # 13 pairs * PAIR D6: 4,7 ROW 6 H6: 4,7,8 # reduction candidate for 4,7 H6: 4,7 # 15 pairs H6: 8 # 14 pairs * PAIR D6: 4,7 COL D D3: 4,7,3,9 # reduction candidate for 4,7 D3: 3,9 # 16 pairs D3: 4,7 # 14 pairs * PAIR I6: 4,8 BLK 6 H6: 4,8,7 # reduction candidate for 4,8 H6: 7 => CTR * .3967.8...57.8.....2..1.7.....15...6....48.15915.26378..2.37.....1294563....61..7 H6: 4,8 # 13 pairs * PAIR I6: 4,8 COL I I7: 4,8,1,9 # reduction candidate for 4,8 I7: 4,8 # 20 pairs I7: 1,9 # 13 pairs * PAIR B8: 7,8 BLK 7 A8: 7,8,3 # reduction candidate for 7,8 A8: 3 => CTR * .3967.85..57.8.6..826.154797..1539262639487159157263846.2537...371294568594861237 A8: 7,8 # 15 pairs * PAIR B8: 7,8 COL B B4: 7,8,4 # reduction candidate for 7,8 B4: 4 # 18 pairs B4: 7,8 # 15 pairs * PAIR D7: 5,8 ROW 7 A7: 5,8,4,6 # reduction candidate for 5,8 A7: 5,8 # 21 pairs A7: 4,6 # 16 pairs * PAIR D9: 5,8 ROW 9 A9: 5,8,3,4 # reduction candidate for 5,8 A9: 3,4 # 19 pairs A9: 5,8 # 16 pairs * PAIR I8: 3,8 BLK 9 H9: 3,8,2,4,9 # reduction candidate for 3,8 H9: 3,8 # 18 pairs H9: 2,4,9 # 17 pairs * PAIR I8: 3,8 ROW 8 A8: 3,8,7 # reduction candidate for 3,8 A8: 3,8 # 17 pairs A8: 7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190320-absurd-base-pr-000.dot * REASONING * PRF # A2: 6 => SOL * DIS # A5: 4,7 => CTR => A5: 2,3,6 * DIS # G5: 4,7 => CTR => G5: 2,9 * DIS # H6: 7 => CTR => H6: 4,8 * DIS # A8: 3 => CTR => A8: 7,8 * CNT 5 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,D5,D6,D7,D9,E1,E5,F1,F4,I6,I8) * .396..8...57.8.....2..1.......15...6.....8.15915.263....2.37.....129456.....61..7 * PAIR A1: 1,4 BLK 1 A2: 1,4,6 # reduction candidate for 1,4 A2: 6 => SOLVED * 139672854657489132824315679248153796376948215915726348462537981781294563593861427 * DURATION: 0:00:02.283265 START: 04:41:06.952693 END: 04:41:09.235958 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190320-absurd-base-pr-001.dot * REASONING * PRF # A2: 6 => SOL * STA A2: 6 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190320, absurd
Solution
position: 139672854657489132824315679248153796376948215915726348462537981781294563593861427 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 # A2: 1,4 => UNS * PRF # A2: 6 => SOL * INC # I1: 1,4 => UNS * INC # I1: 2 => UNS * INC # D3: 4,7 => UNS * INC # D3: 3,9 => UNS * INC # H1: 4,7 => UNS * INC # H1: 5 => UNS * INC # F2: 3,9 => UNS * INC # F3: 3,9 => UNS * INC # D2: 3,9 => UNS * INC # D3: 3,9 => UNS * DIS # A5: 4,7 => CTR => A5: 2,3,6 * INC # A5: 2,3,6 => UNS * INC # B5: 4,7 => UNS * DIS # G5: 4,7 => CTR => G5: 2,9 * INC # G5: 2,9 => UNS * INC # H6: 4,7 => UNS * INC # H6: 8 => UNS * INC # D3: 4,7 => UNS * INC # D3: 3,9 => UNS * INC # H6: 4,8 => UNS * DIS # H6: 7 => CTR => H6: 4,8 * INC # I7: 4,8 => UNS * INC # I7: 1,9 => UNS * INC # A8: 7,8 => UNS * DIS # A8: 3 => CTR => A8: 7,8 * INC # B4: 7,8 => UNS * INC # B4: 4 => UNS * INC # A7: 5,8 => UNS * INC # A7: 4,6 => UNS * INC # A9: 5,8 => UNS * INC # A9: 3,4 => UNS * INC # H9: 3,8 => UNS * INC # H9: 2,4,9 => UNS * INC # A8: 3,8 => UNS * INC # A8: 7 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 1,4 => UNS * PRF # A2: 6 => SOL * STA A2: 6 * CNT 2 HDP CHAINS / 2 HYP OPENED