Analysis of zz-www.sudokuwiki.org-0342-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=342

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=342

position: .6.7.........8......5..9.1.8...6......9.25.3..7......4.....35.1....9..2...2...3.. initial

Autosolve

position: .6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 3,4 => CTR => E1: 1,5
* DIS # A5: 1,4 => CTR => A5: 6
* DIS # D5: 8 => CTR => D5: 1,4
* DIS # C6: 6 => CTR => C6: 1,3
* CNT   4 HDP CHAINS /  32 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # E1: 3,4 => CTR => E1: 1,5
* DIS E1: 1,5 # A5: 1,4 => CTR => A5: 6
* DIS E1: 1,5 + A5: 6 # C7: 4,7 => CTR => C7: 6,8
* PRF E1: 1,5 + A5: 6 + C7: 6,8 # C8: 6,8 => SOL
* STA E1: 1,5 + A5: 6 + C7: 6,8 + C8: 6,8
* CNT   4 HDP CHAINS /  51 HYP OPENED

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

Details

Positions

.6.7.........8......5..9.1.8...6......9.25.3..7......4.....35.1....9..2...2...3.. initial
.6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3.. autosolve
361752948297184653485639712824367195619425837573918264946273581738591426152846379 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
D3: 3,6
E3: 3,4
B4: 2,5
C4: 3,4
B5: 1,4
A6: 2,5
D4: 3,4
E6: 1,3
F6: 1,8
H4: 5,9
E7: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F2: 2.. / F1 = 2  => 11 pairs (_) / F2 = 2  => 12 pairs (_)
B4,A6: 2.. / B4 = 2  => 11 pairs (_) / A6 = 2  => 10 pairs (_)
I4,G6: 2.. / I4 = 2  => 10 pairs (_) / G6 = 2  => 11 pairs (_)
B4,I4: 2.. / B4 = 2  => 11 pairs (_) / I4 = 2  => 10 pairs (_)
A6,G6: 2.. / A6 = 2  => 10 pairs (_) / G6 = 2  => 11 pairs (_)
C4,C6: 3.. / C4 = 3  => 11 pairs (_) / C6 = 3  => 12 pairs (_)
D4,E6: 3.. / D4 = 3  => 12 pairs (_) / E6 = 3  => 11 pairs (_)
A8,B8: 3.. / A8 = 3  => 11 pairs (_) / B8 = 3  => 11 pairs (_)
C4,D4: 3.. / C4 = 3  => 11 pairs (_) / D4 = 3  => 12 pairs (_)
C6,E6: 3.. / C6 = 3  => 12 pairs (_) / E6 = 3  => 11 pairs (_)
D4,D5: 4.. / D4 = 4  => 11 pairs (_) / D5 = 4  => 12 pairs (_)
C4,D4: 4.. / C4 = 4  => 12 pairs (_) / D4 = 4  => 11 pairs (_)
E1,D2: 5.. / E1 = 5  => 12 pairs (_) / D2 = 5  => 13 pairs (_)
B4,A6: 5.. / B4 = 5  => 10 pairs (_) / A6 = 5  => 11 pairs (_)
A6,H6: 5.. / A6 = 5  => 11 pairs (_) / H6 = 5  => 10 pairs (_)
E1,E9: 5.. / E1 = 5  => 12 pairs (_) / E9 = 5  => 13 pairs (_)
A5,C6: 6.. / A5 = 6  => 16 pairs (_) / C6 = 6  =>  0 pairs (X)
G5,I5: 7.. / G5 = 7  => 12 pairs (_) / I5 = 7  => 13 pairs (_)
E7,E9: 7.. / E7 = 7  => 10 pairs (_) / E9 = 7  =>  0 pairs (X)
C1,B3: 8.. / C1 = 8  => 12 pairs (_) / B3 = 8  => 13 pairs (_)
D5,F6: 8.. / D5 = 8  =>  0 pairs (X) / F6 = 8  => 16 pairs (_)
G1,G2: 9.. / G1 = 9  => 11 pairs (_) / G2 = 9  => 11 pairs (_)
H4,I4: 9.. / H4 = 9  => 11 pairs (_) / I4 = 9  => 11 pairs (_)
A1,G1: 9.. / A1 = 9  => 11 pairs (_) / G1 = 9  => 11 pairs (_)
I4,I9: 9.. / I4 = 9  => 11 pairs (_) / I9 = 9  => 11 pairs (_)
* DURATION: 0:00:23.619740  START: 19:03:30.702514  END: 19:03:54.322254 2019-04-28
* CP COUNT: (25)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B4,B5,C4,D3,D4,E3,E6,E7,F6,H4)
* .6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3..
* PAIR D3: 3,6 BLK 2
D2: 3,6,1,5                              # reduction candidate for 3,6
D2: 3,6                                  # 23 pairs
D2: 1,5                                  # 12 pairs
* PAIR D3: 3,6 ROW 3
I3: 3,6,2,7,8                            # reduction candidate for 3,6
I3: 3,6                                  # 14 pairs
I3: 2,7,8                                # 11 pairs
* PAIR E3: 3,4 BLK 2
E1: 3,4,1,5                              # reduction candidate for 3,4
E1: 3,4 => CTR
* .687.......758......56.9.1.8.43671..619425.3..73918..4..62735.1..189..2.7.215.3..
E1: 1,5                                  # 12 pairs
* PAIR E3: 3,4 ROW 3
A3: 3,4,2,7                              # reduction candidate for 3,4
A3: 3,4                                  # 13 pairs
B3: 3,4,2,8                              # reduction candidate for 3,4
B3: 3,4                                  # 13 pairs
* PAIR B4: 2,5 ROW 4
I4: 2,5,9                                # reduction candidate for 2,5
I4: 9                                    # 11 pairs
I4: 2,5                                  # 11 pairs
* PAIR B5: 1,4 BLK 4
A5: 1,4,6                                # reduction candidate for 1,4
A5: 1,4 => CTR
* .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3..
A5: 6                                    # 16 pairs
* PAIR B5: 1,4 ROW 5
D5: 1,4,8                                # reduction candidate for 1,4
D5: 8 => CTR
* .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3..
D5: 1,4                                  # 16 pairs
* PAIR B5: 1,4 COL B
B2: 1,4,2,3,9                            # reduction candidate for 1,4
B2: 1,4                                  # 13 pairs
B8: 1,4,3,5,8                            # reduction candidate for 1,4
B8: 1,4                                  # 14 pairs
B9: 1,4,5,8,9                            # reduction candidate for 1,4
B9: 1,4                                  # 13 pairs
* PAIR E6: 1,3 ROW 6
C6: 1,3,6                                # reduction candidate for 1,3
C6: 6 => CTR
* .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3..
C6: 1,3                                  # 16 pairs
* PAIR E6: 1,3 COL E
E1: 1,3,4,5                              # reduction candidate for 1,3
E1: 1,3                                  # 13 pairs
E1: 4,5                                  # 12 pairs
* PAIR F6: 1,8 BLK 5
D5: 1,8,4                                # reduction candidate for 1,8
D5: 4                                    # 12 pairs
D5: 1,8                                  # 11 pairs
* PAIR F6: 1,8 COL F
F8: 1,8,4,6                              # reduction candidate for 1,8
F8: 1,8                                  # 16 pairs
F9: 1,8,4,6                              # reduction candidate for 1,8
F9: 1,8                                  # 16 pairs
* PAIR H4: 5,9 BLK 6
I4: 5,9,2                                # reduction candidate for 5,9
I4: 5,9                                  # 11 pairs
I4: 2                                    # 10 pairs
* PAIR E7: 4,7 BLK 8
E9: 4,7,1,5                              # reduction candidate for 4,7
E9: 4,7                                  # 21 pairs
E9: 1,5                                  # 12 pairs
* PAIR E7: 4,7 ROW 7
A7: 4,7,6,9                              # reduction candidate for 4,7
A7: 4,7                                  # 14 pairs
C7: 4,7,6,8                              # reduction candidate for 4,7
C7: 4,7                                  # 14 pairs
H7: 4,7,6,8,9                            # reduction candidate for 4,7
H7: 4,7                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0342-base-pr-000.dot
* REASONING
* DIS # E1: 3,4 => CTR => E1: 1,5
* DIS # A5: 1,4 => CTR => A5: 6
* DIS # D5: 8 => CTR => D5: 1,4
* DIS # C6: 6 => CTR => C6: 1,3
* CNT   4 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B4,B5,C4,D3,D4,E3,E6,E7,F6,H4)
* .6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3..
* PAIR D3: 3,6 BLK 2
D2: 3,6,1,5                              # reduction candidate for 3,6
D2: 3,6                                  # 23 pairs
D2: 1,5                                  # 12 pairs
* PAIR D3: 3,6 ROW 3
I3: 3,6,2,7,8                            # reduction candidate for 3,6
I3: 3,6                                  # 14 pairs
I3: 2,7,8                                # 11 pairs
* PAIR E3: 3,4 BLK 2
E1: 3,4,1,5                              # reduction candidate for 3,4
E1: 3,4 => CTR
* .687.......758......56.9.1.8.43671..619425.3..73918..4..62735.1..189..2.7.215.3..
* PAIR E3: 3,4 ROW 3
A3: 3,4,2,7                              # reduction candidate for 3,4
A3: 3,4                                  # 14 pairs
B3: 3,4,2,8                              # reduction candidate for 3,4
B3: 3,4                                  # 14 pairs
* PAIR B4: 2,5 ROW 4
I4: 2,5,9                                # reduction candidate for 2,5
I4: 9                                    # 12 pairs
I4: 2,5                                  # 12 pairs
* PAIR B5: 1,4 BLK 4
A5: 1,4,6                                # reduction candidate for 1,4
A5: 1,4 => CTR
* .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3..
* PAIR B5: 1,4 COL B
B2: 1,4,2,3,9                            # reduction candidate for 1,4
B2: 1,4                                  # 21 pairs
B8: 1,4,3,5,8                            # reduction candidate for 1,4
B8: 1,4                                  # 20 pairs
B9: 1,4,5,8,9                            # reduction candidate for 1,4
B9: 1,4                                  # 19 pairs
* PAIR H4: 5,9 BLK 6
I4: 5,9,2                                # reduction candidate for 5,9
I4: 5,9                                  # 14 pairs
I4: 2                                    # 13 pairs
* PAIR E7: 4,7 BLK 8
E9: 4,7,1,5                              # reduction candidate for 4,7
E9: 4,7                                  # 21 pairs
E9: 1,5                                  # 15 pairs
* PAIR E7: 4,7 ROW 7
A7: 4,7,9                                # reduction candidate for 4,7
A7: 4,7                                  # 20 pairs
C7: 4,7,6,8                              # reduction candidate for 4,7
C7: 4,7 => CTR
* .687...4..9..8..7.7.5..9.1.85..671926.9.25.3.27.9.8654987243561..6891427..2.76389
H7: 4,7,6,8,9                            # reduction candidate for 4,7
H7: 4,7                                  # 25 pairs
* PAIR RESTART
* PAIR E7: 4,7 BLK 8
E9: 4,7,1,5                              # reduction candidate for 4,7
E9: 4,7                                  # 21 pairs
E9: 1,5                                  # 16 pairs
* PAIR E7: 4,7 ROW 7
A7: 4,7,9                                # reduction candidate for 4,7
A7: 4,7                                  # 20 pairs
H7: 4,7,6,8,9                            # reduction candidate for 4,7
H7: 4,7                                  # 25 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,B4,B5,C4,C6,C7,D3,D4,D5,E1,E3,E6,E7,G5,G6,H4,H6,I5)
* .6.7.........8......5..9.1.8...671..6.9.25.3..7.9.8..4...2.35.1....9..2...2...3..
* PAIR E1: 1,5 BLK 2
D2: 1,5,3,6                              # reduction candidate for 1,5
D2: 3,6                                  # 24 pairs
D2: 1,5                                  # 20 pairs
* PAIR E1: 1,5 COL E
E9: 1,5,4,7                              # reduction candidate for 1,5
E9: 4,7                                  # 21 pairs
E9: 1,5                                  # 16 pairs
* PAIR D3: 3,6 BLK 2
D2: 3,6,1,5                              # reduction candidate for 3,6
D2: 3,6                                  # 24 pairs
D2: 1,5                                  # 20 pairs
* PAIR D3: 3,6 ROW 3
I3: 3,6,2,7,8                            # reduction candidate for 3,6
I3: 3,6                                  # 21 pairs
I3: 2,7,8                                # 18 pairs
* PAIR E3: 3,4 ROW 3
A3: 3,4,2,7                              # reduction candidate for 3,4
A3: 3,4                                  # 21 pairs
B3: 3,4,2,8                              # reduction candidate for 3,4
B3: 3,4                                  # 22 pairs
* PAIR B4: 2,5 ROW 4
I4: 2,5,9                                # reduction candidate for 2,5
I4: 2,5                                  # 18 pairs
I4: 9                                    # 15 pairs
* PAIR B5: 1,4 COL B
B2: 1,4,2,3,9                            # reduction candidate for 1,4
B2: 1,4                                  # 21 pairs
B8: 1,4,3,5,8                            # reduction candidate for 1,4
B8: 1,4                                  # 21 pairs
B9: 1,4,5,8,9                            # reduction candidate for 1,4
B9: 1,4                                  # 20 pairs
* PAIR H4: 5,9 BLK 6
I4: 5,9,2                                # reduction candidate for 5,9
I4: 5,9                                  # 14 pairs
I4: 2                                    # 14 pairs
* PAIR G5: 7,8 COL G
G3: 7,8,2,4,6                            # reduction candidate for 7,8
G3: 7,8                                  # 20 pairs
G8: 7,8,4,6                              # reduction candidate for 7,8
G8: 7,8                                  # 20 pairs
* PAIR I5: 7,8 COL I
I3: 7,8,2,3,6                            # reduction candidate for 7,8
I3: 7,8                                  # 19 pairs
I8: 7,8,6                                # reduction candidate for 7,8
I8: 7,8                                  # 20 pairs
I9: 7,8,6,9                              # reduction candidate for 7,8
I9: 7,8                                  # 17 pairs
* PAIR G6: 2,6 COL G
G2: 2,6,4,7,9                            # reduction candidate for 2,6
G2: 2,6                                  # 19 pairs
G3: 2,6,4,7,8                            # reduction candidate for 2,6
G3: 2,6                                  # 19 pairs
* PAIR H6: 5,6 COL H
H2: 5,6,4,7                              # reduction candidate for 5,6
H2: 5,6                                  # 22 pairs
H2: 4,7                                  # 19 pairs
* PAIR C7: 6,8 BLK 7
C8: 6,8,1,4,7                            # reduction candidate for 6,8
C8: 6,8 => SOLVED
* 361752948297184653485639712824367195619425837573918264946273581738591426152846379
* DURATION: 0:00:33.651285  START: 19:04:11.953653  END: 19:04:45.604938 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0342-base-pr-001.dot
* REASONING
* DIS # E1: 3,4 => CTR => E1: 1,5
* DIS E1: 1,5 # A5: 1,4 => CTR => A5: 6
* DIS E1: 1,5 + A5: 6 # C7: 4,7 => CTR => C7: 6,8
* PRF E1: 1,5 + A5: 6 + C7: 6,8 # C8: 6,8 => SOL
* STA E1: 1,5 + A5: 6 + C7: 6,8 + C8: 6,8
* CNT   4 HDP CHAINS /  51 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=342

Solution

position: 361752948297184653485639712824367195619425837573918264946273581738591426152846379 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:

* INC # D2: 3,6 => UNS
* INC # D2: 1,5 => UNS
* INC # I3: 3,6 => UNS
* INC # I3: 2,7,8 => UNS
* DIS # E1: 3,4 => CTR => E1: 1,5
* INC # E1: 1,5 => UNS
* INC # A3: 3,4 => UNS
* INC # B3: 3,4 => UNS
* INC # I4: 2,5 => UNS
* INC # I4: 9 => UNS
* DIS # A5: 1,4 => CTR => A5: 6
* INC # A5: 6 => UNS
* INC # D5: 1,4 => UNS
* DIS # D5: 8 => CTR => D5: 1,4
* INC # B2: 1,4 => UNS
* INC # B8: 1,4 => UNS
* INC # B9: 1,4 => UNS
* INC # C6: 1,3 => UNS
* DIS # C6: 6 => CTR => C6: 1,3
* INC # E1: 1,3 => UNS
* INC # E1: 4,5 => UNS
* INC # D5: 1,8 => UNS
* INC # D5: 4 => UNS
* INC # F8: 1,8 => UNS
* INC # F9: 1,8 => UNS
* INC # I4: 5,9 => UNS
* INC # I4: 2 => UNS
* INC # E9: 4,7 => UNS
* INC # E9: 1,5 => UNS
* INC # A7: 4,7 => UNS
* INC # C7: 4,7 => UNS
* INC # H7: 4,7 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D2: 3,6 => UNS
* INC # D2: 1,5 => UNS
* INC # I3: 3,6 => UNS
* INC # I3: 2,7,8 => UNS
* DIS # E1: 3,4 => CTR => E1: 1,5
* INC E1: 1,5 # A3: 3,4 => UNS
* INC E1: 1,5 # B3: 3,4 => UNS
* INC E1: 1,5 # I4: 2,5 => UNS
* INC E1: 1,5 # I4: 9 => UNS
* DIS E1: 1,5 # A5: 1,4 => CTR => A5: 6
* INC E1: 1,5 + A5: 6 # B2: 1,4 => UNS
* INC E1: 1,5 + A5: 6 # B8: 1,4 => UNS
* INC E1: 1,5 + A5: 6 # B9: 1,4 => UNS
* INC E1: 1,5 + A5: 6 # I4: 5,9 => UNS
* INC E1: 1,5 + A5: 6 # I4: 2 => UNS
* INC E1: 1,5 + A5: 6 # E9: 4,7 => UNS
* INC E1: 1,5 + A5: 6 # E9: 1,5 => UNS
* INC E1: 1,5 + A5: 6 # A7: 4,7 => UNS
* DIS E1: 1,5 + A5: 6 # C7: 4,7 => CTR => C7: 6,8
* INC E1: 1,5 + A5: 6 + C7: 6,8 # H7: 4,7 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 4,7 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 1,5 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # A7: 4,7 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # H7: 4,7 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 1,5 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 3,6 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 1,5 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 4,7 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 3,6 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 1,5 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I3: 3,6 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I3: 2,7,8 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # A3: 3,4 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # B3: 3,4 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 2,5 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 9 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # B2: 1,4 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # B8: 1,4 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # B9: 1,4 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 5,9 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 2 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # G3: 7,8 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # G8: 7,8 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I3: 7,8 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I8: 7,8 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # I9: 7,8 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # G2: 2,6 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # G3: 2,6 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # H2: 5,6 => UNS
* INC E1: 1,5 + A5: 6 + C7: 6,8 # H2: 4,7 => UNS
* PRF E1: 1,5 + A5: 6 + C7: 6,8 # C8: 6,8 => SOL
* STA E1: 1,5 + A5: 6 + C7: 6,8 + C8: 6,8
* CNT  51 HDP CHAINS /  51 HYP OPENED