Analysis of zz-www.sudokuwiki.org-0024-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=24

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=24

position: 85...2.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3...97 initial

Autosolve

position: 85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H3: 8 => CTR => H3: 5,7
* CNT   1 HDP CHAINS /  28 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 # H3: 8 => CTR => H3: 5,7
* DIS H3: 5,7 # H8: 1,2 => CTR => H8: 6,8
* DIS H3: 5,7 + H8: 6,8 # H2: 8 => CTR => H2: 1,2
* DIS H3: 5,7 + H8: 6,8 + H2: 1,2 # I8: 1,2 => CTR => I8: 6,8
* PRF H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 3,5 => SOL
* STA H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 + F3: 3,5
* CNT   5 HDP CHAINS /  33 HYP OPENED

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

Details

Positions

85...2.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3...97 initial
85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97 autosolve
851462739364975821279183654145837962687219543923654178436798215792541386518326497 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
D1: 4,9
G1: 7,9
G5: 5,7
H6: 5,7
A9: 4,5
C9: 2,8
E9: 2,5
G7: 2,4
H7: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,A2: 1.. / C1 = 1  =>  9 pairs (_) / A2 = 1  => 11 pairs (_)
E7,F8: 1.. / E7 = 1  =>  0 pairs (X) / F8 = 1  =>  9 pairs (_)
C1,I1: 1.. / C1 = 1  =>  9 pairs (_) / I1 = 1  => 11 pairs (_)
A4,E4: 1.. / A4 = 1  =>  9 pairs (_) / E4 = 1  =>  9 pairs (_)
E7,H7: 1.. / E7 = 1  =>  0 pairs (X) / H7 = 1  =>  9 pairs (_)
C1,C5: 1.. / C1 = 1  =>  9 pairs (_) / C5 = 1  => 11 pairs (_)
F5,F8: 1.. / F5 = 1  =>  0 pairs (X) / F8 = 1  =>  9 pairs (_)
A7,B7: 3.. / A7 = 3  =>  9 pairs (_) / B7 = 3  => 11 pairs (_)
D1,F3: 4.. / D1 = 4  =>  9 pairs (_) / F3 = 4  =>  0 pairs (X)
I1,I3: 4.. / I1 = 4  =>  0 pairs (X) / I3 = 4  =>  9 pairs (_)
D4,F6: 4.. / D4 = 4  =>  0 pairs (X) / F6 = 4  =>  9 pairs (_)
G7,G9: 4.. / G7 = 4  =>  8 pairs (_) / G9 = 4  => 12 pairs (_)
D1,I1: 4.. / D1 = 4  =>  9 pairs (_) / I1 = 4  =>  0 pairs (X)
F3,I3: 4.. / F3 = 4  =>  0 pairs (X) / I3 = 4  =>  9 pairs (_)
A9,G9: 4.. / A9 = 4  =>  8 pairs (_) / G9 = 4  => 12 pairs (_)
D1,D4: 4.. / D1 = 4  =>  9 pairs (_) / D4 = 4  =>  0 pairs (X)
F3,F6: 4.. / F3 = 4  =>  0 pairs (X) / F6 = 4  =>  9 pairs (_)
G5,H6: 5.. / G5 = 5  =>  9 pairs (_) / H6 = 5  =>  0 pairs (X)
A8,A9: 5.. / A8 = 5  =>  8 pairs (_) / A9 = 5  => 12 pairs (_)
A9,E9: 5.. / A9 = 5  => 12 pairs (_) / E9 = 5  =>  8 pairs (_)
G2,G5: 5.. / G2 = 5  =>  0 pairs (X) / G5 = 5  =>  9 pairs (_)
A2,B2: 6.. / A2 = 6  => 11 pairs (_) / B2 = 6  =>  9 pairs (_)
H8,I8: 6.. / H8 = 6  => 10 pairs (_) / I8 = 6  =>  9 pairs (_)
A5,I5: 6.. / A5 = 6  =>  9 pairs (_) / I5 = 6  => 10 pairs (_)
B2,B4: 6.. / B2 = 6  =>  9 pairs (_) / B4 = 6  => 11 pairs (_)
H4,H8: 6.. / H4 = 6  =>  9 pairs (_) / H8 = 6  => 10 pairs (_)
G1,H3: 7.. / G1 = 7  =>  9 pairs (_) / H3 = 7  =>  0 pairs (X)
G5,H6: 7.. / G5 = 7  =>  0 pairs (X) / H6 = 7  =>  9 pairs (_)
D7,D8: 7.. / D7 = 7  =>  9 pairs (_) / D8 = 7  => 11 pairs (_)
C1,G1: 7.. / C1 = 7  =>  0 pairs (X) / G1 = 7  =>  9 pairs (_)
G1,G5: 7.. / G1 = 7  =>  9 pairs (_) / G5 = 7  =>  0 pairs (X)
H3,H6: 7.. / H3 = 7  =>  0 pairs (X) / H6 = 7  =>  9 pairs (_)
D2,E3: 8.. / D2 = 8  =>  9 pairs (_) / E3 = 8  => 13 pairs (_)
C8,C9: 8.. / C8 = 8  => 10 pairs (_) / C9 = 8  => 12 pairs (_)
E6,I6: 8.. / E6 = 8  =>  9 pairs (_) / I6 = 8  => 12 pairs (_)
C9,G9: 8.. / C9 = 8  => 12 pairs (_) / G9 = 8  => 10 pairs (_)
D2,D4: 8.. / D2 = 8  =>  9 pairs (_) / D4 = 8  => 13 pairs (_)
* DURATION: 0:00:44.667159  START: 03:51:59.801736  END: 03:52:44.468895 2017-05-01
* CP COUNT: (37)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C9,D1,E9,G1,G5,G7,H6,H7)
* 85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97
* PAIR D1: 4,9 BLK 2
F3: 4,9,3,5                              # reduction candidate for 4,9
F3: 4,9                                  # 12 pairs
F3: 3,5                                  # 10 pairs
* PAIR D1: 4,9 ROW 1
I1: 4,9,1                                # reduction candidate for 4,9
I1: 1                                    # 11 pairs
I1: 4,9                                  #  9 pairs
* PAIR D1: 4,9 COL D
D4: 4,9,2,8                              # reduction candidate for 4,9
D4: 4,9                                  # 14 pairs
D4: 2,8                                  # 10 pairs
* PAIR G1: 7,9 ROW 1
C1: 7,9,1                                # reduction candidate for 7,9
C1: 7,9                                  # 11 pairs
C1: 1                                    #  9 pairs
* PAIR H6: 5,7 COL H
H3: 5,7,8                                # reduction candidate for 5,7
H3: 8 => CTR
* 85..6273...487.9522..15468...5..78...8....54....68517...67.8215...541368518326497
H3: 5,7                                  # 10 pairs
* PAIR C9: 2,8 BLK 7
C8: 2,8,7,9                              # reduction candidate for 2,8
C8: 7,9                                  # 13 pairs
C8: 2,8                                  # 11 pairs
* PAIR C9: 2,8 ROW 9
G9: 2,8,4                                # reduction candidate for 2,8
G9: 4                                    # 12 pairs
G9: 2,8                                  #  8 pairs
* PAIR E9: 2,5 BLK 8
D8: 2,5,7,9                              # reduction candidate for 2,5
D8: 2,5                                  # 12 pairs
D8: 7,9                                  # 10 pairs
* PAIR E9: 2,5 COL E
E5: 2,5,1,3,9                            # reduction candidate for 2,5
E5: 2,5                                  # 11 pairs
E6: 2,5,3,8,9                            # reduction candidate for 2,5
E6: 2,5                                  # 14 pairs
* PAIR G7: 2,4 BLK 9
G9: 2,4,8                                # reduction candidate for 2,4
G9: 2,4                                  # 12 pairs
G9: 8                                    # 10 pairs
* PAIR G7: 2,4 ROW 7
B7: 2,4,3,7,9                            # reduction candidate for 2,4
B7: 2,4                                  # 10 pairs
B7: 3,7,9                                #  9 pairs
* PAIR H7: 1,2 BLK 9
H8: 1,2,6,8                              # reduction candidate for 1,2
H8: 1,2                                  # 13 pairs
I8: 1,2,6,8                              # reduction candidate for 1,2
I8: 1,2                                  # 14 pairs
* PAIR H7: 1,2 ROW 7
E7: 1,2,9                                # reduction candidate for 1,2
E7: 1,2                                  # 10 pairs
E7: 9                                    #  9 pairs
* PAIR H7: 1,2 COL H
H2: 1,2,5,8                              # reduction candidate for 1,2
H2: 1,2                                  # 13 pairs
H2: 5,8                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0024-base-pr-000.dot
* REASONING
* DIS # H3: 8 => CTR => H3: 5,7
* CNT   1 HDP CHAINS /  28 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C9,D1,E9,G1,G5,G7,H6,H7)
* 85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97
* PAIR D1: 4,9 BLK 2
F3: 4,9,3,5                              # reduction candidate for 4,9
F3: 4,9                                  # 12 pairs
F3: 3,5                                  # 10 pairs
* PAIR D1: 4,9 ROW 1
I1: 4,9,1                                # reduction candidate for 4,9
I1: 1                                    # 11 pairs
I1: 4,9                                  #  9 pairs
* PAIR D1: 4,9 COL D
D4: 4,9,2,8                              # reduction candidate for 4,9
D4: 4,9                                  # 14 pairs
D4: 2,8                                  # 10 pairs
* PAIR G1: 7,9 ROW 1
C1: 7,9,1                                # reduction candidate for 7,9
C1: 7,9                                  # 11 pairs
C1: 1                                    #  9 pairs
* PAIR H6: 5,7 COL H
H3: 5,7,8                                # reduction candidate for 5,7
H3: 8 => CTR
* 85..6273...487.9522..15468...5..78...8....54....68517...67.8215...541368518326497
* PAIR RESTART
* PAIR C9: 2,8 BLK 7
C8: 2,8,7,9                              # reduction candidate for 2,8
C8: 7,9                                  # 15 pairs
C8: 2,8                                  # 12 pairs
* PAIR C9: 2,8 ROW 9
G9: 2,8,4                                # reduction candidate for 2,8
G9: 4                                    # 14 pairs
G9: 2,8                                  #  9 pairs
* PAIR E9: 2,5 BLK 8
D8: 2,5,7,9                              # reduction candidate for 2,5
D8: 2,5                                  # 13 pairs
D8: 7,9                                  # 11 pairs
* PAIR E9: 2,5 COL E
E5: 2,5,1,3,9                            # reduction candidate for 2,5
E5: 2,5                                  # 12 pairs
E6: 2,5,3,8,9                            # reduction candidate for 2,5
E6: 2,5                                  # 15 pairs
* PAIR G7: 2,4 BLK 9
G9: 2,4,8                                # reduction candidate for 2,4
G9: 2,4                                  # 14 pairs
G9: 8                                    # 11 pairs
* PAIR G7: 2,4 ROW 7
B7: 2,4,3,7,9                            # reduction candidate for 2,4
B7: 2,4                                  # 12 pairs
B7: 3,7,9                                # 10 pairs
* PAIR H7: 1,2 BLK 9
H8: 1,2,6,8                              # reduction candidate for 1,2
H8: 1,2 => CTR
* 8574629311649735822..185674.4581726.6815297437296341589.6..84.55.8.4.3.6412356897
I8: 1,2,6,8                              # reduction candidate for 1,2
I8: 1,2                                  # 15 pairs
* RESTART
* PAIR H7: 1,2 BLK 9
I8: 1,2,6,8                              # reduction candidate for 1,2
I8: 1,2                                  # 15 pairs
I8: 6,8                                  # 14 pairs
* PAIR H7: 1,2 ROW 7
E7: 1,2,9                                # reduction candidate for 1,2
E7: 9                                    # 12 pairs
E7: 1,2                                  # 12 pairs
* PAIR H7: 1,2 COL H
H2: 1,2,8                                # reduction candidate for 1,2
H2: 8 => CTR
* 85.462.3...4.7.28.2..18.654..58.792..8....54..2.6.4178..6..84155.8.41362412356897
* PAIR RESTART
* PAIR H7: 1,2 BLK 9
I8: 1,2,6,8                              # reduction candidate for 1,2
I8: 1,2 => CTR
* 85..62.3...487....2..1..6.8..5..7.8..8.5..74....68.15...6..84.55.8.4.36.412356897

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A9,D1,E7,E9,G1,G4,G5,G7,G9,H3,H4,H6,H8,I8)
* 85..62.3...4.7..2.2..1..6....5..7....8.....4....6..1....6..8.15....413...183.6.97
* PAIR D1: 4,9 BLK 2
F3: 4,9,3,5                              # reduction candidate for 4,9
F3: 3,5 => SOLVED
* 851462739364975821279183654145837962687219543923654178436798215792541386518326497
* DURATION: 0:00:24.013222  START: 03:53:01.674221  END: 03:53:25.687443 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0024-base-pr-001.dot
* REASONING
* DIS # H3: 8 => CTR => H3: 5,7
* DIS H3: 5,7 # H8: 1,2 => CTR => H8: 6,8
* DIS H3: 5,7 + H8: 6,8 # H2: 8 => CTR => H2: 1,2
* DIS H3: 5,7 + H8: 6,8 + H2: 1,2 # I8: 1,2 => CTR => I8: 6,8
* PRF H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 3,5 => SOL
* STA H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 + F3: 3,5
* CNT   5 HDP CHAINS /  33 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=24

Solution

position: 851462739364975821279183654145837962687219543923654178436798215792541386518326497 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 # F3: 4,9 => UNS
* INC # F3: 3,5 => UNS
* INC # I1: 4,9 => UNS
* INC # I1: 1 => UNS
* INC # D4: 4,9 => UNS
* INC # D4: 2,8 => UNS
* INC # C1: 7,9 => UNS
* INC # C1: 1 => UNS
* INC # H3: 5,7 => UNS
* DIS # H3: 8 => CTR => H3: 5,7
* INC # C8: 2,8 => UNS
* INC # C8: 7,9 => UNS
* INC # G9: 2,8 => UNS
* INC # G9: 4 => UNS
* INC # D8: 2,5 => UNS
* INC # D8: 7,9 => UNS
* INC # E5: 2,5 => UNS
* INC # E6: 2,5 => UNS
* INC # G9: 2,4 => UNS
* INC # G9: 8 => UNS
* INC # B7: 2,4 => UNS
* INC # B7: 3,7,9 => UNS
* INC # H8: 1,2 => UNS
* INC # I8: 1,2 => UNS
* INC # E7: 1,2 => UNS
* INC # E7: 9 => UNS
* INC # H2: 1,2 => UNS
* INC # H2: 5,8 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F3: 4,9 => UNS
* INC # F3: 3,5 => UNS
* INC # I1: 4,9 => UNS
* INC # I1: 1 => UNS
* INC # D4: 4,9 => UNS
* INC # D4: 2,8 => UNS
* INC # C1: 7,9 => UNS
* INC # C1: 1 => UNS
* INC # H3: 5,7 => UNS
* DIS # H3: 8 => CTR => H3: 5,7
* INC H3: 5,7 # C8: 2,8 => UNS
* INC H3: 5,7 # C8: 7,9 => UNS
* INC H3: 5,7 # G9: 2,8 => UNS
* INC H3: 5,7 # G9: 4 => UNS
* INC H3: 5,7 # D8: 2,5 => UNS
* INC H3: 5,7 # D8: 7,9 => UNS
* INC H3: 5,7 # E5: 2,5 => UNS
* INC H3: 5,7 # E6: 2,5 => UNS
* INC H3: 5,7 # G9: 2,4 => UNS
* INC H3: 5,7 # G9: 8 => UNS
* INC H3: 5,7 # B7: 2,4 => UNS
* INC H3: 5,7 # B7: 3,7,9 => UNS
* DIS H3: 5,7 # H8: 1,2 => CTR => H8: 6,8
* INC H3: 5,7 + H8: 6,8 # I8: 1,2 => UNS
* INC H3: 5,7 + H8: 6,8 # I8: 1,2 => UNS
* INC H3: 5,7 + H8: 6,8 # I8: 6,8 => UNS
* INC H3: 5,7 + H8: 6,8 # E7: 1,2 => UNS
* INC H3: 5,7 + H8: 6,8 # E7: 9 => UNS
* INC H3: 5,7 + H8: 6,8 # H2: 1,2 => UNS
* DIS H3: 5,7 + H8: 6,8 # H2: 8 => CTR => H2: 1,2
* DIS H3: 5,7 + H8: 6,8 + H2: 1,2 # I8: 1,2 => CTR => I8: 6,8
* INC H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 4,9 => UNS
* PRF H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 3,5 => SOL
* STA H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 + F3: 3,5
* CNT  33 HDP CHAINS /  33 HYP OPENED