Analysis of zz-www.sudokuwiki.org-0014-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=14
level: medium
position: .........6..9...2..28..53....5.248..9.2.5.1.4..487.5....34..95..5...8..1......... initial
Autosolve
position: 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 3 => CTR => F2: 1,7 * DIS # D1: 6,7 => CTR => D1: 2,3 * DIS # D1: 3,6 => CTR => D1: 2,7 * DIS # A7: 1,7 => CTR => A7: 2,8 * DIS # F7: 1,7 => CTR => F7: 2,6 * DIS # B1: 3 => CTR => B1: 4,9 * DIS # F7: 1,6 => CTR => F7: 2,7 * DIS # E1: 1,6 => CTR => E1: 3,4 * CNT 8 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 # F2: 3 => CTR => F2: 1,7 * DIS F2: 1,7 # D1: 6,7 => CTR => D1: 2,3 * DIS F2: 1,7 + D1: 2,3 # F1: 6,7 => CTR => F1: 1,2,3 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 # I3: 6,7 => CTR => I3: 9 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 2,3 => CTR => D8: 6,7 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 # H8: 3,6 => CTR => H8: 4 * PRF F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 => SOL * STA F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 * CNT 7 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .........6..9...2..28..53....5.248..9.2.5.1.4..487.5....34..95..5...8..1......... | initial |
| 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5..... | autosolve |
| 591243687637981425428765319765124893982356174314879562873412956259638741146597238 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B2: 3,4 C2: 1,7 D3: 6,7 G2: 4,7 A4: 3,7 B4: 6,7 A6: 1,3 B6: 1,6 D5: 3,6 F5: 3,6 H6: 3,6 B7: 1,7 B9: 4,9 E7: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 16 pairs (_) / H3 = 1 => 17 pairs (_) A6,B6: 1.. / A6 = 1 => 16 pairs (_) / B6 = 1 => 15 pairs (_) C2,F2: 1.. / C2 = 1 => 16 pairs (_) / F2 = 1 => 17 pairs (_) B6,B7: 1.. / B6 = 1 => 15 pairs (_) / B7 = 1 => 16 pairs (_) D1,F1: 2.. / D1 = 2 => 14 pairs (_) / F1 = 2 => 0 pairs (X) G8,G9: 2.. / G8 = 2 => 17 pairs (_) / G9 = 2 => 14 pairs (_) A7,F7: 2.. / A7 = 2 => 0 pairs (X) / F7 = 2 => 14 pairs (_) D1,D8: 2.. / D1 = 2 => 14 pairs (_) / D8 = 2 => 0 pairs (X) B1,B2: 3.. / B1 = 3 => 0 pairs (X) / B2 = 3 => 15 pairs (_) A4,A6: 3.. / A4 = 3 => 16 pairs (_) / A6 = 3 => 15 pairs (_) D5,F5: 3.. / D5 = 3 => 12 pairs (_) / F5 = 3 => 18 pairs (_) B2,F2: 3.. / B2 = 3 => 15 pairs (_) / F2 = 3 => 0 pairs (X) A6,H6: 3.. / A6 = 3 => 15 pairs (_) / H6 = 3 => 16 pairs (_) I4,I9: 3.. / I4 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) E1,E3: 4.. / E1 = 4 => 19 pairs (_) / E3 = 4 => 18 pairs (_) B2,G2: 4.. / B2 = 4 => 0 pairs (X) / G2 = 4 => 15 pairs (_) B4,B6: 6.. / B4 = 6 => 15 pairs (_) / B6 = 6 => 16 pairs (_) D5,F5: 6.. / D5 = 6 => 18 pairs (_) / F5 = 6 => 12 pairs (_) C8,C9: 6.. / C8 = 6 => 15 pairs (_) / C9 = 6 => 16 pairs (_) B6,H6: 6.. / B6 = 6 => 16 pairs (_) / H6 = 6 => 15 pairs (_) A4,B4: 7.. / A4 = 7 => 15 pairs (_) / B4 = 7 => 16 pairs (_) B4,B7: 7.. / B4 = 7 => 16 pairs (_) / B7 = 7 => 15 pairs (_) H1,I1: 8.. / H1 = 8 => 18 pairs (_) / I1 = 8 => 15 pairs (_) A7,A9: 8.. / A7 = 8 => 15 pairs (_) / A9 = 8 => 0 pairs (X) A7,I7: 8.. / A7 = 8 => 15 pairs (_) / I7 = 8 => 0 pairs (X) H1,H9: 8.. / H1 = 8 => 18 pairs (_) / H9 = 8 => 15 pairs (_) B1,C1: 9.. / B1 = 9 => 22 pairs (_) / C1 = 9 => 18 pairs (_) H3,I3: 9.. / H3 = 9 => 22 pairs (_) / I3 = 9 => 15 pairs (_) H4,I4: 9.. / H4 = 9 => 15 pairs (_) / I4 = 9 => 22 pairs (_) E8,E9: 9.. / E8 = 9 => 15 pairs (_) / E9 = 9 => 22 pairs (_) C8,E8: 9.. / C8 = 9 => 22 pairs (_) / E8 = 9 => 15 pairs (_) B1,B9: 9.. / B1 = 9 => 22 pairs (_) / B9 = 9 => 18 pairs (_) H3,H4: 9.. / H3 = 9 => 22 pairs (_) / H4 = 9 => 15 pairs (_) I3,I4: 9.. / I3 = 9 => 15 pairs (_) / I4 = 9 => 22 pairs (_) * DURATION: 0:00:53.010560 START: 03:38:23.136989 END: 03:39:16.147549 2017-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B2,B4,B6,B7,B9,C2,D3,D5,E7,F5,G2,H6) * 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5..... * PAIR B2: 3,4 BLK 1 B1: 3,4,9 # reduction candidate for 3,4 B1: 9 # 22 pairs B1: 3,4 # 18 pairs * PAIR C2: 1,7 BLK 1 C1: 1,7,9 # reduction candidate for 1,7 C1: 1,7 # 22 pairs A3: 1,7,4 # reduction candidate for 1,7 A3: 1,7 # 18 pairs * PAIR C2: 1,7 ROW 2 F2: 1,7,3 # reduction candidate for 1,7 F2: 3 => CTR * 539......6419837257286.53.9375124896982356174164879532.1346.95..5...8..1...5..... F2: 1,7 # 15 pairs * PAIR C2: 1,7 COL C C9: 1,7,6,9 # reduction candidate for 1,7 C9: 1,7 # 19 pairs C9: 6,9 # 16 pairs * PAIR D3: 6,7 BLK 2 D1: 6,7,2,3 # reduction candidate for 6,7 D1: 6,7 => CTR * 5....2.8.6..98..25.28..5319..512489.982356174164879532213467958.5.238..18..5912.3 D1: 2,3 # 15 pairs F1: 6,7,1,2,3 # reduction candidate for 6,7 F1: 6,7 # 18 pairs * PAIR D3: 6,7 ROW 3 I3: 6,7,9 # reduction candidate for 6,7 I3: 6,7 # 22 pairs I3: 9 # 15 pairs * PAIR D3: 6,7 COL D D8: 6,7,2,3 # reduction candidate for 6,7 D8: 2,3 # 16 pairs D8: 6,7 # 13 pairs * PAIR G2: 4,7 BLK 3 G1: 4,7,6 # reduction candidate for 4,7 G1: 4,7 # 22 pairs G1: 6 # 16 pairs * PAIR G2: 4,7 COL G G8: 4,7,2,6 # reduction candidate for 4,7 G8: 4,7 # 17 pairs G9: 4,7,2,6 # reduction candidate for 4,7 G9: 4,7 # 20 pairs * PAIR D5: 3,6 COL D D1: 3,6,2,7 # reduction candidate for 3,6 D1: 3,6 => CTR * 5....2.8.6..98..25.287.5319..512489.982.5.174164879532213467958.5.238..18..5912.3 D1: 2,7 # 15 pairs D8: 3,6,2,7 # reduction candidate for 3,6 D8: 3,6 # 23 pairs * PAIR F5: 3,6 COL F F1: 3,6,1,2,7 # reduction candidate for 3,6 F1: 3,6 # 16 pairs F9: 3,6,1,2,7 # reduction candidate for 3,6 F9: 3,6 # 19 pairs * PAIR H6: 3,6 BLK 6 H4: 3,6,9 # reduction candidate for 3,6 H4: 3,6 # 22 pairs I4: 3,6,9 # reduction candidate for 3,6 I4: 3,6 # 15 pairs * PAIR H6: 3,6 COL H H8: 3,6,4 # reduction candidate for 3,6 H8: 3,6 # 18 pairs H9: 3,6,4,8 # reduction candidate for 3,6 H9: 3,6 # 20 pairs * PAIR B7: 1,7 BLK 7 A7: 1,7,2,8 # reduction candidate for 1,7 A7: 1,7 => CTR * 59.2...8.63.98.425428..5319..512489.982.5.174..48795.2..346295825...8..184.5..2.. A7: 2,8 # 15 pairs A9: 1,7,2,4,8 # reduction candidate for 1,7 A9: 1,7 # 22 pairs C9: 1,7,6,9 # reduction candidate for 1,7 C9: 1,7 # 19 pairs * PAIR B7: 1,7 ROW 7 F7: 1,7,2,6 # reduction candidate for 1,7 F7: 1,7 => CTR * 5......876.7981.25.28..5319..512489.982.5.174164879532213467958.5...8..18..5....3 F7: 2,6 # 15 pairs * PAIR B9: 4,9 COL B B1: 4,9,3 # reduction candidate for 4,9 B1: 3 => CTR * 539......64.9837257286.53.9375124896982356174164879532.1346.95..5...8..1...5..... B1: 4,9 # 15 pairs * PAIR E7: 1,6 BLK 8 F7: 1,6,2,7 # reduction candidate for 1,6 F7: 1,6 => CTR * 5......8.6..98..25.28..5319..512489.982.5.1741648795.22.34..958.5...8..18..5..... F7: 2,7 # 15 pairs E9: 1,6,3,9 # reduction candidate for 1,6 E9: 1,6 # 19 pairs F9: 1,6,2,3,7 # reduction candidate for 1,6 F9: 1,6 # 19 pairs * PAIR E7: 1,6 COL E E1: 1,6,3,4 # reduction candidate for 1,6 E1: 1,6 => CTR * 5.9......6.7981425128.4539...51248.3982.5.174314879562.734..95..56.98.31.9153.... E1: 3,4 # 15 pairs E3: 1,6,4 # reduction candidate for 1,6 E3: 1,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0014-base-pr-000.dot * REASONING * DIS # F2: 3 => CTR => F2: 1,7 * DIS # D1: 6,7 => CTR => D1: 2,3 * DIS # D1: 3,6 => CTR => D1: 2,7 * DIS # A7: 1,7 => CTR => A7: 2,8 * DIS # F7: 1,7 => CTR => F7: 2,6 * DIS # B1: 3 => CTR => B1: 4,9 * DIS # F7: 1,6 => CTR => F7: 2,7 * DIS # E1: 1,6 => CTR => E1: 3,4 * CNT 8 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B2,B4,B6,B7,B9,C2,D3,D5,E7,F5,G2,H6) * 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5..... * PAIR B2: 3,4 BLK 1 B1: 3,4,9 # reduction candidate for 3,4 B1: 9 # 22 pairs B1: 3,4 # 18 pairs * PAIR C2: 1,7 BLK 1 C1: 1,7,9 # reduction candidate for 1,7 C1: 1,7 # 22 pairs A3: 1,7,4 # reduction candidate for 1,7 A3: 1,7 # 18 pairs * PAIR C2: 1,7 ROW 2 F2: 1,7,3 # reduction candidate for 1,7 F2: 3 => CTR * 539......6419837257286.53.9375124896982356174164879532.1346.95..5...8..1...5..... * PAIR C2: 1,7 COL C C9: 1,7,6,9 # reduction candidate for 1,7 C9: 1,7 # 19 pairs C9: 6,9 # 17 pairs * PAIR RESTART * PAIR C2: 1,7 BLK 1 C1: 1,7,9 # reduction candidate for 1,7 C1: 1,7 # 22 pairs A3: 1,7,4 # reduction candidate for 1,7 A3: 1,7 # 17 pairs * PAIR C2: 1,7 COL C C9: 1,7,6,9 # reduction candidate for 1,7 C9: 1,7 # 19 pairs C9: 6,9 # 17 pairs * PAIR D3: 6,7 BLK 2 D1: 6,7,2,3 # reduction candidate for 6,7 D1: 6,7 => CTR * 5...32.8.63.98.425.28.45319..512489.98235617416487953221346795845.298.618965..2.. F1: 6,7,1,2,3 # reduction candidate for 6,7 F1: 6,7 => CTR * 54923.61863798142512864539776512483998235.174314879562873412956.56.98..1.9156..8. * RESTART * PAIR D3: 6,7 ROW 3 I3: 6,7,9 # reduction candidate for 6,7 I3: 6,7 => CTR * 597243618631987425428615397..51248.9982356174..48795.28.34.295..5..38.41...59..83 * PAIR D3: 6,7 COL D D8: 6,7,2,3 # reduction candidate for 6,7 D8: 2,3 => CTR * 5..3.2.8.637981425.287.5319..512489.982653174164879532213467958.5.2.8..18..5..2.. * PAIR RESTART * PAIR H6: 3,6 COL H H8: 3,6,4 # reduction candidate for 3,6 H8: 3,6 => CTR * 5492...8.631987425728645319375124896982356174..48795.2..34..95.45..98231.9.5...4. H8: 4 => SOLVED * 591243687637981425428765319765124893982356174314879562873412956259638741146597238 * DURATION: 0:00:19.456567 START: 03:39:52.467987 END: 03:40:11.924554 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0014-base-pr-001.dot * REASONING * DIS # F2: 3 => CTR => F2: 1,7 * DIS F2: 1,7 # D1: 6,7 => CTR => D1: 2,3 * DIS F2: 1,7 + D1: 2,3 # F1: 6,7 => CTR => F1: 1,2,3 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 # I3: 6,7 => CTR => I3: 9 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 2,3 => CTR => D8: 6,7 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 # H8: 3,6 => CTR => H8: 4 * PRF F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 => SOL * STA F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 * CNT 7 HDP CHAINS / 18 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=14
Solution
position: 591243687637981425428765319765124893982356174314879562873412956259638741146597238 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 # B1: 3,4 => UNS * INC # B1: 9 => UNS * INC # C1: 1,7 => UNS * INC # A3: 1,7 => UNS * INC # F2: 1,7 => UNS * DIS # F2: 3 => CTR => F2: 1,7 * INC # C9: 1,7 => UNS * INC # C9: 6,9 => UNS * DIS # D1: 6,7 => CTR => D1: 2,3 * INC # D1: 2,3 => UNS * INC # F1: 6,7 => UNS * INC # I3: 6,7 => UNS * INC # I3: 9 => UNS * INC # D8: 6,7 => UNS * INC # D8: 2,3 => UNS * INC # G1: 4,7 => UNS * INC # G1: 6 => UNS * INC # G8: 4,7 => UNS * INC # G9: 4,7 => UNS * DIS # D1: 3,6 => CTR => D1: 2,7 * INC # D1: 2,7 => UNS * INC # D8: 3,6 => UNS * INC # F1: 3,6 => UNS * INC # F9: 3,6 => UNS * INC # H4: 3,6 => UNS * INC # I4: 3,6 => UNS * INC # H8: 3,6 => UNS * INC # H9: 3,6 => UNS * DIS # A7: 1,7 => CTR => A7: 2,8 * INC # A7: 2,8 => UNS * INC # A9: 1,7 => UNS * INC # C9: 1,7 => UNS * DIS # F7: 1,7 => CTR => F7: 2,6 * INC # F7: 2,6 => UNS * INC # B1: 4,9 => UNS * DIS # B1: 3 => CTR => B1: 4,9 * DIS # F7: 1,6 => CTR => F7: 2,7 * INC # F7: 2,7 => UNS * INC # E9: 1,6 => UNS * INC # F9: 1,6 => UNS * DIS # E1: 1,6 => CTR => E1: 3,4 * INC # E1: 3,4 => UNS * INC # E3: 1,6 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,4 => UNS * INC # B1: 9 => UNS * INC # C1: 1,7 => UNS * INC # A3: 1,7 => UNS * INC # F2: 1,7 => UNS * DIS # F2: 3 => CTR => F2: 1,7 * INC F2: 1,7 # C9: 1,7 => UNS * INC F2: 1,7 # C9: 6,9 => UNS * INC F2: 1,7 # C1: 1,7 => UNS * INC F2: 1,7 # A3: 1,7 => UNS * INC F2: 1,7 # C9: 1,7 => UNS * INC F2: 1,7 # C9: 6,9 => UNS * DIS F2: 1,7 # D1: 6,7 => CTR => D1: 2,3 * DIS F2: 1,7 + D1: 2,3 # F1: 6,7 => CTR => F1: 1,2,3 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 # I3: 6,7 => CTR => I3: 9 * INC F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 6,7 => UNS * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 2,3 => CTR => D8: 6,7 * DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 # H8: 3,6 => CTR => H8: 4 * PRF F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 => SOL * STA F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 * CNT 19 HDP CHAINS / 18 HYP OPENED