Analysis of zz-www.sudokuoftheday.co.uk-20190224-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: ...4..6..7..3.5..4.2...9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 initial
Autosolve
position: ...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 1,9 => CTR => B1: 3,5,8 * PRF # B8: 1,9 => SOL * PRF # D8: 7,8 => SOL * DIS # D8: 9 => CTR => D8: 7,8 * PRF # H1: 7 => SOL * DIS # G3: 5,7 => CTR => G3: 3 * DIS # H6: 5,7 => CTR => H6: 1,2,4 * DIS # H9: 5,7 => CTR => H9: 1,8 * DIS # C5: 2,3 => CTR => C5: 7,9 * DIS # I6: 2,3 => CTR => I6: 5,7 * DIS # A7: 2,3 => CTR => A7: 6,8,9 * DIS # D4: 2,7 => CTR => D4: 9 * PRF # D4: 9 => SOL * DIS # H6: 2,7 => CTR => H6: 1,4,5 * DIS # I6: 2,7 => CTR => I6: 3,5 * CNT 15 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 1,9 => CTR => B1: 3,5,8 * PRF B1: 3,5,8 # B8: 1,9 => SOL * STA B1: 3,5,8 + B8: 1,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4..6..7..3.5..4.2...9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 | initial |
| ...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 | autosolve |
| 935418672716325894824769351571986423249531768368247915683192547197854236452673189 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B2: 1,9 C2: 6,9 D3: 7,8 E3: 6,7 H2: 2,9 H3: 5,7 A6: 2,3 D6: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,B8: 1.. / A8 = 1 => 8 pairs (_) / B8 = 1 => 0 pairs (X) G9,H9: 1.. / G9 = 1 => 9 pairs (_) / H9 = 1 => 10 pairs (_) B2,E2: 1.. / B2 = 1 => 8 pairs (_) / E2 = 1 => 0 pairs (X) A1,A8: 1.. / A1 = 1 => 0 pairs (X) / A8 = 1 => 8 pairs (_) G5,G9: 1.. / G5 = 1 => 10 pairs (_) / G9 = 1 => 9 pairs (_) D4,D6: 2.. / D4 = 2 => 0 pairs (X) / D6 = 2 => 0 pairs (_) E2,H2: 2.. / E2 = 2 => 8 pairs (_) / H2 = 2 => 10 pairs (_) C9,E9: 2.. / C9 = 2 => 9 pairs (_) / E9 = 2 => 17 pairs (_) F1,F7: 2.. / F1 = 2 => 16 pairs (_) / F7 = 2 => 9 pairs (_) I1,G3: 3.. / I1 = 3 => 0 pairs (X) / G3 = 3 => 12 pairs (_) E5,E6: 3.. / E5 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) A3,G3: 3.. / A3 = 3 => 0 pairs (X) / G3 = 3 => 12 pairs (_) E8,F8: 4.. / E8 = 4 => 9 pairs (_) / F8 = 4 => 0 pairs (*) G7,H7: 4.. / G7 = 4 => 9 pairs (_) / H7 = 4 => 10 pairs (_) E6,E8: 4.. / E6 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) G4,G7: 4.. / G4 = 4 => 10 pairs (_) / G7 = 4 => 9 pairs (_) B1,C1: 5.. / B1 = 5 => 10 pairs (_) / C1 = 5 => 9 pairs (_) G3,H3: 5.. / G3 = 5 => 0 pairs (X) / H3 = 5 => 8 pairs (_) H6,I6: 5.. / H6 = 5 => 0 pairs (X) / I6 = 5 => 8 pairs (_) C2,A3: 6.. / C2 = 6 => 8 pairs (_) / A3 = 6 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 0 pairs (X) / E3 = 6 => 8 pairs (_) F4,F5: 6.. / F4 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) C2,E2: 6.. / C2 = 6 => 8 pairs (_) / E2 = 6 => 0 pairs (X) A3,E3: 6.. / A3 = 6 => 0 pairs (X) / E3 = 6 => 8 pairs (_) B4,C5: 7.. / B4 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) F1,D3: 8.. / F1 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 8 pairs (_) / I5 = 8 => 8 pairs (_) A3,D3: 8.. / A3 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) B9,H9: 8.. / B9 = 8 => 8 pairs (_) / H9 = 8 => 10 pairs (_) D3,D8: 8.. / D3 = 8 => 9 pairs (_) / D8 = 8 => 0 pairs (*) H1,H2: 9.. / H1 = 9 => 10 pairs (_) / H2 = 9 => 8 pairs (_) D4,E5: 9.. / D4 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) B4,D4: 9.. / B4 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) D4,D8: 9.. / D4 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) * DURATION: 0:00:41.016753 START: 03:58:48.886262 END: 03:59:29.903015 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C2,D3,D6,E3,H2,H3) * ...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 * PAIR B2: 1,9 BLK 1 A1: 1,9,3,8 # reduction candidate for 1,9 A1: 1,9 # 10 pairs B1: 1,9,3,5,8 # reduction candidate for 1,9 B1: 1,9 => CTR * ..54..6..7..3.58.4.248.9..15.128....94.5.....2687..9..6..1.....1..9..2364..6.3..9 B1: 3,5,8 # 8 pairs * PAIR B2: 1,9 COL B B8: 1,9,5,7,8 # reduction candidate for 1,9 B8: 1,9 => SOLVED * 935418672716325894824769351571986423249531768368247915683192547197854236452673189 B8: 5,7,8 # 8 pairs * PAIR C2: 6,9 COL C C7: 6,9,2,3,5,7 # reduction candidate for 6,9 C7: 6,9 # 11 pairs C8: 6,9,5,7 # reduction candidate for 6,9 C8: 6,9 # 10 pairs * PAIR D3: 7,8 BLK 2 F1: 7,8,1,2 # reduction candidate for 7,8 F1: 7,8 # 11 pairs F1: 1,2 # 11 pairs * PAIR D3: 7,8 COL D D8: 7,8,9 # reduction candidate for 7,8 D8: 7,8 => SOLVED * 935418672716325894824769351571986423249531768368247915683192547197854236452673189 D8: 9 => CTR * ...41.6..71.3.58.46248793515912847633475961..268731945...1..4..1..94.23.4..6.3.19 * PAIR H2: 2,9 BLK 3 H1: 2,9,7 # reduction candidate for 2,9 H1: 7 => SOLVED * 935418672716325894824769351571986423249531768368247915683192547197854236452673189 H1: 2,9 # 10 pairs * PAIR H3: 5,7 BLK 3 G3: 5,7,3 # reduction candidate for 5,7 G3: 5,7 => CTR * ...4..6.37.63.58.4324869..1591.8.....4.5.....26873.9.5...1........94.23.4..6.3..9 G3: 3 # 12 pairs * PAIR H3: 5,7 COL H H6: 5,7,1,2,4 # reduction candidate for 5,7 H6: 5,7 => CTR * ...4..6.37..3.58.4.24..9..1571986342.4.5371..3682..9...3.1..4........23.4..6.3.19 H6: 1,2,4 # 11 pairs H7: 5,7,4,6,8 # reduction candidate for 5,7 H7: 5,7 # 18 pairs H9: 5,7,1,8 # reduction candidate for 5,7 H9: 5,7 => CTR * 8..4..6.37.63.58.4324869571591.8.....4.5.....26873.9.5...1..4.....94.23.48.6.3159 H9: 1,8 # 9 pairs * PAIR A6: 2,3 BLK 4 A5: 2,3,9 # reduction candidate for 2,3 A5: 2,3 # 18 pairs C5: 2,3,7,9 # reduction candidate for 2,3 C5: 2,3 => CTR * ...4.269.7..3.582462487935157198.4629425.....3682..9..2..1........7..23.4..623..9 C5: 7,9 # 9 pairs * PAIR A6: 2,3 ROW 6 I6: 2,3,5,7 # reduction candidate for 2,3 I6: 2,3 => CTR * ...4..6.37..3.58.43248695715.1.8.....4.5.....268...95....1...........23.4..6.3..9 I6: 5,7 # 9 pairs * PAIR A6: 2,3 COL A A7: 2,3,6,8,9 # reduction candidate for 2,3 A7: 2,3 => CTR * ...4.26.77..3.5824.248793515.198...29425....33682..9.52..1...........23.4..623..9 A7: 6,8,9 # 8 pairs * PAIR D6: 2,7 BLK 5 D4: 2,7,9 # reduction candidate for 2,7 D4: 2,7 => CTR * ...41.6..71.3.58.46248793515912847633475961..268731945...1..4..1..94.23.4..6.3.19 D4: 9 => SOLVED * 935418672716325894824769351571986423249531768368247915683192547197854236452673189 * PAIR D6: 2,7 ROW 6 H6: 2,7,1,4,5 # reduction candidate for 2,7 H6: 2,7 => CTR * ...4..6.37..3.58.4.24..9751571986342.4.5371..3682..975.3.1..4.....7..23.4.7623519 H6: 1,4,5 # 8 pairs I6: 2,7,3,5 # reduction candidate for 2,7 I6: 2,7 => CTR * ...4..6.37..3.58.43248695715.1.8.....4.5.....2687..95....1...........23.4..6.3..9 I6: 3,5 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190224-absurd-base-pr-000.dot * REASONING * DIS # B1: 1,9 => CTR => B1: 3,5,8 * PRF # B8: 1,9 => SOL * PRF # D8: 7,8 => SOL * DIS # D8: 9 => CTR => D8: 7,8 * PRF # H1: 7 => SOL * DIS # G3: 5,7 => CTR => G3: 3 * DIS # H6: 5,7 => CTR => H6: 1,2,4 * DIS # H9: 5,7 => CTR => H9: 1,8 * DIS # C5: 2,3 => CTR => C5: 7,9 * DIS # I6: 2,3 => CTR => I6: 5,7 * DIS # A7: 2,3 => CTR => A7: 6,8,9 * DIS # D4: 2,7 => CTR => D4: 9 * PRF # D4: 9 => SOL * DIS # H6: 2,7 => CTR => H6: 1,4,5 * DIS # I6: 2,7 => CTR => I6: 3,5 * CNT 15 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C2,D3,D6,E3,H2,H3) * ...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 * PAIR B2: 1,9 BLK 1 A1: 1,9,3,8 # reduction candidate for 1,9 A1: 1,9 # 10 pairs B1: 1,9,3,5,8 # reduction candidate for 1,9 B1: 1,9 => CTR * ..54..6..7..3.58.4.248.9..15.128....94.5.....2687..9..6..1.....1..9..2364..6.3..9 * RESTART * PAIR B2: 1,9 BLK 1 A1: 1,9,3,8 # reduction candidate for 1,9 A1: 1,9 # 10 pairs A1: 3,8 # 9 pairs * PAIR B2: 1,9 COL B B8: 1,9,5,7,8 # reduction candidate for 1,9 B8: 1,9 => SOLVED * 935418672716325894824769351571986423249531768368247915683192547197854236452673189 * DURATION: 0:00:04.644161 START: 03:59:52.446942 END: 03:59:57.091103 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190224-absurd-base-pr-001.dot * REASONING * DIS # B1: 1,9 => CTR => B1: 3,5,8 * PRF B1: 3,5,8 # B8: 1,9 => SOL * STA B1: 3,5,8 + B8: 1,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190224, absurd
Solution
position: 935418672716325894824769351571986423249531768368247915683192547197854236452673189 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 # A1: 1,9 => UNS * DIS # B1: 1,9 => CTR => B1: 3,5,8 * INC # B1: 3,5,8 => UNS * PRF # B8: 1,9 => SOL * INC # B8: 5,7,8 => UNS * INC # C7: 6,9 => UNS * INC # C8: 6,9 => UNS * INC # F1: 7,8 => UNS * INC # F1: 1,2 => UNS * PRF # D8: 7,8 => SOL * DIS # D8: 9 => CTR => D8: 7,8 * INC # H1: 2,9 => UNS * PRF # H1: 7 => SOL * DIS # G3: 5,7 => CTR => G3: 3 * INC # G3: 3 => UNS * DIS # H6: 5,7 => CTR => H6: 1,2,4 * INC # H6: 1,2,4 => UNS * INC # H7: 5,7 => UNS * DIS # H9: 5,7 => CTR => H9: 1,8 * INC # H9: 1,8 => UNS * INC # A5: 2,3 => UNS * DIS # C5: 2,3 => CTR => C5: 7,9 * INC # C5: 7,9 => UNS * DIS # I6: 2,3 => CTR => I6: 5,7 * INC # I6: 5,7 => UNS * DIS # A7: 2,3 => CTR => A7: 6,8,9 * INC # A7: 6,8,9 => UNS * DIS # D4: 2,7 => CTR => D4: 9 * PRF # D4: 9 => SOL * DIS # H6: 2,7 => CTR => H6: 1,4,5 * INC # H6: 1,4,5 => UNS * DIS # I6: 2,7 => CTR => I6: 3,5 * INC # I6: 3,5 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 1,9 => UNS * DIS # B1: 1,9 => CTR => B1: 3,5,8 * INC B1: 3,5,8 # A1: 1,9 => UNS * INC B1: 3,5,8 # A1: 3,8 => UNS * PRF B1: 3,5,8 # B8: 1,9 => SOL * STA B1: 3,5,8 + B8: 1,9 * CNT 5 HDP CHAINS / 5 HYP OPENED