Analysis of zz-www.sudokuwiki.org-0102-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=102
level: medium
position: 52....6..3.7..8.......7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9....57 initial
Autosolve
position: 528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1,6 => CTR => B3: 9 * DIS # I1: 3 => CTR => I1: 4,9 * DIS # F3: 3,9 => CTR => F3: 2,5,6 * DIS # B7: 7,8 => CTR => B7: 3,4,5 * DIS # A8: 7,8 => CTR => A8: 2 * DIS # B9: 6,8 => CTR => B9: 3,4 * DIS # D9: 3,4 => CTR => D9: 1,8 * DIS # B9: 6,8 => CTR => B9: 3,4 * CNT 8 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 1,6 => CTR => B3: 9 * DIS B3: 9 # E2: 6 => CTR => E2: 4,9 * PRF B3: 9 + E2: 4,9 # G6: 1 => SOL * STA B3: 9 + E2: 4,9 + G6: 1 * CNT 3 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 52....6..3.7..8.......7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9....57 | initial |
| 528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257 | autosolve |
| 528319674367248519194576823932861745715432968486957132851724396273695481649183257 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A3: 1,6 D2: 2,4 H2: 1,2 I2: 4,9 H3: 1,2 I3: 3,9 G4: 3,7 I5: 6,8 A7: 7,8 A9: 6,8 F9: 3,4 G7: 3,9 I7: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E1: 1.. / D1 = 1 => 14 pairs (_) / E1 = 1 => 15 pairs (_) H2,H3: 1.. / H2 = 1 => 14 pairs (_) / H3 = 1 => 0 pairs (X) G5,G6: 1.. / G5 = 1 => 22 pairs (_) / G6 = 1 => 14 pairs (_) D9,E9: 1.. / D9 = 1 => 15 pairs (_) / E9 = 1 => 14 pairs (_) B2,H2: 1.. / B2 = 1 => 0 pairs (X) / H2 = 1 => 14 pairs (_) B6,G6: 1.. / B6 = 1 => 22 pairs (_) / G6 = 1 => 14 pairs (_) A3,A5: 1.. / A3 = 1 => 14 pairs (_) / A5 = 1 => 0 pairs (X) D1,D9: 1.. / D1 = 1 => 14 pairs (_) / D9 = 1 => 15 pairs (_) E1,E9: 1.. / E1 = 1 => 15 pairs (_) / E9 = 1 => 14 pairs (_) H2,H3: 2.. / H2 = 2 => 0 pairs (X) / H3 = 2 => 14 pairs (_) A8,C8: 2.. / A8 = 2 => 14 pairs (_) / C8 = 2 => 0 pairs (X) D2,H2: 2.. / D2 = 2 => 14 pairs (_) / H2 = 2 => 0 pairs (X) C4,D4: 2.. / C4 = 2 => 15 pairs (_) / D4 = 2 => 0 pairs (X) A5,A8: 2.. / A5 = 2 => 0 pairs (X) / A8 = 2 => 14 pairs (_) F3,F5: 2.. / F3 = 2 => 0 pairs (X) / F5 = 2 => 15 pairs (_) I1,I3: 3.. / I1 = 3 => 0 pairs (X) / I3 = 3 => 14 pairs (_) I1,I2: 4.. / I1 = 4 => 17 pairs (_) / I2 = 4 => 15 pairs (_) H4,H5: 4.. / H4 = 4 => 14 pairs (_) / H5 = 4 => 13 pairs (_) B7,B9: 4.. / B7 = 4 => 16 pairs (_) / B9 = 4 => 17 pairs (_) D3,F3: 5.. / D3 = 5 => 13 pairs (_) / F3 = 5 => 0 pairs (X) E6,E8: 5.. / E6 = 5 => 16 pairs (_) / E8 = 5 => 0 pairs (X) E2,F3: 6.. / E2 = 6 => 16 pairs (_) / F3 = 6 => 14 pairs (_) A9,B9: 6.. / A9 = 6 => 14 pairs (_) / B9 = 6 => 0 pairs (X) H7,I7: 6.. / H7 = 6 => 17 pairs (_) / I7 = 6 => 12 pairs (_) B2,E2: 6.. / B2 = 6 => 14 pairs (_) / E2 = 6 => 16 pairs (_) A3,A9: 6.. / A3 = 6 => 0 pairs (X) / A9 = 6 => 14 pairs (_) I5,I7: 6.. / I5 = 6 => 17 pairs (_) / I7 = 6 => 12 pairs (_) I5,I7: 8.. / I5 = 8 => 12 pairs (_) / I7 = 8 => 17 pairs (_) B2,B3: 9.. / B2 = 9 => 0 pairs (X) / B3 = 9 => 15 pairs (_) G5,H5: 9.. / G5 = 9 => 13 pairs (_) / H5 = 9 => 16 pairs (_) G5,G7: 9.. / G5 = 9 => 13 pairs (_) / G7 = 9 => 16 pairs (_) * DURATION: 0:00:45.806012 START: 05:16:44.601953 END: 05:17:30.407965 2017-05-01 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,D2,F9,G4,G7,H2,H3,I2,I3,I5,I7) * 528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257 * PAIR A3: 1,6 BLK 1 B2: 1,6,9 # reduction candidate for 1,6 B2: 1,6 # 15 pairs B3: 1,6,9 # reduction candidate for 1,6 B3: 1,6 => CTR * 528...67.397268514..4.7.82.932..1765..67329484..9.6.32..1.2.3.62.36..4.1..9...257 B3: 9 # 15 pairs * PAIR D2: 2,4 COL D D4: 2,4,7,8 # reduction candidate for 2,4 D4: 2,4 # 16 pairs D5: 2,4,5,7,8 # reduction candidate for 2,4 D5: 2,4 # 21 pairs * PAIR I2: 4,9 BLK 3 I1: 4,9,3 # reduction candidate for 4,9 I1: 3 => CTR * 528...673397268514..4.7.829932..1765..6.32.484..9.6.32..1.2.3.62.36..4.1..9...257 I1: 4,9 # 14 pairs * PAIR I2: 4,9 ROW 2 E2: 4,9,6 # reduction candidate for 4,9 E2: 6 # 16 pairs E2: 4,9 # 14 pairs * PAIR I3: 3,9 BLK 3 I1: 3,9,4 # reduction candidate for 3,9 I1: 4 # 17 pairs I1: 3,9 # 15 pairs * PAIR I3: 3,9 ROW 3 F3: 3,9,2,5,6 # reduction candidate for 3,9 F3: 3,9 => CTR * 528...67.3.7268514..457.82.9.2..1.65..6.32.484..956.32..1.2....2..6..4.1..9...257 F3: 2,5,6 # 13 pairs * PAIR G4: 3,7 BLK 6 G6: 3,7,1 # reduction candidate for 3,7 G6: 3,7 # 22 pairs G6: 1 # 14 pairs * PAIR G4: 3,7 ROW 4 B4: 3,7,8 # reduction candidate for 3,7 B4: 3,7 # 15 pairs B4: 8 # 14 pairs * PAIR I5: 6,8 BLK 6 H4: 6,8,3,4 # reduction candidate for 6,8 H4: 6,8 # 15 pairs H5: 6,8,4,9 # reduction candidate for 6,8 H5: 6,8 # 18 pairs H6: 6,8,3 # reduction candidate for 6,8 H6: 6,8 # 16 pairs * PAIR A7: 7,8 BLK 7 B7: 7,8,3,4,5 # reduction candidate for 7,8 B7: 7,8 => CTR * 528...67.3.72.851.1.4.7.82.9.2..1..5....32..848.956..2..1.2....2..697481649..3257 B7: 3,4,5 # 13 pairs A8: 7,8,2 # reduction candidate for 7,8 A8: 7,8 => CTR * 528...67.3.7..85..1.4.728..9....1..52...3....4..9....2..1.2......26..4.1..9...257 A8: 2 # 14 pairs B8: 7,8,3,5 # reduction candidate for 7,8 B8: 7,8 # 19 pairs * PAIR A7: 7,8 ROW 7 D7: 7,8,3,4,5 # reduction candidate for 7,8 D7: 7,8 # 18 pairs D7: 3,4,5 # 16 pairs * PAIR A7: 7,8 COL A A5: 7,8,1,2 # reduction candidate for 7,8 A5: 1,2 # 15 pairs A5: 7,8 # 14 pairs * PAIR A9: 6,8 BLK 7 B9: 6,8,3,4 # reduction candidate for 6,8 B9: 6,8 => CTR * 528.9.67.3.7.685....4.7.8..9...41..5.5..329464.3956.82741.2...8235687491..9...257 B9: 3,4 # 18 pairs * PAIR F9: 3,4 BLK 8 D7: 3,4,5,7,8 # reduction candidate for 3,4 D7: 3,4 # 22 pairs F7: 3,4,5,7,9 # reduction candidate for 3,4 F7: 3,4 # 27 pairs D9: 3,4,1,8 # reduction candidate for 3,4 D9: 3,4 => CTR * 5281..67.3.7.685....4.7.8..9...41..5....329464.3956.82741.2...82..687491..9.1.257 D9: 1,8 # 14 pairs * PAIR F9: 3,4 ROW 9 B9: 3,4,6,8 # reduction candidate for 3,4 B9: 6,8 => CTR * 528.9.67.3.7.685....4.7.8..9...41..5.5..329464.3956.82741.2...8235687491..9...257 B9: 3,4 # 18 pairs * PAIR F9: 3,4 COL F F1: 3,4,9 # reduction candidate for 3,4 F1: 9 # 19 pairs F1: 3,4 # 14 pairs * PAIR G7: 3,9 BLK 9 H7: 3,9,6,8 # reduction candidate for 3,9 H7: 3,9 # 15 pairs H8: 3,9,8 # reduction candidate for 3,9 H8: 3,9 # 18 pairs * PAIR G7: 3,9 ROW 7 F7: 3,9,4,5,7 # reduction candidate for 3,9 F7: 3,9 # 21 pairs F7: 4,5,7 # 14 pairs * PAIR I7: 6,8 BLK 9 H7: 6,8,3,9 # reduction candidate for 6,8 H7: 6,8 # 18 pairs H7: 3,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0102-base-pr-000.dot * REASONING * DIS # B3: 1,6 => CTR => B3: 9 * DIS # I1: 3 => CTR => I1: 4,9 * DIS # F3: 3,9 => CTR => F3: 2,5,6 * DIS # B7: 7,8 => CTR => B7: 3,4,5 * DIS # A8: 7,8 => CTR => A8: 2 * DIS # B9: 6,8 => CTR => B9: 3,4 * DIS # D9: 3,4 => CTR => D9: 1,8 * DIS # B9: 6,8 => CTR => B9: 3,4 * CNT 8 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,D2,F9,G4,G7,H2,H3,I2,I3,I5,I7) * 528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257 * PAIR A3: 1,6 BLK 1 B2: 1,6,9 # reduction candidate for 1,6 B2: 1,6 # 15 pairs B3: 1,6,9 # reduction candidate for 1,6 B3: 1,6 => CTR * 528...67.397268514..4.7.82.932..1765..67329484..9.6.32..1.2.3.62.36..4.1..9...257 * RESTART * PAIR D2: 2,4 COL D D4: 2,4,7,8 # reduction candidate for 2,4 D4: 2,4 # 21 pairs D5: 2,4,5,7,8 # reduction candidate for 2,4 D5: 2,4 # 25 pairs * PAIR I2: 4,9 ROW 2 E2: 4,9,6 # reduction candidate for 4,9 E2: 6 => CTR * 528.93674317468529694.7.8139...41..51...32946473956182741.2...82..687491869...257 * PAIR RESTART * PAIR G4: 3,7 BLK 6 G6: 3,7,1 # reduction candidate for 3,7 G6: 1 => SOLVED * 528319674367248519194576823932861745715432968486957132851724396273695481649183257 * DURATION: 0:00:09.523924 START: 05:18:05.550706 END: 05:18:15.074630 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0102-base-pr-001.dot * REASONING * DIS # B3: 1,6 => CTR => B3: 9 * DIS B3: 9 # E2: 6 => CTR => E2: 4,9 * PRF B3: 9 + E2: 4,9 # G6: 1 => SOL * STA B3: 9 + E2: 4,9 + G6: 1 * CNT 3 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=102
Solution
position: 528319674367248519194576823932861745715432968486957132851724396273695481649183257 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: 1,6 => UNS * DIS # B3: 1,6 => CTR => B3: 9 * INC # B3: 9 => UNS * INC # D4: 2,4 => UNS * INC # D5: 2,4 => UNS * INC # I1: 4,9 => UNS * DIS # I1: 3 => CTR => I1: 4,9 * INC # E2: 4,9 => UNS * INC # E2: 6 => UNS * INC # I1: 3,9 => UNS * INC # I1: 4 => UNS * DIS # F3: 3,9 => CTR => F3: 2,5,6 * INC # F3: 2,5,6 => UNS * INC # G6: 3,7 => UNS * INC # G6: 1 => UNS * INC # B4: 3,7 => UNS * INC # B4: 8 => UNS * INC # H4: 6,8 => UNS * INC # H5: 6,8 => UNS * INC # H6: 6,8 => UNS * DIS # B7: 7,8 => CTR => B7: 3,4,5 * INC # B7: 3,4,5 => UNS * DIS # A8: 7,8 => CTR => A8: 2 * INC # A8: 2 => UNS * INC # B8: 7,8 => UNS * INC # D7: 7,8 => UNS * INC # D7: 3,4,5 => UNS * INC # A5: 7,8 => UNS * INC # A5: 1,2 => UNS * DIS # B9: 6,8 => CTR => B9: 3,4 * INC # B9: 3,4 => UNS * INC # D7: 3,4 => UNS * INC # F7: 3,4 => UNS * DIS # D9: 3,4 => CTR => D9: 1,8 * INC # D9: 1,8 => UNS * INC # B9: 3,4 => UNS * DIS # B9: 6,8 => CTR => B9: 3,4 * INC # F1: 3,4 => UNS * INC # F1: 9 => UNS * INC # H7: 3,9 => UNS * INC # H8: 3,9 => UNS * INC # F7: 3,9 => UNS * INC # F7: 4,5,7 => UNS * INC # H7: 6,8 => UNS * INC # H7: 3,9 => UNS * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,6 => UNS * DIS # B3: 1,6 => CTR => B3: 9 * INC B3: 9 # D4: 2,4 => UNS * INC B3: 9 # D5: 2,4 => UNS * INC B3: 9 # E2: 4,9 => UNS * DIS B3: 9 # E2: 6 => CTR => E2: 4,9 * INC B3: 9 + E2: 4,9 # G6: 3,7 => UNS * PRF B3: 9 + E2: 4,9 # G6: 1 => SOL * STA B3: 9 + E2: 4,9 + G6: 1 * CNT 8 HDP CHAINS / 8 HYP OPENED