Analysis of zz-www.sudokuwiki.org-0104-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=104
level: medium
position: .6...45........3......5.81..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. initial
Autosolve
position: .6...45..5.....3......5.81..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 6 => CTR => H2: 2,7 * DIS # I2: 7,9 => CTR => I2: 4,6 * DIS # I3: 7,9 => CTR => I3: 4,6 * PRF # D1: 7,9 => SOL * CNT 4 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 6 => CTR => H2: 2,7 * DIS H2: 2,7 # B3: 3,4 => CTR => B3: 7,9 * PRF H2: 2,7 + B3: 7,9 # F3: 7,9 => SOL * STA H2: 2,7 + B3: 7,9 + F3: 7,9 * CNT 3 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6...45........3......5.81..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. | initial |
| .6...45..5.....3......5.81..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. | autosolve |
| 368714529591862374472359816926571438784936152153248697615427983249183765837695241 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) H1: 2,7 I1: 7,9 B8: 3,4 B9: 3,8 E9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D8,E9: 1.. / D8 = 1 => 9 pairs (_) / E9 = 1 => 6 pairs (_) C5,G5: 1.. / C5 = 1 => 9 pairs (_) / G5 = 1 => 10 pairs (_) A1,A6: 1.. / A1 = 1 => 8 pairs (_) / A6 = 1 => 9 pairs (_) F2,F3: 2.. / F2 = 2 => 6 pairs (_) / F3 = 2 => 9 pairs (_) H1,H2: 2.. / H1 = 2 => 5 pairs (_) / H2 = 2 => 0 pairs (X) A8,A9: 2.. / A8 = 2 => 12 pairs (_) / A9 = 2 => 7 pairs (_) G8,G9: 2.. / G8 = 2 => 7 pairs (_) / G9 = 2 => 12 pairs (_) C1,H1: 2.. / C1 = 2 => 0 pairs (X) / H1 = 2 => 5 pairs (_) C3,F3: 2.. / C3 = 2 => 6 pairs (_) / F3 = 2 => 9 pairs (_) A8,G8: 2.. / A8 = 2 => 12 pairs (_) / G8 = 2 => 7 pairs (_) A9,G9: 2.. / A9 = 2 => 7 pairs (_) / G9 = 2 => 12 pairs (_) A6,C6: 3.. / A6 = 3 => 10 pairs (_) / C6 = 3 => 6 pairs (_) I2,I3: 4.. / I2 = 4 => 5 pairs (_) / I3 = 4 => 12 pairs (_) E4,E6: 4.. / E4 = 4 => 9 pairs (_) / E6 = 4 => 5 pairs (_) D7,D8: 4.. / D7 = 4 => 5 pairs (_) / D8 = 4 => 13 pairs (_) A7,D7: 4.. / A7 = 4 => 13 pairs (_) / D7 = 4 => 5 pairs (_) I4,H5: 5.. / I4 = 5 => 7 pairs (_) / H5 = 5 => 7 pairs (_) D4,I4: 5.. / D4 = 5 => 7 pairs (_) / I4 = 5 => 7 pairs (_) F9,I9: 5.. / F9 = 5 => 6 pairs (_) / I9 = 5 => 8 pairs (_) H5,H8: 5.. / H5 = 5 => 7 pairs (_) / H8 = 5 => 7 pairs (_) A7,A8: 6.. / A7 = 6 => 7 pairs (_) / A8 = 6 => 8 pairs (_) F3,I3: 6.. / F3 = 6 => 10 pairs (_) / I3 = 6 => 8 pairs (_) B2,B3: 7.. / B2 = 7 => 6 pairs (_) / B3 = 7 => 7 pairs (_) H5,H7: 8.. / H5 = 8 => 9 pairs (_) / H7 = 8 => 6 pairs (_) A4,B5: 9.. / A4 = 9 => 10 pairs (_) / B5 = 9 => 9 pairs (_) G7,G9: 9.. / G7 = 9 => 7 pairs (_) / G9 = 9 => 7 pairs (_) * DURATION: 0:00:31.053156 START: 05:19:45.781493 END: 05:20:16.834649 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,E9,H1,I1) * .6...45..5.....3......5.81..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. * PAIR H1: 2,7 BLK 3 H2: 2,7,6 # reduction candidate for 2,7 H2: 6 => CTR * .6.37452959481236737295681492...1.3.7415396828532...9..15.2.....3918....28769.14. H2: 2,7 # 10 pairs * PAIR I1: 7,9 BLK 3 I2: 7,9,4,6 # reduction candidate for 7,9 I2: 7,9 => CTR * .6..7452959481236737295681492...1.3.74.539.82.532.879..1542.978439187256287695143 I2: 4,6 # 6 pairs I3: 7,9,4,6 # reduction candidate for 7,9 I3: 7,9 => CTR * .6...452.5....2364..2.5681..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. I3: 4,6 # 6 pairs * PAIR I1: 7,9 ROW 1 D1: 7,9,1,3,8 # reduction candidate for 7,9 D1: 7,9 => SOLVED * 368714529591862374472359816926571438784936152153248697615427983249183765837695241 D1: 1,3,8 # 5 pairs E1: 7,9,1 # reduction candidate for 7,9 E1: 7,9 # 6 pairs * PAIR B8: 3,4 BLK 7 A7: 3,4,6,8 # reduction candidate for 3,4 A7: 3,4 # 10 pairs A8: 3,4,2,6 # reduction candidate for 3,4 A8: 3,4 # 13 pairs * PAIR B8: 3,4 ROW 8 D8: 3,4,1,5,7 # reduction candidate for 3,4 D8: 3,4 # 9 pairs D8: 1,5,7 # 5 pairs * PAIR B8: 3,4 COL B B3: 3,4,7,9 # reduction candidate for 3,4 B3: 3,4 # 11 pairs B3: 7,9 # 7 pairs * PAIR B9: 3,8 BLK 7 A7: 3,8,4,6 # reduction candidate for 3,8 A7: 3,8 # 11 pairs A9: 3,8,2 # reduction candidate for 3,8 A9: 3,8 # 12 pairs * PAIR B9: 3,8 ROW 9 I9: 3,8,1,5 # reduction candidate for 3,8 I9: 3,8 # 8 pairs I9: 1,5 # 6 pairs * PAIR E9: 1,9 ROW 9 G9: 1,9,2 # reduction candidate for 1,9 G9: 2 # 12 pairs G9: 1,9 # 7 pairs * PAIR E9: 1,9 COL E E1: 1,9,7 # reduction candidate for 1,9 E1: 1,9 # 7 pairs E2: 1,9,6,7 # reduction candidate for 1,9 E2: 1,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0104-base-pr-000.dot * REASONING * DIS # H2: 6 => CTR => H2: 2,7 * DIS # I2: 7,9 => CTR => I2: 4,6 * DIS # I3: 7,9 => CTR => I3: 4,6 * PRF # D1: 7,9 => SOL * CNT 4 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,E9,H1,I1) * .6...45..5.....3......5.81..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. * PAIR H1: 2,7 BLK 3 H2: 2,7,6 # reduction candidate for 2,7 H2: 6 => CTR * .6.37452959481236737295681492...1.3.7415396828532...9..15.2.....3918....28769.14. * PAIR B8: 3,4 BLK 7 A7: 3,4,6,8 # reduction candidate for 3,4 A7: 3,4 # 15 pairs A8: 3,4,2,6 # reduction candidate for 3,4 A8: 3,4 # 18 pairs * PAIR B8: 3,4 ROW 8 D8: 3,4,1,5,7 # reduction candidate for 3,4 D8: 3,4 # 14 pairs D8: 1,5,7 # 10 pairs * PAIR B8: 3,4 COL B B3: 3,4,7,9 # reduction candidate for 3,4 B3: 3,4 => CTR * 862314579571.6932493475281642.9716357965381.21532...9..15.2......918.....8769.241 * PAIR RESTART * PAIR B8: 3,4 ROW 8 D8: 3,4,1,5,7 # reduction candidate for 3,4 D8: 1,5,7 # 15 pairs D8: 3,4 # 14 pairs * PAIR B9: 3,8 ROW 9 I9: 3,8,1,5 # reduction candidate for 3,8 I9: 3,8 # 15 pairs I9: 1,5 # 14 pairs * PAIR E9: 1,9 ROW 9 G9: 1,9,2 # reduction candidate for 1,9 G9: 2 # 18 pairs G9: 1,9 # 14 pairs * PAIR E9: 1,9 COL E E2: 1,9,6,7 # reduction candidate for 1,9 E2: 1,9 # 16 pairs E2: 6,7 # 13 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A9,B3,B8,B9,E1,E9,H1,H2,H7,H8,I2,I3) * .6...45.95.....3......5.81..2...1.3.7...3...2.5.2...9..15.2......9.8......76...4. * PAIR B3: 7,9 BLK 1 B2: 7,9,4,8 # reduction candidate for 7,9 B2: 4,8 # 20 pairs B2: 7,9 # 15 pairs * PAIR B3: 7,9 ROW 3 D3: 7,9,3 # reduction candidate for 7,9 D3: 7,9 # 16 pairs F3: 7,9,2,3,6 # reduction candidate for 7,9 F3: 7,9 => SOLVED * 368714529591862374472359816926571438784936152153248697615427983249183765837695241 * DURATION: 0:00:18.216953 START: 05:20:33.798779 END: 05:20:52.015732 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0104-base-pr-001.dot * REASONING * DIS # H2: 6 => CTR => H2: 2,7 * DIS H2: 2,7 # B3: 3,4 => CTR => B3: 7,9 * PRF H2: 2,7 + B3: 7,9 # F3: 7,9 => SOL * STA H2: 2,7 + B3: 7,9 + F3: 7,9 * CNT 3 HDP CHAINS / 19 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=104
Solution
position: 368714529591862374472359816926571438784936152153248697615427983249183765837695241 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 # H2: 2,7 => UNS * DIS # H2: 6 => CTR => H2: 2,7 * DIS # I2: 7,9 => CTR => I2: 4,6 * INC # I2: 4,6 => UNS * DIS # I3: 7,9 => CTR => I3: 4,6 * INC # I3: 4,6 => UNS * PRF # D1: 7,9 => SOL * INC # D1: 1,3,8 => UNS * INC # E1: 7,9 => UNS * INC # A7: 3,4 => UNS * INC # A8: 3,4 => UNS * INC # D8: 3,4 => UNS * INC # D8: 1,5,7 => UNS * INC # B3: 3,4 => UNS * INC # B3: 7,9 => UNS * INC # A7: 3,8 => UNS * INC # A9: 3,8 => UNS * INC # I9: 3,8 => UNS * INC # I9: 1,5 => UNS * INC # G9: 1,9 => UNS * INC # G9: 2 => UNS * INC # E1: 1,9 => UNS * INC # E2: 1,9 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 2,7 => UNS * DIS # H2: 6 => CTR => H2: 2,7 * INC H2: 2,7 # A7: 3,4 => UNS * INC H2: 2,7 # A8: 3,4 => UNS * INC H2: 2,7 # D8: 3,4 => UNS * INC H2: 2,7 # D8: 1,5,7 => UNS * DIS H2: 2,7 # B3: 3,4 => CTR => B3: 7,9 * INC H2: 2,7 + B3: 7,9 # D8: 3,4 => UNS * INC H2: 2,7 + B3: 7,9 # D8: 1,5,7 => UNS * INC H2: 2,7 + B3: 7,9 # I9: 3,8 => UNS * INC H2: 2,7 + B3: 7,9 # I9: 1,5 => UNS * INC H2: 2,7 + B3: 7,9 # G9: 1,9 => UNS * INC H2: 2,7 + B3: 7,9 # G9: 2 => UNS * INC H2: 2,7 + B3: 7,9 # E2: 1,9 => UNS * INC H2: 2,7 + B3: 7,9 # E2: 6,7 => UNS * INC H2: 2,7 + B3: 7,9 # B2: 7,9 => UNS * INC H2: 2,7 + B3: 7,9 # B2: 4,8 => UNS * INC H2: 2,7 + B3: 7,9 # D3: 7,9 => UNS * PRF H2: 2,7 + B3: 7,9 # F3: 7,9 => SOL * STA H2: 2,7 + B3: 7,9 + F3: 7,9 * CNT 19 HDP CHAINS / 19 HYP OPENED