Analysis of zz-www.sudokuwiki.org-0277-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=277
level: medium
position: 41.9.6..........7...5.4....6.....59.....5...18.4..3......3....29.8.......3....6.. initial
Autosolve
position: 41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G2: 2,3 => CTR => G2: 1,4,8,9 * DIS # C5: 2,7 => CTR => C5: 3,9 * DIS # C5: 2,7 => CTR => C5: 3,9 * DIS # H3: 1,3,8 => CTR => H3: 2,6 * DIS # C5: 2,7 => CTR => C5: 3,9 * CNT 5 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G2: 2,3 => CTR => G2: 1,4,8,9 * DIS G2: 1,4,8,9 # E2: 1,8 => CTR => E2: 2,3 * DIS G2: 1,4,8,9 + E2: 2,3 # A5: 7 => CTR => A5: 2,3 * DIS G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B3: 6,9 => CTR => B3: 8 * PRF G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 # H1: 5,8 => SOL * STA G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 + H1: 5,8 * CNT 5 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 41.9.6..........7...5.4....6.....59.....5...18.4..3......3....29.8.......3....6.. | initial |
| 41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6.. | autosolve |
| 413976258296538174785241369671824593329657841854193726147365982968712435532489617 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 2,3 C2: 6,9 I1: 5,8 B4: 2,7 F5: 2,7 G5: 4,8 H5: 4,8 G6: 2,7 H6: 2,6 I6: 6,7 A7: 1,5 C7: 6,7 A9: 1,5 C9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,A9: 1.. / A7 = 1 => 12 pairs (_) / A9 = 1 => 12 pairs (_) G6,H6: 2.. / G6 = 2 => 13 pairs (_) / H6 = 2 => 15 pairs (_) B8,C9: 2.. / B8 = 2 => 0 pairs (X) / C9 = 2 => 15 pairs (_) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 17 pairs (_) A5,C5: 3.. / A5 = 3 => 18 pairs (_) / C5 = 3 => 17 pairs (_) G8,H8: 3.. / G8 = 3 => 16 pairs (_) / H8 = 3 => 14 pairs (_) C1,C5: 3.. / C1 = 3 => 18 pairs (_) / C5 = 3 => 17 pairs (_) G2,I2: 4.. / G2 = 4 => 14 pairs (_) / I2 = 4 => 16 pairs (_) D4,F4: 4.. / D4 = 4 => 14 pairs (_) / F4 = 4 => 14 pairs (_) G5,H5: 4.. / G5 = 4 => 16 pairs (_) / H5 = 4 => 13 pairs (_) B7,B8: 4.. / B7 = 4 => 14 pairs (_) / B8 = 4 => 18 pairs (_) D2,F2: 5.. / D2 = 5 => 14 pairs (_) / F2 = 5 => 15 pairs (_) H1,I1: 5.. / H1 = 5 => 17 pairs (_) / I1 = 5 => 14 pairs (_) A7,A9: 5.. / A7 = 5 => 12 pairs (_) / A9 = 5 => 12 pairs (_) H6,I6: 6.. / H6 = 6 => 13 pairs (_) / I6 = 6 => 15 pairs (_) E7,E8: 6.. / E7 = 6 => 21 pairs (_) / E8 = 6 => 14 pairs (_) B8,E8: 6.. / B8 = 6 => 21 pairs (_) / E8 = 6 => 14 pairs (_) C2,C7: 6.. / C2 = 6 => 22 pairs (_) / C7 = 6 => 15 pairs (_) H3,H6: 6.. / H3 = 6 => 15 pairs (_) / H6 = 6 => 13 pairs (_) C1,A3: 7.. / C1 = 7 => 24 pairs (_) / A3 = 7 => 18 pairs (_) G6,I6: 7.. / G6 = 7 => 15 pairs (_) / I6 = 7 => 13 pairs (_) C1,E1: 7.. / C1 = 7 => 24 pairs (_) / E1 = 7 => 18 pairs (_) A3,A5: 7.. / A3 = 7 => 18 pairs (_) / A5 = 7 => 24 pairs (_) B2,B3: 8.. / B2 = 8 => 17 pairs (_) / B3 = 8 => 18 pairs (_) G5,H5: 8.. / G5 = 8 => 13 pairs (_) / H5 = 8 => 16 pairs (_) B5,C5: 9.. / B5 = 9 => 15 pairs (_) / C5 = 9 => 22 pairs (_) F7,F9: 9.. / F7 = 9 => 16 pairs (_) / F9 = 9 => 14 pairs (_) G7,I9: 9.. / G7 = 9 => 14 pairs (_) / I9 = 9 => 16 pairs (_) F7,G7: 9.. / F7 = 9 => 16 pairs (_) / G7 = 9 => 14 pairs (_) F9,I9: 9.. / F9 = 9 => 14 pairs (_) / I9 = 9 => 16 pairs (_) C2,C5: 9.. / C2 = 9 => 15 pairs (_) / C5 = 9 => 22 pairs (_) * DURATION: 0:00:28.116817 START: 14:41:15.140799 END: 14:41:43.257616 2019-04-28 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A9,B4,C2,C7,C9,F5,G5,G6,H5,H6,I1,I6) * 41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6.. * PAIR A2: 2,3 BLK 1 C1: 2,3,7 # reduction candidate for 2,3 C1: 2,3 # 18 pairs A3: 2,3,7 # reduction candidate for 2,3 A3: 2,3 # 24 pairs * PAIR A2: 2,3 ROW 2 E2: 2,3,1,8 # reduction candidate for 2,3 E2: 2,3 # 16 pairs G2: 2,3,1,4,8,9 # reduction candidate for 2,3 G2: 2,3 => CTR * 417936...2.....374385.4....6.1...5937.3652..1854193.....63....29.8.6..3..32...6.. G2: 1,4,8,9 # 14 pairs * PAIR A2: 2,3 COL A A5: 2,3,7 # reduction candidate for 2,3 A5: 7 # 24 pairs A5: 2,3 # 18 pairs * PAIR C2: 6,9 BLK 1 B2: 6,9,8 # reduction candidate for 6,9 B2: 6,9 # 18 pairs B3: 6,9,8 # reduction candidate for 6,9 B3: 6,9 # 17 pairs * PAIR C2: 6,9 ROW 2 I2: 6,9,4,8 # reduction candidate for 6,9 I2: 6,9 # 16 pairs I2: 4,8 # 16 pairs * PAIR I1: 5,8 BLK 3 H1: 5,8,2,3 # reduction candidate for 5,8 H1: 5,8 # 19 pairs H1: 2,3 # 15 pairs * PAIR I1: 5,8 COL I I9: 5,8,4,7,9 # reduction candidate for 5,8 I9: 5,8 # 17 pairs I9: 4,7,9 # 15 pairs * PAIR B4: 2,7 BLK 4 A5: 2,7,3 # reduction candidate for 2,7 A5: 2,7 # 17 pairs B5: 2,7,9 # reduction candidate for 2,7 B5: 2,7 # 22 pairs C5: 2,7,3,9 # reduction candidate for 2,7 C5: 2,7 => CTR * 413976.252.9.3..7.7.5.4....6.1...59339.65...1854193267..63..7.29.8.6...4.3....6.. C5: 3,9 # 15 pairs * PAIR B4: 2,7 ROW 4 D4: 2,7,4,8 # reduction candidate for 2,7 D4: 2,7 # 16 pairs E4: 2,7,8 # reduction candidate for 2,7 E4: 2,7 # 17 pairs F4: 2,7,4,8 # reduction candidate for 2,7 F4: 2,7 # 17 pairs * PAIR B4: 2,7 COL B B8: 2,7,4,6 # reduction candidate for 2,7 B8: 4,6 # 16 pairs B8: 2,7 # 15 pairs * PAIR F5: 2,7 BLK 5 D4: 2,7,4,8 # reduction candidate for 2,7 D4: 2,7 # 16 pairs E4: 2,7,8 # reduction candidate for 2,7 E4: 2,7 # 17 pairs F4: 2,7,4,8 # reduction candidate for 2,7 F4: 2,7 # 17 pairs * PAIR F5: 2,7 ROW 5 A5: 2,7,3 # reduction candidate for 2,7 A5: 2,7 # 17 pairs B5: 2,7,9 # reduction candidate for 2,7 B5: 2,7 # 22 pairs C5: 2,7,3,9 # reduction candidate for 2,7 C5: 2,7 => CTR * 413976.252.9.3..7.7.5.4....6.1...59339.65...1854193267..63..7.29.8.6...4.3....6.. C5: 3,9 # 15 pairs * PAIR F5: 2,7 COL F F3: 2,7,1,8 # reduction candidate for 2,7 F3: 2,7 # 16 pairs F8: 2,7,1,4,5 # reduction candidate for 2,7 F8: 2,7 # 17 pairs F9: 2,7,1,4,5,8,9 # reduction candidate for 2,7 F9: 2,7 # 20 pairs * PAIR G5: 4,8 COL G G2: 4,8,1,2,3,9 # reduction candidate for 4,8 G2: 4,8 # 17 pairs G7: 4,8,1,7,9 # reduction candidate for 4,8 G7: 4,8 # 19 pairs * PAIR H5: 4,8 COL H H7: 4,8,1,5 # reduction candidate for 4,8 H7: 4,8 # 16 pairs H9: 4,8,1,5 # reduction candidate for 4,8 H9: 4,8 # 16 pairs * PAIR H6: 2,6 COL H H3: 2,6,1,3,8 # reduction candidate for 2,6 H3: 1,3,8 => CTR * 41.986325....3147.3.5.4....6.1...5937.3652841854193267.4.3....2978.65134.32...6.. H3: 2,6 # 15 pairs * PAIR A7: 1,5 ROW 7 F7: 1,5,4,7,8,9 # reduction candidate for 1,5 F7: 1,5 # 17 pairs H7: 1,5,4,8 # reduction candidate for 1,5 H7: 1,5 # 15 pairs * PAIR C7: 6,7 BLK 7 B7: 6,7,4 # reduction candidate for 6,7 B7: 6,7 # 18 pairs B8: 6,7,2,4 # reduction candidate for 6,7 B8: 6,7 # 16 pairs * PAIR C7: 6,7 ROW 7 E7: 6,7,1,8 # reduction candidate for 6,7 E7: 6,7 # 15 pairs E7: 1,8 # 15 pairs * PAIR A9: 1,5 ROW 9 F9: 1,5,2,4,7,8,9 # reduction candidate for 1,5 F9: 1,5 # 19 pairs H9: 1,5,4,8 # reduction candidate for 1,5 H9: 1,5 # 15 pairs * PAIR C9: 2,7 BLK 7 B8: 2,7,4,6 # reduction candidate for 2,7 B8: 4,6 # 16 pairs B8: 2,7 # 15 pairs * PAIR C9: 2,7 ROW 9 D9: 2,7,4,5,8 # reduction candidate for 2,7 D9: 2,7 # 16 pairs E9: 2,7,1,8 # reduction candidate for 2,7 E9: 2,7 # 15 pairs F9: 2,7,1,4,5,8,9 # reduction candidate for 2,7 F9: 2,7 # 20 pairs * PAIR C9: 2,7 COL C C1: 2,7,3 # reduction candidate for 2,7 C1: 2,7 # 17 pairs C5: 2,7,3,9 # reduction candidate for 2,7 C5: 2,7 => CTR * 413976.252.9.3..7.7.5.4....6.1...59339.65...1854193267..63..7.29.8.6...4.3....6.. C5: 3,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0277-base-pr-000.dot * REASONING * DIS # G2: 2,3 => CTR => G2: 1,4,8,9 * DIS # C5: 2,7 => CTR => C5: 3,9 * DIS # C5: 2,7 => CTR => C5: 3,9 * DIS # H3: 1,3,8 => CTR => H3: 2,6 * DIS # C5: 2,7 => CTR => C5: 3,9 * CNT 5 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A9,B4,C2,C7,C9,F5,G5,G6,H5,H6,I1,I6) * 41.9.6..........7...5.4....6.1...593...65...1854193......3....29.8.......3....6.. * PAIR A2: 2,3 BLK 1 C1: 2,3,7 # reduction candidate for 2,3 C1: 2,3 # 18 pairs A3: 2,3,7 # reduction candidate for 2,3 A3: 2,3 # 24 pairs * PAIR A2: 2,3 ROW 2 E2: 2,3,1,8 # reduction candidate for 2,3 E2: 2,3 # 16 pairs G2: 2,3,1,4,8,9 # reduction candidate for 2,3 G2: 2,3 => CTR * 417936...2.....374385.4....6.1...5937.3652..1854193.....63....29.8.6..3..32...6.. * RESTART * PAIR A2: 2,3 ROW 2 E2: 2,3,1,8 # reduction candidate for 2,3 E2: 1,8 => CTR * 417936...3.9....7.2.5.4....6.1...593793652..1854193.....63....29.8.6.....32...6.. * PAIR A2: 2,3 COL A A5: 2,3,7 # reduction candidate for 2,3 A5: 7 => CTR * 4179.68.5.695.8174.85741269621874593793652481854193726.763..9.2948265317.32..96.8 * PAIR RESTART * PAIR C2: 6,9 BLK 1 B2: 6,9,8 # reduction candidate for 6,9 B2: 6,9 # 22 pairs B3: 6,9,8 # reduction candidate for 6,9 B3: 6,9 => CTR * 413976.2528.531.7.7.5.4....6.1...5933..65...1854193267...3....29.8.....4.3....6.8 * RESTART * PAIR I1: 5,8 BLK 3 H1: 5,8,2 # reduction candidate for 5,8 H1: 5,8 => SOLVED * 413976258296538174785241369671824593329657841854193726147365982968712435532489617 * DURATION: 0:00:08.181824 START: 14:42:11.314733 END: 14:42:19.496557 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0277-base-pr-001.dot * REASONING * DIS # G2: 2,3 => CTR => G2: 1,4,8,9 * DIS G2: 1,4,8,9 # E2: 1,8 => CTR => E2: 2,3 * DIS G2: 1,4,8,9 + E2: 2,3 # A5: 7 => CTR => A5: 2,3 * DIS G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B3: 6,9 => CTR => B3: 8 * PRF G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 # H1: 5,8 => SOL * STA G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 + H1: 5,8 * CNT 5 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=277
Solution
position: 413976258296538174785241369671824593329657841854193726147365982968712435532489617 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 # C1: 2,3 => UNS * INC # A3: 2,3 => UNS * INC # E2: 2,3 => UNS * DIS # G2: 2,3 => CTR => G2: 1,4,8,9 * INC # G2: 1,4,8,9 => UNS * INC # A5: 2,3 => UNS * INC # A5: 7 => UNS * INC # B2: 6,9 => UNS * INC # B3: 6,9 => UNS * INC # I2: 6,9 => UNS * INC # I2: 4,8 => UNS * INC # H1: 5,8 => UNS * INC # H1: 2,3 => UNS * INC # I9: 5,8 => UNS * INC # I9: 4,7,9 => UNS * INC # A5: 2,7 => UNS * INC # B5: 2,7 => UNS * DIS # C5: 2,7 => CTR => C5: 3,9 * INC # C5: 3,9 => UNS * INC # D4: 2,7 => UNS * INC # E4: 2,7 => UNS * INC # F4: 2,7 => UNS * INC # B8: 2,7 => UNS * INC # B8: 4,6 => UNS * INC # D4: 2,7 => UNS * INC # E4: 2,7 => UNS * INC # F4: 2,7 => UNS * INC # A5: 2,7 => UNS * INC # B5: 2,7 => UNS * DIS # C5: 2,7 => CTR => C5: 3,9 * INC # C5: 3,9 => UNS * INC # F3: 2,7 => UNS * INC # F8: 2,7 => UNS * INC # F9: 2,7 => UNS * INC # G2: 4,8 => UNS * INC # G7: 4,8 => UNS * INC # H7: 4,8 => UNS * INC # H9: 4,8 => UNS * INC # H3: 2,6 => UNS * DIS # H3: 1,3,8 => CTR => H3: 2,6 * INC # F7: 1,5 => UNS * INC # H7: 1,5 => UNS * INC # B7: 6,7 => UNS * INC # B8: 6,7 => UNS * INC # E7: 6,7 => UNS * INC # E7: 1,8 => UNS * INC # F9: 1,5 => UNS * INC # H9: 1,5 => UNS * INC # B8: 2,7 => UNS * INC # B8: 4,6 => UNS * INC # D9: 2,7 => UNS * INC # E9: 2,7 => UNS * INC # F9: 2,7 => UNS * INC # C1: 2,7 => UNS * DIS # C5: 2,7 => CTR => C5: 3,9 * INC # C5: 3,9 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,3 => UNS * INC # A3: 2,3 => UNS * INC # E2: 2,3 => UNS * DIS # G2: 2,3 => CTR => G2: 1,4,8,9 * INC G2: 1,4,8,9 # E2: 2,3 => UNS * DIS G2: 1,4,8,9 # E2: 1,8 => CTR => E2: 2,3 * INC G2: 1,4,8,9 + E2: 2,3 # A5: 2,3 => UNS * DIS G2: 1,4,8,9 + E2: 2,3 # A5: 7 => CTR => A5: 2,3 * INC G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B2: 6,9 => UNS * DIS G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 # B3: 6,9 => CTR => B3: 8 * PRF G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 # H1: 5,8 => SOL * STA G2: 1,4,8,9 + E2: 2,3 + A5: 2,3 + B3: 8 + H1: 5,8 * CNT 11 HDP CHAINS / 11 HYP OPENED