Analysis of zz-www.sudokuwiki.org-0135-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=135

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=135

position: 1.5.....4.....13...8.3.4.....6....49.9..6..3.84....7.......7.6...28.....9.....1.5 initial

Autosolve

position: 135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C2: 7,9 => SOL
* DIS # H3: 7,9 => CTR => H3: 1,2,5
* DIS # C7: 1,3 => CTR => C7: 4,8
* DIS # H3: 7,9 => CTR => H3: 1,2,5
* CNT   4 HDP CHAINS /  33 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C2: 7,9 => SOL
* STA C2: 7,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

1.5.....4.....13...8.3.4.....6....49.9..6..3.84....7.......7.6...28.....9.....1.5 initial
135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5 autosolve
135789624429651378687324951256173849791468532843592716518947263362815497974236185 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
C3: 7,9
C5: 1,7
C6: 1,3
B7: 1,5
B9: 6,7
D9: 2,6
G8: 4,9
H8: 7,9
I8: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H3,I3: 1.. / H3 = 1  => 11 pairs (_) / I3 = 1  =>  0 pairs (*)
I5,H6: 1.. / I5 = 1  => 11 pairs (_) / H6 = 1  =>  0 pairs (*)
C5,I5: 1.. / C5 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
B8,E8: 1.. / B8 = 1  => 15 pairs (_) / E8 = 1  =>  9 pairs (_)
H3,H6: 1.. / H3 = 1  => 11 pairs (_) / H6 = 1  =>  0 pairs (*)
I3,I5: 1.. / I3 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
B2,B4: 2.. / B2 = 2  => 13 pairs (_) / B4 = 2  => 17 pairs (_)
A4,C6: 3.. / A4 = 3  => 15 pairs (_) / C6 = 3  =>  9 pairs (_)
I7,I8: 3.. / I7 = 3  => 15 pairs (_) / I8 = 3  =>  9 pairs (_)
A2,C2: 4.. / A2 = 4  =>  0 pairs (*) / C2 = 4  =>  0 pairs (X)
G7,G8: 4.. / G7 = 4  => 10 pairs (_) / G8 = 4  =>  8 pairs (_)
C9,E9: 4.. / C9 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
G1,G3: 6.. / G1 = 6  => 14 pairs (_) / G3 = 6  => 12 pairs (_)
A3,G3: 6.. / A3 = 6  => 14 pairs (_) / G3 = 6  => 12 pairs (_)
A5,C5: 7.. / A5 = 7  =>  0 pairs (*) / C5 = 7  =>  0 pairs (X)
D4,E4: 7.. / D4 = 7  =>  9 pairs (_) / E4 = 7  =>  9 pairs (_)
C7,C9: 8.. / C7 = 8  => 13 pairs (_) / C9 = 8  => 11 pairs (_)
C9,H9: 8.. / C9 = 8  => 11 pairs (_) / H9 = 8  => 13 pairs (_)
C2,C3: 9.. / C2 = 9  =>  0 pairs (*) / C3 = 9  =>  0 pairs (X)
* DURATION: 0:00:24.673022  START: 06:02:59.770792  END: 06:03:24.443814 2017-05-01
* CP COUNT: (19)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,C3,C5,C6,D9,G8,H8,I8)
* 135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5
* PAIR C3: 7,9 BLK 1
C2: 7,9,4                                # reduction candidate for 7,9
C2: 7,9 => SOLVED
* 135789624429651378687324951256173849791468532843592716518947263362815497974236185
C2: 4                                    #  8 pairs
* PAIR C3: 7,9 ROW 3
E3: 7,9,2,5                              # reduction candidate for 7,9
E3: 7,9                                  # 15 pairs
H3: 7,9,1,2,5                            # reduction candidate for 7,9
H3: 7,9 => CTR
* 135.8..244....135828.354671526..3849791468532843...7163....7.6...28.....9.4.3.185
H3: 1,2,5                                #  9 pairs
* PAIR C6: 1,3 ROW 6
E6: 1,3,2,5,9                            # reduction candidate for 1,3
E6: 1,3                                  # 12 pairs
E6: 2,5,9                                #  9 pairs
* PAIR C6: 1,3 COL C
C7: 1,3,4,8                              # reduction candidate for 1,3
C7: 1,3 => CTR
* 1356729846.498135..8935461.3.672..49.9746..3184...97264.3.97268..2816493968243175
C7: 4,8                                  # 13 pairs
* PAIR B7: 1,5 BLK 7
B8: 1,5,6,7                              # reduction candidate for 1,5
B8: 1,5                                  # 17 pairs
B8: 6,7                                  # 13 pairs
* PAIR B7: 1,5 ROW 7
D7: 1,5,2,9                              # reduction candidate for 1,5
D7: 1,5                                  # 14 pairs
E7: 1,5,2,3,4,9                          # reduction candidate for 1,5
E7: 1,5                                  # 13 pairs
* PAIR B7: 1,5 COL B
B4: 1,5,2                                # reduction candidate for 1,5
B4: 2                                    # 17 pairs
B4: 1,5                                  # 13 pairs
* PAIR B9: 6,7 BLK 7
A8: 6,7,3,4,5                            # reduction candidate for 6,7
A8: 6,7                                  # 18 pairs
B8: 6,7,1,5                              # reduction candidate for 6,7
B8: 6,7                                  # 13 pairs
* PAIR B9: 6,7 COL B
B2: 6,7,2                                # reduction candidate for 6,7
B2: 6,7                                  # 17 pairs
B2: 2                                    # 13 pairs
* PAIR D9: 2,6 BLK 8
F9: 2,6,3                                # reduction candidate for 2,6
F9: 2,6                                  # 16 pairs
F9: 3                                    # 10 pairs
* PAIR D9: 2,6 COL D
D1: 2,6,7,9                              # reduction candidate for 2,6
D1: 2,6                                  # 14 pairs
D2: 2,6,5,7,9                            # reduction candidate for 2,6
D2: 2,6                                  # 11 pairs
* PAIR G8: 4,9 BLK 9
G7: 4,9,2,8                              # reduction candidate for 4,9
G7: 2,8                                  # 12 pairs
G7: 4,9                                  # 10 pairs
* PAIR G8: 4,9 ROW 8
E8: 4,9,1,3,5                            # reduction candidate for 4,9
E8: 4,9                                  # 20 pairs
E8: 1,3,5                                #  9 pairs
* PAIR H8: 7,9 COL H
H1: 7,9,2,8                              # reduction candidate for 7,9
H1: 7,9                                  # 11 pairs
H2: 7,9,2,5,8                            # reduction candidate for 7,9
H2: 7,9                                  # 16 pairs
H3: 7,9,1,2,5                            # reduction candidate for 7,9
H3: 7,9 => CTR
* 135.8..244....135828.354671526..3849791468532843...7163....7.6...28.....9.4.3.185
H3: 1,2,5                                #  9 pairs
* PAIR I8: 3,7 ROW 8
A8: 3,7,4,5,6                            # reduction candidate for 3,7
A8: 3,7                                  # 16 pairs
A8: 4,5,6                                #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0135-base-pr-000.dot
* REASONING
* PRF # C2: 7,9 => SOL
* DIS # H3: 7,9 => CTR => H3: 1,2,5
* DIS # C7: 1,3 => CTR => C7: 4,8
* DIS # H3: 7,9 => CTR => H3: 1,2,5
* CNT   4 HDP CHAINS /  33 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,C3,C5,C6,D9,G8,H8,I8)
* 135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5
* PAIR C3: 7,9 BLK 1
C2: 7,9,4                                # reduction candidate for 7,9
C2: 7,9 => SOLVED
* 135789624429651378687324951256173849791468532843592716518947263362815497974236185
* DURATION: 0:00:02.592881  START: 06:03:46.510108  END: 06:03:49.102989 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0135-base-pr-001.dot
* REASONING
* PRF # C2: 7,9 => SOL
* STA C2: 7,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=135

Solution

position: 135789624429651378687324951256173849791468532843592716518947263362815497974236185 solved
Solution

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:

* PRF # C2: 7,9 => SOL
* INC # C2: 4 => UNS
* INC # E3: 7,9 => UNS
* DIS # H3: 7,9 => CTR => H3: 1,2,5
* INC # H3: 1,2,5 => UNS
* INC # E6: 1,3 => UNS
* INC # E6: 2,5,9 => UNS
* DIS # C7: 1,3 => CTR => C7: 4,8
* INC # C7: 4,8 => UNS
* INC # B8: 1,5 => UNS
* INC # B8: 6,7 => UNS
* INC # D7: 1,5 => UNS
* INC # E7: 1,5 => UNS
* INC # B4: 1,5 => UNS
* INC # B4: 2 => UNS
* INC # A8: 6,7 => UNS
* INC # B8: 6,7 => UNS
* INC # B2: 6,7 => UNS
* INC # B2: 2 => UNS
* INC # F9: 2,6 => UNS
* INC # F9: 3 => UNS
* INC # D1: 2,6 => UNS
* INC # D2: 2,6 => UNS
* INC # G7: 4,9 => UNS
* INC # G7: 2,8 => UNS
* INC # E8: 4,9 => UNS
* INC # E8: 1,3,5 => UNS
* INC # H1: 7,9 => UNS
* INC # H2: 7,9 => UNS
* DIS # H3: 7,9 => CTR => H3: 1,2,5
* INC # H3: 1,2,5 => UNS
* INC # A8: 3,7 => UNS
* INC # A8: 4,5,6 => UNS
* CNT  33 HDP CHAINS /  33 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C2: 7,9 => SOL
* STA C2: 7,9
* CNT   1 HDP CHAINS /   1 HYP OPENED