Analysis of zz-www.sudokuwiki.org-0116-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=116

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=116

position: ...8....398.....7...4..31...2.9....5....4....7....5.1...72..6...5..8..242....9... initial

Autosolve

position: ..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 2,6 => CTR => E2: 1,5
* DIS # I5: 2,6 => CTR => I5: 7,8,9
* PRF # B6: 3,6 => SOL
* DIS # D9: 3,6 => CTR => D9: 1,4,5,7
* CNT   4 HDP CHAINS /  34 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 # E2: 2,6 => CTR => E2: 1,5
* DIS E2: 1,5 # I5: 2,6 => CTR => I5: 7,8,9
* PRF E2: 1,5 + I5: 7,8,9 # B6: 3,6 => SOL
* STA E2: 1,5 + I5: 7,8,9 + B6: 3,6
* CNT   3 HDP CHAINS /  30 HYP OPENED

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

Details

Positions

...8....398.....7...4..31...2.9....5....4....7....5.1...72..6...5..8..242....9... initial
..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9... autosolve
512876943983412576674593182421968735395741268768325419837254691159687324246139857 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A3: 5,6
B3: 6,7
E3: 2,9
I2: 2,6
H3: 8,9
D6: 3,6
F7: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 1.. / A1 = 1  => 11 pairs (_) / B1 = 1  =>  9 pairs (_)
I7,I9: 1.. / I7 = 1  => 13 pairs (_) / I9 = 1  =>  9 pairs (_)
F5,E6: 2.. / F5 = 2  => 13 pairs (_) / E6 = 2  =>  8 pairs (_)
E3,I3: 2.. / E3 = 2  => 14 pairs (_) / I3 = 2  =>  7 pairs (_)
F2,F5: 2.. / F2 = 2  =>  8 pairs (_) / F5 = 2  => 13 pairs (_)
A4,B6: 4.. / A4 = 4  =>  9 pairs (_) / B6 = 4  => 16 pairs (_)
F7,D9: 4.. / F7 = 4  =>  9 pairs (_) / D9 = 4  => 11 pairs (_)
B6,G6: 4.. / B6 = 4  => 16 pairs (_) / G6 = 4  =>  9 pairs (_)
B9,D9: 4.. / B9 = 4  =>  9 pairs (_) / D9 = 4  => 11 pairs (_)
A4,A7: 4.. / A4 = 4  =>  9 pairs (_) / A7 = 4  => 16 pairs (_)
D2,D9: 4.. / D2 = 4  =>  9 pairs (_) / D9 = 4  => 11 pairs (_)
H1,H4: 4.. / H1 = 4  =>  9 pairs (_) / H4 = 4  => 19 pairs (_)
A1,A3: 5.. / A1 = 5  =>  8 pairs (_) / A3 = 5  => 10 pairs (_)
A3,D3: 5.. / A3 = 5  => 10 pairs (_) / D3 = 5  =>  8 pairs (_)
E7,H7: 5.. / E7 = 5  =>  7 pairs (_) / H7 = 5  =>  9 pairs (_)
H1,I2: 6.. / H1 = 6  =>  0 pairs (X) / I2 = 6  =>  6 pairs (_)
B1,B3: 7.. / B1 = 7  =>  9 pairs (_) / B3 = 7  =>  8 pairs (_)
B3,D3: 7.. / B3 = 7  =>  8 pairs (_) / D3 = 7  =>  9 pairs (_)
I5,I9: 7.. / I5 = 7  =>  8 pairs (_) / I9 = 7  => 14 pairs (_)
H3,I3: 8.. / H3 = 8  =>  8 pairs (_) / I3 = 8  => 15 pairs (_)
F4,F5: 8.. / F4 = 8  =>  8 pairs (_) / F5 = 8  => 11 pairs (_)
A7,C9: 8.. / A7 = 8  => 11 pairs (_) / C9 = 8  => 16 pairs (_)
E1,E3: 9.. / E1 = 9  => 14 pairs (_) / E3 = 9  =>  7 pairs (_)
B7,C8: 9.. / B7 = 9  => 10 pairs (_) / C8 = 9  =>  9 pairs (_)
C8,G8: 9.. / C8 = 9  =>  9 pairs (_) / G8 = 9  => 10 pairs (_)
C6,C8: 9.. / C6 = 9  => 10 pairs (_) / C8 = 9  =>  9 pairs (_)
* DURATION: 0:00:30.098905  START: 05:35:47.437472  END: 05:36:17.536377 2017-05-01
* CP COUNT: (26)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,D6,E3,F7,H3,I2)
* ..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9...
* PAIR A3: 5,6 BLK 1
A1: 5,6,1                                # reduction candidate for 5,6
A1: 1                                    # 11 pairs
A1: 5,6                                  #  9 pairs
* PAIR A3: 5,6 ROW 3
D3: 5,6,7                                # reduction candidate for 5,6
D3: 7                                    #  9 pairs
D3: 5,6                                  #  8 pairs
* PAIR B3: 6,7 BLK 1
B1: 6,7,1                                # reduction candidate for 6,7
B1: 6,7                                  # 11 pairs
B1: 1                                    #  9 pairs
* PAIR B3: 6,7 ROW 3
D3: 6,7,5                                # reduction candidate for 6,7
D3: 6,7                                  # 10 pairs
D3: 5                                    #  8 pairs
* PAIR E3: 2,9 ROW 3
I3: 2,9,8                                # reduction candidate for 2,9
I3: 8                                    # 15 pairs
I3: 2,9                                  #  8 pairs
* PAIR I2: 2,6 ROW 2
E2: 2,6,1,5                              # reduction candidate for 2,6
E2: 2,6 => CTR
* ..28....39831.457...45.31...2.918745815742...749..52184972.16...5..8..242.84.9..1
E2: 1,5                                  #  8 pairs
F2: 2,6,1,4                              # reduction candidate for 2,6
F2: 2,6                                  # 10 pairs
* PAIR I2: 2,6 COL I
I5: 2,6,7,8,9                            # reduction candidate for 2,6
I5: 2,6 => CTR
* ..28...439834...76..4..31..42.9....5..5.4...27...2541...72.46.1.5..8..2424...9..7
I5: 7,8,9                                #  7 pairs
I6: 2,6,8,9                              # reduction candidate for 2,6
I6: 2,6                                  # 21 pairs
* PAIR H3: 8,9 BLK 3
I3: 8,9,2                                # reduction candidate for 8,9
I3: 8,9                                  # 14 pairs
I3: 2                                    #  7 pairs
* PAIR H3: 8,9 COL H
H5: 8,9,3,6                              # reduction candidate for 8,9
H5: 8,9                                  # 14 pairs
H7: 8,9,3,5                              # reduction candidate for 8,9
H7: 8,9                                  # 12 pairs
* PAIR D6: 3,6 BLK 5
E4: 3,6,1,7                              # reduction candidate for 3,6
E4: 3,6                                  # 10 pairs
D5: 3,6,1,7                              # reduction candidate for 3,6
D5: 3,6                                  # 14 pairs
E6: 3,6,2                                # reduction candidate for 3,6
E6: 3,6                                  # 13 pairs
* PAIR D6: 3,6 ROW 6
B6: 3,6,4,9                              # reduction candidate for 3,6
B6: 3,6 => SOLVED
* 512876943983412576674593182421968735395741268768325419837254691159687324246139857
B6: 4,9                                  #  8 pairs
* PAIR D6: 3,6 COL D
D8: 3,6,1,7                              # reduction candidate for 3,6
D8: 3,6                                  # 12 pairs
D9: 3,6,1,4,5,7                          # reduction candidate for 3,6
D9: 3,6 => CTR
* 5128..94398341257667459318242193..65..5.4.23.73..2541...72.46...59.8..242463.9.5.
D9: 1,4,5,7                              #  7 pairs
* PAIR F7: 1,4 BLK 8
D9: 1,4,3,5,6,7                          # reduction candidate for 1,4
D9: 1,4                                  # 11 pairs
D9: 3,5,6,7                              #  9 pairs
* PAIR F7: 1,4 ROW 7
A7: 1,4,3,8                              # reduction candidate for 1,4
A7: 1,4                                  # 16 pairs
B7: 1,4,3,9                              # reduction candidate for 1,4
B7: 1,4                                  # 20 pairs
* PAIR F7: 1,4 COL F
F2: 1,4,2,6                              # reduction candidate for 1,4
F2: 1,4                                  # 17 pairs
F2: 2,6                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0116-base-pr-000.dot
* REASONING
* DIS # E2: 2,6 => CTR => E2: 1,5
* DIS # I5: 2,6 => CTR => I5: 7,8,9
* PRF # B6: 3,6 => SOL
* DIS # D9: 3,6 => CTR => D9: 1,4,5,7
* CNT   4 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,D6,E3,F7,H3,I2)
* ..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9...
* PAIR A3: 5,6 BLK 1
A1: 5,6,1                                # reduction candidate for 5,6
A1: 1                                    # 11 pairs
A1: 5,6                                  #  9 pairs
* PAIR A3: 5,6 ROW 3
D3: 5,6,7                                # reduction candidate for 5,6
D3: 7                                    #  9 pairs
D3: 5,6                                  #  8 pairs
* PAIR B3: 6,7 BLK 1
B1: 6,7,1                                # reduction candidate for 6,7
B1: 6,7                                  # 11 pairs
B1: 1                                    #  9 pairs
* PAIR B3: 6,7 ROW 3
D3: 6,7,5                                # reduction candidate for 6,7
D3: 6,7                                  # 10 pairs
D3: 5                                    #  8 pairs
* PAIR E3: 2,9 ROW 3
I3: 2,9,8                                # reduction candidate for 2,9
I3: 8                                    # 15 pairs
I3: 2,9                                  #  8 pairs
* PAIR I2: 2,6 ROW 2
E2: 2,6,1,5                              # reduction candidate for 2,6
E2: 2,6 => CTR
* ..28....39831.457...45.31...2.918745815742...749..52184972.16...5..8..242.84.9..1
F2: 2,6,1,4                              # reduction candidate for 2,6
F2: 2,6                                  # 10 pairs
* RESTART
* PAIR I2: 2,6 ROW 2
F2: 2,6,1,4                              # reduction candidate for 2,6
F2: 1,4                                  # 19 pairs
F2: 2,6                                  # 10 pairs
* PAIR I2: 2,6 COL I
I5: 2,6,7,8,9                            # reduction candidate for 2,6
I5: 2,6 => CTR
* ..28...439834...76..4..31..42.9....5..5.4...27...2541...72.46.1.5..8..2424...9..7
I6: 2,6,8,9                              # reduction candidate for 2,6
I6: 2,6                                  # 21 pairs
* RESTART
* PAIR I2: 2,6 COL I
I6: 2,6,8,9                              # reduction candidate for 2,6
I6: 2,6                                  # 21 pairs
I6: 8,9                                  #  8 pairs
* PAIR RESTART
* PAIR I2: 2,6 ROW 2
F2: 2,6,1,4                              # reduction candidate for 2,6
F2: 1,4                                  # 21 pairs
F2: 2,6                                  # 10 pairs
* PAIR I2: 2,6 COL I
I6: 2,6,8,9                              # reduction candidate for 2,6
I6: 2,6                                  # 21 pairs
I6: 8,9                                  #  8 pairs
* PAIR H3: 8,9 BLK 3
I3: 8,9,2                                # reduction candidate for 8,9
I3: 8,9                                  # 21 pairs
I3: 2                                    #  8 pairs
* PAIR H3: 8,9 COL H
H5: 8,9,3,6                              # reduction candidate for 8,9
H5: 8,9                                  # 15 pairs
H7: 8,9,3,5                              # reduction candidate for 8,9
H7: 8,9                                  # 12 pairs
* PAIR D6: 3,6 BLK 5
E4: 3,6,1,7                              # reduction candidate for 3,6
E4: 3,6                                  # 10 pairs
D5: 3,6,1,7                              # reduction candidate for 3,6
D5: 3,6                                  # 14 pairs
E6: 3,6,2                                # reduction candidate for 3,6
E6: 3,6                                  # 21 pairs
* PAIR D6: 3,6 ROW 6
B6: 3,6,4,9                              # reduction candidate for 3,6
B6: 3,6 => SOLVED
* 512876943983412576674593182421968735395741268768325419837254691159687324246139857
* DURATION: 0:00:22.468963  START: 05:36:40.849638  END: 05:37:03.318601 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0116-base-pr-001.dot
* REASONING
* DIS # E2: 2,6 => CTR => E2: 1,5
* DIS E2: 1,5 # I5: 2,6 => CTR => I5: 7,8,9
* PRF E2: 1,5 + I5: 7,8,9 # B6: 3,6 => SOL
* STA E2: 1,5 + I5: 7,8,9 + B6: 3,6
* CNT   3 HDP CHAINS /  30 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=116

Solution

position: 512876943983412576674593182421968735395741268768325419837254691159687324246139857 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 # A1: 5,6 => UNS
* INC # A1: 1 => UNS
* INC # D3: 5,6 => UNS
* INC # D3: 7 => UNS
* INC # B1: 6,7 => UNS
* INC # B1: 1 => UNS
* INC # D3: 6,7 => UNS
* INC # D3: 5 => UNS
* INC # I3: 2,9 => UNS
* INC # I3: 8 => UNS
* DIS # E2: 2,6 => CTR => E2: 1,5
* INC # E2: 1,5 => UNS
* INC # F2: 2,6 => UNS
* DIS # I5: 2,6 => CTR => I5: 7,8,9
* INC # I5: 7,8,9 => UNS
* INC # I6: 2,6 => UNS
* INC # I3: 8,9 => UNS
* INC # I3: 2 => UNS
* INC # H5: 8,9 => UNS
* INC # H7: 8,9 => UNS
* INC # E4: 3,6 => UNS
* INC # D5: 3,6 => UNS
* INC # E6: 3,6 => UNS
* PRF # B6: 3,6 => SOL
* INC # B6: 4,9 => UNS
* INC # D8: 3,6 => UNS
* DIS # D9: 3,6 => CTR => D9: 1,4,5,7
* INC # D9: 1,4,5,7 => UNS
* INC # D9: 1,4 => UNS
* INC # D9: 3,5,6,7 => UNS
* INC # A7: 1,4 => UNS
* INC # B7: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # F2: 2,6 => UNS
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 5,6 => UNS
* INC # A1: 1 => UNS
* INC # D3: 5,6 => UNS
* INC # D3: 7 => UNS
* INC # B1: 6,7 => UNS
* INC # B1: 1 => UNS
* INC # D3: 6,7 => UNS
* INC # D3: 5 => UNS
* INC # I3: 2,9 => UNS
* INC # I3: 8 => UNS
* DIS # E2: 2,6 => CTR => E2: 1,5
* INC E2: 1,5 # F2: 2,6 => UNS
* INC E2: 1,5 # F2: 2,6 => UNS
* INC E2: 1,5 # F2: 1,4 => UNS
* DIS E2: 1,5 # I5: 2,6 => CTR => I5: 7,8,9
* INC E2: 1,5 + I5: 7,8,9 # I6: 2,6 => UNS
* INC E2: 1,5 + I5: 7,8,9 # I6: 2,6 => UNS
* INC E2: 1,5 + I5: 7,8,9 # I6: 8,9 => UNS
* INC E2: 1,5 + I5: 7,8,9 # F2: 2,6 => UNS
* INC E2: 1,5 + I5: 7,8,9 # F2: 1,4 => UNS
* INC E2: 1,5 + I5: 7,8,9 # I6: 2,6 => UNS
* INC E2: 1,5 + I5: 7,8,9 # I6: 8,9 => UNS
* INC E2: 1,5 + I5: 7,8,9 # I3: 8,9 => UNS
* INC E2: 1,5 + I5: 7,8,9 # I3: 2 => UNS
* INC E2: 1,5 + I5: 7,8,9 # H5: 8,9 => UNS
* INC E2: 1,5 + I5: 7,8,9 # H7: 8,9 => UNS
* INC E2: 1,5 + I5: 7,8,9 # E4: 3,6 => UNS
* INC E2: 1,5 + I5: 7,8,9 # D5: 3,6 => UNS
* INC E2: 1,5 + I5: 7,8,9 # E6: 3,6 => UNS
* PRF E2: 1,5 + I5: 7,8,9 # B6: 3,6 => SOL
* STA E2: 1,5 + I5: 7,8,9 + B6: 3,6
* CNT  30 HDP CHAINS /  30 HYP OPENED