Analysis of zz-www.sudokuwiki.org-0026-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=26

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=26

position: ..61.54..2..74...8....9.....8.....9.1...8...4.5.....2.....7....3...19..7..76.32.. initial

Autosolve

position: 8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D3: 8 => CTR => D3: 2,3
* DIS # D3: 2,8 => CTR => D3: 3
* DIS # F7: 2,8 => CTR => F7: 4
* DIS # B5: 2,7 => CTR => B5: 3,6,9
* DIS # E4: 2 => CTR => E4: 3,6
* DIS # I6: 1 => CTR => I6: 3,6
* DIS # B9: 1 => CTR => B9: 4,9
* DIS # A6: 4,9 => CTR => A6: 6,7
* DIS # H8: 5,6 => CTR => H8: 4
* DIS # G4: 5,6 => CTR => G4: 1,3,7
* DIS # I7: 1,9 => CTR => I7: 3,5,6
* CNT  11 HDP CHAINS /  46 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 # D3: 8 => CTR => D3: 2,3
* DIS D3: 2,3 # B5: 2,7 => CTR => B5: 3,6,9
* DIS D3: 2,3 + B5: 3,6,9 # E4: 2 => CTR => E4: 3,6
* DIS D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 1 => CTR => I6: 3,6
* PRF D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 # B7: 2,6 => SOL
* STA D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 + B7: 2,6
* CNT   5 HDP CHAINS /  22 HYP OPENED

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

Details

Positions

..61.54..2..74...8....9.....8.....9.1...8...4.5.....2.....7....3...19..7..76.32.. initial
8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328. autosolve
836125479219746358475398612682437195193582764754961823521874936368219547947653281 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
E1: 2,3
F3: 2,8
H1: 3,7
F5: 2,7
E6: 3,6
B8: 2,6
A9: 4,9
G8: 5,6
I9: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F4,F6: 1.. / F4 = 1  =>  0 pairs (X) / F6 = 1  => 15 pairs (_)
F6,I6: 1.. / F6 = 1  => 15 pairs (_) / I6 = 1  =>  0 pairs (X)
B9,I9: 1.. / B9 = 1  =>  0 pairs (X) / I9 = 1  => 23 pairs (_)
I1,I3: 2.. / I1 = 2  =>  0 pairs (X) / I3 = 2  => 11 pairs (_)
E1,I1: 2.. / E1 = 2  => 11 pairs (_) / I1 = 2  =>  0 pairs (X)
E1,E4: 2.. / E1 = 2  => 11 pairs (_) / E4 = 2  =>  0 pairs (X)
E1,D3: 3.. / E1 = 3  =>  0 pairs (X) / D3 = 3  => 11 pairs (_)
A9,B9: 4.. / A9 = 4  => 11 pairs (_) / B9 = 4  => 23 pairs (_)
H7,H8: 4.. / H7 = 4  =>  0 pairs (X) / H8 = 4  => 10 pairs (_)
D8,H8: 4.. / D8 = 4  =>  0 pairs (X) / H8 = 4  => 10 pairs (_)
B3,B9: 4.. / B3 = 4  => 11 pairs (_) / B9 = 4  => 23 pairs (_)
D4,D5: 5.. / D4 = 5  =>  9 pairs (_) / D5 = 5  => 11 pairs (_)
A3,A7: 5.. / A3 = 5  => 13 pairs (_) / A7 = 5  => 12 pairs (_)
E4,E6: 6.. / E4 = 6  => 15 pairs (_) / E6 = 6  => 10 pairs (_)
B1,H1: 7.. / B1 = 7  =>  0 pairs (X) / H1 = 7  =>  9 pairs (_)
A6,F6: 7.. / A6 = 7  => 13 pairs (_) / F6 = 7  =>  0 pairs (X)
D3,F3: 8.. / D3 = 8  =>  0 pairs (X) / F3 = 8  => 10 pairs (_)
C7,C8: 8.. / C7 = 8  => 13 pairs (_) / C8 = 8  => 10 pairs (_)
C8,D8: 8.. / C8 = 8  => 10 pairs (_) / D8 = 8  => 13 pairs (_)
F3,F7: 8.. / F3 = 8  => 10 pairs (_) / F7 = 8  =>  0 pairs (X)
I1,G2: 9.. / I1 = 9  => 23 pairs (_) / G2 = 9  => 11 pairs (_)
D5,D6: 9.. / D5 = 9  => 11 pairs (_) / D6 = 9  => 11 pairs (_)
B1,I1: 9.. / B1 = 9  => 11 pairs (_) / I1 = 9  => 23 pairs (_)
G2,G7: 9.. / G2 = 9  => 11 pairs (_) / G7 = 9  => 23 pairs (_)
* DURATION: 0:00:31.458276  START: 03:55:31.377243  END: 03:56:02.835519 2017-05-01
* CP COUNT: (24)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,E1,E6,F3,F5,G8,H1,I9)
* 8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328.
* PAIR E1: 2,3 BLK 2
D3: 2,3,8                                # reduction candidate for 2,3
D3: 8 => CTR
* 8961354722..7469.8.7.892....8..2.79.1...87..475..6.82.....78...3.8.19..7.47653281
D3: 2,3                                  # 10 pairs
* PAIR E1: 2,3 ROW 1
I1: 2,3,9                                # reduction candidate for 2,3
I1: 9                                    # 23 pairs
I1: 2,3                                  # 11 pairs
* PAIR E1: 2,3 COL E
E4: 2,3,6                                # reduction candidate for 2,3
E4: 6                                    # 15 pairs
E4: 2,3                                  # 10 pairs
* PAIR F3: 2,8 BLK 2
D3: 2,8,3                                # reduction candidate for 2,8
D3: 2,8 => CTR
* 8961354722..7469.8.7..9.....8..2.79.1...87..475..6.82.....7....3...19..7.47653281
D3: 3                                    # 11 pairs
* PAIR F3: 2,8 COL F
F7: 2,8,4                                # reduction candidate for 2,8
F7: 2,8 => CTR
* 8961.547.23.746..8....9.....8....79.1...87..475....82.....7....3...19..7.17653289
F7: 4                                    # 15 pairs
* PAIR H1: 3,7 BLK 3
G3: 3,7,1,5,6                            # reduction candidate for 3,7
G3: 3,7                                  # 13 pairs
H3: 3,7,1,5,6                            # reduction candidate for 3,7
H3: 3,7                                  # 14 pairs
* PAIR H1: 3,7 ROW 1
B1: 3,7,9                                # reduction candidate for 3,7
B1: 3,7                                  # 23 pairs
B1: 9                                    # 11 pairs
* PAIR H1: 3,7 COL H
H5: 3,7,5,6                              # reduction candidate for 3,7
H5: 3,7                                  # 11 pairs
H5: 5,6                                  # 10 pairs
* PAIR F5: 2,7 BLK 5
F4: 2,7,1,4                              # reduction candidate for 2,7
F4: 2,7                                  # 20 pairs
F4: 1,4                                  # 10 pairs
* PAIR F5: 2,7 ROW 5
B5: 2,7,3,6,9                            # reduction candidate for 2,7
B5: 2,7 => CTR
* 89612547323.7469.874.398..2682.3179517.582..495...7821....7....3...19..7417653289
B5: 3,6,9                                # 11 pairs
* PAIR E6: 3,6 BLK 5
E4: 3,6,2                                # reduction candidate for 3,6
E4: 2 => CTR
* 8.61354722..7469.8.7..9.....8..2.79.1...87..475..6.82.....7....3...19..7.47653281
E4: 3,6                                  # 11 pairs
* PAIR E6: 3,6 ROW 6
I6: 3,6,1                                # reduction candidate for 3,6
I6: 1 => CTR
* 89612547323.7469.874.398..268243179517.582..495...7821....74...3...19.47417653289
I6: 3,6                                  # 15 pairs
* PAIR B8: 2,6 BLK 7
B7: 2,6,1,9                              # reduction candidate for 2,6
B7: 1,9                                  # 14 pairs
B7: 2,6                                  # 13 pairs
* PAIR B8: 2,6 COL B
B5: 2,6,3,7,9                            # reduction candidate for 2,6
B5: 2,6                                  # 14 pairs
B5: 3,7,9                                # 13 pairs
* PAIR A9: 4,9 BLK 7
B9: 4,9,1                                # reduction candidate for 4,9
B9: 1 => CTR
* 89612547323.7469.874.398..2682.31795173.82..495..678215.9.7....3.8.19..7417653289
B9: 4,9                                  # 23 pairs
* PAIR A9: 4,9 COL A
A6: 4,9,6,7                              # reduction candidate for 4,9
A6: 4,9 => CTR
* 89612547323.7469.874.398..268243179517.582..495..67821....74...3...19.47417653289
A6: 6,7                                  # 11 pairs
* PAIR G8: 5,6 BLK 9
G7: 5,6,1,3,9                            # reduction candidate for 5,6
G7: 5,6                                  # 16 pairs
H7: 5,6,1,3,4                            # reduction candidate for 5,6
H7: 5,6                                  # 11 pairs
I7: 5,6,1,3,9                            # reduction candidate for 5,6
I7: 5,6                                  # 12 pairs
H8: 5,6,4                                # reduction candidate for 5,6
H8: 5,6 => CTR
* 8961.547223.746..8....9.....8....79.1...87..475....82.....7.143328419..7.17653289
H8: 4                                    # 10 pairs
* PAIR G8: 5,6 COL G
G3: 5,6,1,3,7                            # reduction candidate for 5,6
G3: 5,6                                  # 11 pairs
G4: 5,6,1,3,7                            # reduction candidate for 5,6
G4: 5,6 => CTR
* 89612547323.746..8....9.....8.....9.1...82..4.5....82.....7....3...19..7.17653289
G4: 1,3,7                                #  9 pairs
G5: 5,6,3,7                              # reduction candidate for 5,6
G5: 5,6                                  # 10 pairs
* PAIR I9: 1,9 BLK 9
G7: 1,9,3,5,6                            # reduction candidate for 1,9
G7: 1,9                                  # 10 pairs
I7: 1,9,3,5,6                            # reduction candidate for 1,9
I7: 1,9 => CTR
* 8961254732..7469.8.7.398..2.82.371951..582734753..182.....74...3...19.47.47653281
I7: 3,5,6                                #  9 pairs
* PAIR I9: 1,9 ROW 9
B9: 1,9,4                                # reduction candidate for 1,9
B9: 4                                    # 23 pairs
B9: 1,9                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0026-base-pr-000.dot
* REASONING
* DIS # D3: 8 => CTR => D3: 2,3
* DIS # D3: 2,8 => CTR => D3: 3
* DIS # F7: 2,8 => CTR => F7: 4
* DIS # B5: 2,7 => CTR => B5: 3,6,9
* DIS # E4: 2 => CTR => E4: 3,6
* DIS # I6: 1 => CTR => I6: 3,6
* DIS # B9: 1 => CTR => B9: 4,9
* DIS # A6: 4,9 => CTR => A6: 6,7
* DIS # H8: 5,6 => CTR => H8: 4
* DIS # G4: 5,6 => CTR => G4: 1,3,7
* DIS # I7: 1,9 => CTR => I7: 3,5,6
* CNT  11 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,E1,E6,F3,F5,G8,H1,I9)
* 8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328.
* PAIR E1: 2,3 BLK 2
D3: 2,3,8                                # reduction candidate for 2,3
D3: 8 => CTR
* 8961354722..7469.8.7.892....8..2.79.1...87..475..6.82.....78...3.8.19..7.47653281
* PAIR E1: 2,3 ROW 1
I1: 2,3,9                                # reduction candidate for 2,3
I1: 9                                    # 23 pairs
I1: 2,3                                  # 12 pairs
* PAIR E1: 2,3 COL E
E4: 2,3,6                                # reduction candidate for 2,3
E4: 6                                    # 15 pairs
E4: 2,3                                  # 11 pairs
* PAIR H1: 3,7 BLK 3
G3: 3,7,1,5,6                            # reduction candidate for 3,7
G3: 3,7                                  # 14 pairs
H3: 3,7,1,5,6                            # reduction candidate for 3,7
H3: 3,7                                  # 15 pairs
* PAIR H1: 3,7 ROW 1
B1: 3,7,9                                # reduction candidate for 3,7
B1: 3,7                                  # 23 pairs
B1: 9                                    # 12 pairs
* PAIR H1: 3,7 COL H
H5: 3,7,5,6                              # reduction candidate for 3,7
H5: 3,7                                  # 12 pairs
H5: 5,6                                  # 11 pairs
* PAIR F5: 2,7 BLK 5
F4: 2,7,1,4                              # reduction candidate for 2,7
F4: 2,7                                  # 20 pairs
F4: 1,4                                  # 11 pairs
* PAIR F5: 2,7 ROW 5
B5: 2,7,3,6,9                            # reduction candidate for 2,7
B5: 2,7 => CTR
* 89612547323.7469.874.398..268243179517.582..495...7821....74...3...19.47417653289
* PAIR RESTART
* PAIR F5: 2,7 BLK 5
F4: 2,7,1,4                              # reduction candidate for 2,7
F4: 2,7                                  # 21 pairs
F4: 1,4                                  # 13 pairs
* PAIR E6: 3,6 BLK 5
E4: 3,6,2                                # reduction candidate for 3,6
E4: 2 => CTR
* 8.61354722..7469.8.7.298....8..2.79.1.2.87..475..6.82.....72...32..19..7.47653281
* PAIR E6: 3,6 ROW 6
I6: 3,6,1                                # reduction candidate for 3,6
I6: 1 => CTR
* 89612547323.746..8...398..2.8.....9.1...8...4.5....821....7....3...19..7.17653289
* PAIR RESTART
* PAIR B8: 2,6 BLK 7
B7: 2,6,1                                # reduction candidate for 2,6
B7: 2,6 => SOLVED
* 836125479219746358475398612682437195193582764754961823521874936368219547947653281
* DURATION: 0:00:18.448034  START: 03:56:35.779938  END: 03:56:54.227972 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0026-base-pr-001.dot
* REASONING
* DIS # D3: 8 => CTR => D3: 2,3
* DIS D3: 2,3 # B5: 2,7 => CTR => B5: 3,6,9
* DIS D3: 2,3 + B5: 3,6,9 # E4: 2 => CTR => E4: 3,6
* DIS D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 1 => CTR => I6: 3,6
* PRF D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 # B7: 2,6 => SOL
* STA D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 + B7: 2,6
* CNT   5 HDP CHAINS /  22 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=26

Solution

position: 836125479219746358475398612682437195193582764754961823521874936368219547947653281 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 # D3: 2,3 => UNS
* DIS # D3: 8 => CTR => D3: 2,3
* INC # I1: 2,3 => UNS
* INC # I1: 9 => UNS
* INC # E4: 2,3 => UNS
* INC # E4: 6 => UNS
* DIS # D3: 2,8 => CTR => D3: 3
* INC # D3: 3 => UNS
* DIS # F7: 2,8 => CTR => F7: 4
* INC # F7: 4 => UNS
* INC # G3: 3,7 => UNS
* INC # H3: 3,7 => UNS
* INC # B1: 3,7 => UNS
* INC # B1: 9 => UNS
* INC # H5: 3,7 => UNS
* INC # H5: 5,6 => UNS
* INC # F4: 2,7 => UNS
* INC # F4: 1,4 => UNS
* DIS # B5: 2,7 => CTR => B5: 3,6,9
* INC # B5: 3,6,9 => UNS
* INC # E4: 3,6 => UNS
* DIS # E4: 2 => CTR => E4: 3,6
* INC # I6: 3,6 => UNS
* DIS # I6: 1 => CTR => I6: 3,6
* INC # B7: 2,6 => UNS
* INC # B7: 1,9 => UNS
* INC # B5: 2,6 => UNS
* INC # B5: 3,7,9 => UNS
* INC # B9: 4,9 => UNS
* DIS # B9: 1 => CTR => B9: 4,9
* DIS # A6: 4,9 => CTR => A6: 6,7
* INC # A6: 6,7 => UNS
* INC # G7: 5,6 => UNS
* INC # H7: 5,6 => UNS
* INC # I7: 5,6 => UNS
* DIS # H8: 5,6 => CTR => H8: 4
* INC # H8: 4 => UNS
* INC # G3: 5,6 => UNS
* DIS # G4: 5,6 => CTR => G4: 1,3,7
* INC # G4: 1,3,7 => UNS
* INC # G5: 5,6 => UNS
* INC # G7: 1,9 => UNS
* DIS # I7: 1,9 => CTR => I7: 3,5,6
* INC # I7: 3,5,6 => UNS
* INC # B9: 1,9 => UNS
* INC # B9: 4 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D3: 2,3 => UNS
* DIS # D3: 8 => CTR => D3: 2,3
* INC D3: 2,3 # I1: 2,3 => UNS
* INC D3: 2,3 # I1: 9 => UNS
* INC D3: 2,3 # E4: 2,3 => UNS
* INC D3: 2,3 # E4: 6 => UNS
* INC D3: 2,3 # G3: 3,7 => UNS
* INC D3: 2,3 # H3: 3,7 => UNS
* INC D3: 2,3 # B1: 3,7 => UNS
* INC D3: 2,3 # B1: 9 => UNS
* INC D3: 2,3 # H5: 3,7 => UNS
* INC D3: 2,3 # H5: 5,6 => UNS
* INC D3: 2,3 # F4: 2,7 => UNS
* INC D3: 2,3 # F4: 1,4 => UNS
* DIS D3: 2,3 # B5: 2,7 => CTR => B5: 3,6,9
* INC D3: 2,3 + B5: 3,6,9 # F4: 2,7 => UNS
* INC D3: 2,3 + B5: 3,6,9 # F4: 1,4 => UNS
* INC D3: 2,3 + B5: 3,6,9 # E4: 3,6 => UNS
* DIS D3: 2,3 + B5: 3,6,9 # E4: 2 => CTR => E4: 3,6
* INC D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 3,6 => UNS
* DIS D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 1 => CTR => I6: 3,6
* PRF D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 # B7: 2,6 => SOL
* STA D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 + B7: 2,6
* CNT  22 HDP CHAINS /  22 HYP OPENED