Analysis of zz-www.sudokuwiki.org-0020-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=20
level: medium
position: .8.9...1......3.....21.48.38.....5...9..6..7...7.....21.83.57.....8......2...9.4. initial
Autosolve
position: .8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 2 => CTR => E1: 5,7 * DIS # A3: 5,7 => CTR => A3: 6,9 * DIS # H4: 6 => CTR => H4: 3,9 * DIS # G6: 4,6 => CTR => G6: 3,9 * DIS # B8: 4,6 => CTR => B8: 3,7 * DIS # C8: 4,6 => CTR => C8: 3,9 * DIS # E8: 1,7 => CTR => E8: 2,4 * DIS # F8: 2 => CTR => F8: 6,7 * PRF # D2: 2 => SOL * DIS # E8: 1,7 => CTR => E8: 2,4 * DIS # H7: 6,9 => CTR => H7: 2 * CNT 11 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 2 => CTR => E1: 5,7 * DIS E1: 5,7 # A3: 5,7 => CTR => A3: 6,9 * DIS E1: 5,7 + A3: 6,9 # B3: 6 => CTR => B3: 5,7 * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 6 => CTR => H4: 3,9 * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 # C5: 4,5 => CTR => C5: 1,3 * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 6 => CTR => G6: 3,9 * PRF E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 # A8: 4,6 => SOL * STA E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 + A8: 4,6 * CNT 7 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.9...1......3.....21.48.38.....5...9..6..7...7.....21.83.57.....8......2...9.4. | initial |
| .8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48 | autosolve |
| 384976215516283497972154863841792536293568174657431982168345729439827651725619348 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) E3: 5,7 D4: 2,7 E4: 3,9 F4: 2,7 D5: 4,5 D6: 4,5 E6: 3,9 I5: 1,4 B7: 4,6 E7: 2,4 D9: 6,7 E9: 1,7 I7: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 1.. / B2 = 1 => 13 pairs (_) / C2 = 1 => 13 pairs (_) E8,E9: 1.. / E8 = 1 => 0 pairs (X) / E9 = 1 => 13 pairs (_) E9,G9: 1.. / E9 = 1 => 13 pairs (_) / G9 = 1 => 0 pairs (X) B2,B4: 1.. / B2 = 1 => 13 pairs (_) / B4 = 1 => 13 pairs (_) D4,F4: 2.. / D4 = 2 => 15 pairs (_) / F4 = 2 => 0 pairs (*) E7,H7: 2.. / E7 = 2 => 0 pairs (X) / H7 = 2 => 14 pairs (_) D2,D4: 2.. / D2 = 2 => 0 pairs (*) / D4 = 2 => 0 pairs (X) A1,C1: 3.. / A1 = 3 => 13 pairs (_) / C1 = 3 => 19 pairs (_) E4,E6: 3.. / E4 = 3 => 0 pairs (X) / E6 = 3 => 12 pairs (_) C5,G5: 3.. / C5 = 3 => 15 pairs (_) / G5 = 3 => 18 pairs (_) H4,H8: 3.. / H4 = 3 => 15 pairs (_) / H8 = 3 => 18 pairs (_) D5,D6: 4.. / D5 = 4 => 0 pairs (X) / D6 = 4 => 11 pairs (_) E7,E8: 4.. / E7 = 4 => 14 pairs (_) / E8 = 4 => 0 pairs (X) B7,E7: 4.. / B7 = 4 => 0 pairs (X) / E7 = 4 => 14 pairs (_) E1,E3: 5.. / E1 = 5 => 17 pairs (_) / E3 = 5 => 15 pairs (_) D5,D6: 5.. / D5 = 5 => 11 pairs (_) / D6 = 5 => 0 pairs (X) A9,C9: 5.. / A9 = 5 => 15 pairs (_) / C9 = 5 => 11 pairs (_) H8,I8: 5.. / H8 = 5 => 16 pairs (_) / I8 = 5 => 14 pairs (_) C5,D5: 5.. / C5 = 5 => 0 pairs (X) / D5 = 5 => 11 pairs (_) F1,D2: 6.. / F1 = 6 => 17 pairs (_) / D2 = 6 => 14 pairs (_) F8,D9: 6.. / F8 = 6 => 14 pairs (_) / D9 = 6 => 17 pairs (_) D2,D9: 6.. / D2 = 6 => 14 pairs (_) / D9 = 6 => 17 pairs (_) F1,F8: 6.. / F1 = 6 => 17 pairs (_) / F8 = 6 => 14 pairs (_) I1,I2: 7.. / I1 = 7 => 15 pairs (_) / I2 = 7 => 14 pairs (_) D4,F4: 7.. / D4 = 7 => 0 pairs (*) / F4 = 7 => 0 pairs (X) E4,E6: 9.. / E4 = 9 => 12 pairs (_) / E6 = 9 => 0 pairs (X) A8,C8: 9.. / A8 = 9 => 0 pairs (X) / C8 = 9 => 13 pairs (_) H7,I7: 9.. / H7 = 9 => 0 pairs (X) / I7 = 9 => 13 pairs (_) A3,H3: 9.. / A3 = 9 => 14 pairs (_) / H3 = 9 => 0 pairs (X) E6,G6: 9.. / E6 = 9 => 0 pairs (X) / G6 = 9 => 12 pairs (_) C2,C8: 9.. / C2 = 9 => 0 pairs (X) / C8 = 9 => 13 pairs (_) G2,G6: 9.. / G2 = 9 => 0 pairs (X) / G6 = 9 => 12 pairs (_) * DURATION: 0:00:46.264106 START: 03:45:41.841693 END: 03:46:28.105799 2017-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,D4,D5,D6,D9,E3,E4,E6,E7,E9,F4,I5,I7) * .8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48 * PAIR E3: 5,7 BLK 2 E1: 5,7,2 # reduction candidate for 5,7 E1: 2 => CTR * .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48 E1: 5,7 # 18 pairs * PAIR E3: 5,7 ROW 3 A3: 5,7,6,9 # reduction candidate for 5,7 A3: 5,7 => CTR * 38.9...1.47..83....621.48938...9.536293568.7.657431982148325769.3.84.....2..19348 A3: 6,9 # 14 pairs B3: 5,7,6 # reduction candidate for 5,7 B3: 5,7 # 16 pairs * PAIR D4: 2,7 COL D D2: 2,7,6 # reduction candidate for 2,7 D2: 2,7 # 17 pairs D2: 6 # 14 pairs * PAIR E4: 3,9 ROW 4 H4: 3,9,6 # reduction candidate for 3,9 H4: 6 => CTR * .8.9...1.....83.....21.48.38.....56.29..6837...7..1.82148325796.7.846.35.2...9.48 H4: 3,9 # 14 pairs * PAIR F4: 2,7 COL F F1: 2,7,6 # reduction candidate for 2,7 F1: 2,7 # 14 pairs F8: 2,7,6 # reduction candidate for 2,7 F8: 2,7 # 17 pairs * PAIR D5: 4,5 ROW 5 C5: 4,5,1,3 # reduction candidate for 4,5 C5: 4,5 # 18 pairs C5: 1,3 # 12 pairs * PAIR D6: 4,5 ROW 6 A6: 4,5,3,6 # reduction candidate for 4,5 A6: 4,5 # 15 pairs B6: 4,5,3,6 # reduction candidate for 4,5 B6: 4,5 # 15 pairs * PAIR E6: 3,9 ROW 6 G6: 3,9,4,6 # reduction candidate for 3,9 G6: 4,6 => CTR * .8.95..1....68392.9.21748538..23756929..6837..37.91.821.83.57....98...35.2..19648 G6: 3,9 # 14 pairs * PAIR I5: 1,4 BLK 6 I4: 1,4,6,9 # reduction candidate for 1,4 I4: 1,4 # 21 pairs G5: 1,4,3 # reduction candidate for 1,4 G5: 1,4 # 15 pairs * PAIR I5: 1,4 ROW 5 C5: 1,4,3,5 # reduction candidate for 1,4 C5: 1,4 # 21 pairs C5: 3,5 # 14 pairs * PAIR B7: 4,6 BLK 7 A8: 4,6,3,7,9 # reduction candidate for 4,6 A8: 4,6 # 16 pairs B8: 4,6,3,7 # reduction candidate for 4,6 B8: 4,6 => CTR * .8.9..21.4..2839579721548638.4...59629..683716.7.914821683457297498...35.2...9.48 B8: 3,7 # 14 pairs C8: 4,6,3,9 # reduction candidate for 4,6 C8: 4,6 => CTR * .8.9...1..19.83.....21.48938...9.5..29..68.7...7.319821483257699.6847...725619348 C8: 3,9 # 14 pairs * PAIR B7: 4,6 COL B B2: 4,6,1,5,7 # reduction candidate for 4,6 B2: 4,6 # 19 pairs B4: 4,6,1,3 # reduction candidate for 4,6 B4: 4,6 # 19 pairs B6: 4,6,3,5 # reduction candidate for 4,6 B6: 4,6 # 19 pairs * PAIR E7: 2,4 BLK 8 E8: 2,4,1,7 # reduction candidate for 2,4 E8: 1,7 => CTR * .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48 E8: 2,4 # 18 pairs * PAIR D9: 6,7 BLK 8 F8: 6,7,2 # reduction candidate for 6,7 F8: 2 => CTR * .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48 F8: 6,7 # 18 pairs * PAIR D9: 6,7 ROW 9 A9: 6,7,3,5 # reduction candidate for 6,7 A9: 6,7 # 16 pairs A9: 3,5 # 15 pairs * PAIR D9: 6,7 COL D D2: 6,7,2 # reduction candidate for 6,7 D2: 2 => SOLVED * 384976215516283497972154863841792536293568174657431982168345729439827651725619348 D2: 6,7 # 15 pairs * PAIR E9: 1,7 BLK 8 E8: 1,7,2,4 # reduction candidate for 1,7 E8: 1,7 => CTR * .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48 E8: 2,4 # 18 pairs * PAIR I7: 6,9 BLK 9 H7: 6,9,2 # reduction candidate for 6,9 H7: 6,9 => CTR * 38.9...1.4.1.83.9.962174853814.9.536293568.7...7431982148325769.3.84.....2..19348 H7: 2 # 14 pairs * PAIR I7: 6,9 COL I I2: 6,9,4,5,7 # reduction candidate for 6,9 I2: 6,9 # 23 pairs I4: 6,9,1,4 # reduction candidate for 6,9 I4: 6,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0020-base-pr-000.dot * REASONING * DIS # E1: 2 => CTR => E1: 5,7 * DIS # A3: 5,7 => CTR => A3: 6,9 * DIS # H4: 6 => CTR => H4: 3,9 * DIS # G6: 4,6 => CTR => G6: 3,9 * DIS # B8: 4,6 => CTR => B8: 3,7 * DIS # C8: 4,6 => CTR => C8: 3,9 * DIS # E8: 1,7 => CTR => E8: 2,4 * DIS # F8: 2 => CTR => F8: 6,7 * PRF # D2: 2 => SOL * DIS # E8: 1,7 => CTR => E8: 2,4 * DIS # H7: 6,9 => CTR => H7: 2 * CNT 11 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,D4,D5,D6,D9,E3,E4,E6,E7,E9,F4,I5,I7) * .8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48 * PAIR E3: 5,7 BLK 2 E1: 5,7,2 # reduction candidate for 5,7 E1: 2 => CTR * .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48 * PAIR E3: 5,7 ROW 3 A3: 5,7,6,9 # reduction candidate for 5,7 A3: 5,7 => CTR * 38.9...1.47..83....621.48938...9.536293568.7.657431982148325769.3.84.....2..19348 B3: 5,7,6 # reduction candidate for 5,7 B3: 5,7 # 21 pairs * RESTART * PAIR E3: 5,7 ROW 3 B3: 5,7,6 # reduction candidate for 5,7 B3: 6 => CTR * 38495..17.71.83..4962174853816...53.293568471.574319821483257...3984.125.2..19348 * PAIR RESTART * PAIR E4: 3,9 ROW 4 H4: 3,9,6 # reduction candidate for 3,9 H4: 6 => CTR * .8.9...1....683.5.6.21.48938..2.756.29..68.7..67..19821483257.....8...35.2..19648 * PAIR RESTART * PAIR D5: 4,5 ROW 5 C5: 4,5,1,3 # reduction candidate for 4,5 C5: 4,5 => CTR * .8.9...1....683.5...21.48638..23759629..68371.37.914821.83.57.....8..135.2..19648 * PAIR RESTART * PAIR E6: 3,9 ROW 6 G6: 3,9,6 # reduction candidate for 3,9 G6: 6 => CTR * .8.9...1.....839..9.21.48638.....59.29.568374..74916821.83.57.....8......2..19.48 * PAIR RESTART * PAIR B7: 4,6 BLK 7 A8: 4,6,7,9 # reduction candidate for 4,6 A8: 4,6 => SOLVED * 384976215516283497972154863841792536293568174657431982168345729439827651725619348 * DURATION: 0:00:14.429251 START: 03:47:03.620694 END: 03:47:18.049945 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0020-base-pr-001.dot * REASONING * DIS # E1: 2 => CTR => E1: 5,7 * DIS E1: 5,7 # A3: 5,7 => CTR => A3: 6,9 * DIS E1: 5,7 + A3: 6,9 # B3: 6 => CTR => B3: 5,7 * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 6 => CTR => H4: 3,9 * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 # C5: 4,5 => CTR => C5: 1,3 * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 6 => CTR => G6: 3,9 * PRF E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 # A8: 4,6 => SOL * STA E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 + A8: 4,6 * CNT 7 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=20
Solution
position: 384976215516283497972154863841792536293568174657431982168345729439827651725619348 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 # E1: 5,7 => UNS * DIS # E1: 2 => CTR => E1: 5,7 * DIS # A3: 5,7 => CTR => A3: 6,9 * INC # A3: 6,9 => UNS * INC # B3: 5,7 => UNS * INC # D2: 2,7 => UNS * INC # D2: 6 => UNS * INC # H4: 3,9 => UNS * DIS # H4: 6 => CTR => H4: 3,9 * INC # F1: 2,7 => UNS * INC # F8: 2,7 => UNS * INC # C5: 4,5 => UNS * INC # C5: 1,3 => UNS * INC # A6: 4,5 => UNS * INC # B6: 4,5 => UNS * INC # G6: 3,9 => UNS * DIS # G6: 4,6 => CTR => G6: 3,9 * INC # I4: 1,4 => UNS * INC # G5: 1,4 => UNS * INC # C5: 1,4 => UNS * INC # C5: 3,5 => UNS * INC # A8: 4,6 => UNS * DIS # B8: 4,6 => CTR => B8: 3,7 * INC # B8: 3,7 => UNS * DIS # C8: 4,6 => CTR => C8: 3,9 * INC # C8: 3,9 => UNS * INC # B2: 4,6 => UNS * INC # B4: 4,6 => UNS * INC # B6: 4,6 => UNS * INC # E8: 2,4 => UNS * DIS # E8: 1,7 => CTR => E8: 2,4 * INC # F8: 6,7 => UNS * DIS # F8: 2 => CTR => F8: 6,7 * INC # A9: 6,7 => UNS * INC # A9: 3,5 => UNS * INC # D2: 6,7 => UNS * PRF # D2: 2 => SOL * DIS # E8: 1,7 => CTR => E8: 2,4 * INC # E8: 2,4 => UNS * DIS # H7: 6,9 => CTR => H7: 2 * INC # H7: 2 => UNS * INC # I2: 6,9 => UNS * INC # I4: 6,9 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 5,7 => UNS * DIS # E1: 2 => CTR => E1: 5,7 * DIS E1: 5,7 # A3: 5,7 => CTR => A3: 6,9 * INC E1: 5,7 + A3: 6,9 # B3: 5,7 => UNS * INC E1: 5,7 + A3: 6,9 # B3: 5,7 => UNS * DIS E1: 5,7 + A3: 6,9 # B3: 6 => CTR => B3: 5,7 * INC E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 3,9 => UNS * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 6 => CTR => H4: 3,9 * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 # C5: 4,5 => CTR => C5: 1,3 * INC E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 3,9 => UNS * DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 6 => CTR => G6: 3,9 * PRF E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 # A8: 4,6 => SOL * STA E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 + A8: 4,6 * CNT 12 HDP CHAINS / 12 HYP OPENED