Analysis of zz-www.sudokuwiki.org-0031-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=31

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=31

position: ....6..4......17.89....82.........3.35..9...4.8.........23....5..12......7..4..6. initial

Autosolve

position: ....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 1,2 => CTR => A1: 5,7,8
* PRF # H6: 5,9 => SOL
* PRF # G1: 1,5 => SOL
* PRF # H6: 1,5 => SOL
* PRF # C6: 6,7 => SOL
* DIS # D5: 6,7 => CTR => D5: 1,8
* DIS # E4: 2,7 => CTR => E4: 1,5,8
* DIS # C9: 5,8 => CTR => C9: 3,9
* DIS # A1: 5,8 => CTR => A1: 1,2,7
* DIS # C9: 5,9 => CTR => C9: 3,8
* CNT  10 HDP CHAINS /  41 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 # A1: 1,2 => CTR => A1: 5,7,8
* PRF A1: 5,7,8 # G1: 5,9 => SOL
* STA A1: 5,7,8 + G1: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

....6..4......17.89....82.........3.35..9...4.8.........23....5..12......7..4..6. initial
....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62 autosolve
718962543265431798934758216129584637356197824487623951892316475641275389573849162 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
B1: 1,2
H2: 5,9
H3: 1,5
C5: 6,7
F5: 2,7
A9: 5,8
F9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E7,D9: 1.. / E7 = 1  =>  9 pairs (_) / D9 = 1  =>  0 pairs (X)
B3,H3: 1.. / B3 = 1  =>  0 pairs (X) / H3 = 1  => 10 pairs (_)
D9,G9: 1.. / D9 = 1  =>  0 pairs (X) / G9 = 1  =>  9 pairs (_)
F1,E2: 2.. / F1 = 2  =>  0 pairs (*) / E2 = 2  =>  0 pairs (X)
H5,H6: 2.. / H5 = 2  =>  0 pairs (*) / H6 = 2  =>  0 pairs (X)
F5,H5: 2.. / F5 = 2  => 12 pairs (_) / H5 = 2  =>  0 pairs (*)
F1,F5: 2.. / F1 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
E2,E3: 3.. / E2 = 3  =>  0 pairs (*) / E3 = 3  =>  0 pairs (X)
G1,I1: 3.. / G1 = 3  => 12 pairs (_) / I1 = 3  => 20 pairs (_)
B8,C9: 3.. / B8 = 3  =>  0 pairs (X) / C9 = 3  =>  7 pairs (_)
C9,G9: 3.. / C9 = 3  =>  7 pairs (_) / G9 = 3  =>  0 pairs (X)
I1,I8: 3.. / I1 = 3  => 20 pairs (_) / I8 = 3  => 12 pairs (_)
D2,D3: 4.. / D2 = 4  =>  9 pairs (_) / D3 = 4  => 11 pairs (_)
A6,C6: 4.. / A6 = 4  =>  0 pairs (*) / C6 = 4  =>  0 pairs (X)
G7,G8: 4.. / G7 = 4  =>  9 pairs (_) / G8 = 4  =>  7 pairs (_)
F7,F8: 6.. / F7 = 6  =>  9 pairs (_) / F8 = 6  =>  8 pairs (_)
A1,C1: 8.. / A1 = 8  =>  0 pairs (X) / C1 = 8  =>  7 pairs (_)
C1,C9: 8.. / C1 = 8  =>  7 pairs (_) / C9 = 8  =>  0 pairs (X)
D2,H2: 9.. / D2 = 9  =>  0 pairs (X) / H2 = 9  =>  9 pairs (_)
* DURATION: 0:00:24.322409  START: 04:00:00.549043  END: 04:00:24.871452 2017-05-01
* CP COUNT: (19)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,C5,F5,F9,H2,H3)
* ....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62
* PAIR B1: 1,2 BLK 1
A1: 1,2,5,7,8                            # reduction candidate for 1,2
A1: 1,2 => CTR
* ..8.6.543...421798947538216..9.54.3.356.92..4284..3.5...23....5..12......7..4..62
A1: 5,7,8                                #  7 pairs
* PAIR B1: 1,2 COL B
B4: 1,2,6,9                              # reduction candidate for 1,2
B4: 6,9                                  # 13 pairs
B4: 1,2                                  # 11 pairs
* PAIR H2: 5,9 BLK 3
G1: 5,9,1,3                              # reduction candidate for 5,9
G1: 5,9                                  # 20 pairs
G1: 1,3                                  #  8 pairs
* PAIR H2: 5,9 ROW 2
D2: 5,9,4                                # reduction candidate for 5,9
D2: 5,9                                  # 11 pairs
D2: 4                                    #  9 pairs
* PAIR H2: 5,9 COL H
H6: 5,9,1,2,7                            # reduction candidate for 5,9
H6: 5,9 => SOLVED
* 718962543265431798934758216129584637356197824487623951892316475641275389573849162
H6: 1,2,7                                #  7 pairs
* PAIR H3: 1,5 BLK 3
G1: 1,5,3,9                              # reduction candidate for 1,5
G1: 1,5 => SOLVED
* 718962543265431798934758216129584637356197824487623951892316475641275389573849162
G1: 3,9                                  #  8 pairs
* PAIR H3: 1,5 COL H
H6: 1,5,2,7,9                            # reduction candidate for 1,5
H6: 1,5 => SOLVED
* 718962543265431798934758216129584637356197824487623951892316475641275389573849162
H6: 2,7,9                                #  7 pairs
* PAIR C5: 6,7 BLK 4
A4: 6,7,1,2                              # reduction candidate for 6,7
A4: 6,7                                  # 17 pairs
C4: 6,7,9                                # reduction candidate for 6,7
C4: 6,7                                  # 12 pairs
A6: 6,7,1,2,4                            # reduction candidate for 6,7
A6: 6,7                                  # 19 pairs
C6: 6,7,4,9                              # reduction candidate for 6,7
C6: 6,7 => SOLVED
* 718962543265431798934758216129584637356197824487623951892316475641275389573849162
C6: 4,9                                  #  8 pairs
* PAIR C5: 6,7 ROW 5
D5: 6,7,1,8                              # reduction candidate for 6,7
D5: 6,7 => CTR
* .28.6.341.35.2179891..382562....4.3.35..92..4184..3.2...23....5..12....3.73.4..62
D5: 1,8                                  #  8 pairs
* PAIR F5: 2,7 BLK 5
E4: 2,7,1,5,8                            # reduction candidate for 2,7
E4: 2,7 => CTR
* 728.6..4.....217.891.7382562...74.31357192684184..3.27..23....5..12......7..4..62
E4: 1,5,8                                #  7 pairs
E6: 2,7,1,5                              # reduction candidate for 2,7
E6: 2,7                                  #  9 pairs
* PAIR F5: 2,7 ROW 5
H5: 2,7,1,8                              # reduction candidate for 2,7
H5: 1,8                                  # 14 pairs
H5: 2,7                                  # 11 pairs
* PAIR F5: 2,7 COL F
F1: 2,7,5,9                              # reduction candidate for 2,7
F1: 5,9                                  # 18 pairs
F1: 2,7                                  # 12 pairs
* PAIR A9: 5,8 BLK 7
A8: 5,8,4,6                              # reduction candidate for 5,8
A8: 5,8                                  # 10 pairs
C9: 5,8,3,9                              # reduction candidate for 5,8
C9: 5,8 => CTR
* ....6..43.....17.89....82.6.....4.3.35..9...4.8...3....923....5.312......7.149362
C9: 3,9                                  #  8 pairs
* PAIR A9: 5,8 ROW 9
D9: 5,8,1,9                              # reduction candidate for 5,8
D9: 5,8                                  #  9 pairs
D9: 1,9                                  #  8 pairs
* PAIR A9: 5,8 COL A
A1: 5,8,1,2,7                            # reduction candidate for 5,8
A1: 5,8 => CTR
* .1.96254326.4.179894.7.8216.29..4.3.356.97.24.84.2395.4923.61.56312..4.9578149362
A1: 1,2,7                                #  7 pairs
* PAIR F9: 5,9 BLK 8
F8: 5,9,6,7                              # reduction candidate for 5,9
F8: 5,9                                  # 14 pairs
D9: 5,9,1,8                              # reduction candidate for 5,9
D9: 5,9                                  # 24 pairs
* PAIR F9: 5,9 ROW 9
C9: 5,9,3,8                              # reduction candidate for 5,9
C9: 5,9 => CTR
* ..8.6..43.....17.89....82.6.....4.3.35..9...4.8...3.....23....5.312.....87.14.362
C9: 3,8                                  #  8 pairs
* PAIR F9: 5,9 COL F
F1: 5,9,2,7                              # reduction candidate for 5,9
F1: 5,9                                  # 18 pairs
F1: 2,7                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0031-base-pr-000.dot
* REASONING
* DIS # A1: 1,2 => CTR => A1: 5,7,8
* PRF # H6: 5,9 => SOL
* PRF # G1: 1,5 => SOL
* PRF # H6: 1,5 => SOL
* PRF # C6: 6,7 => SOL
* DIS # D5: 6,7 => CTR => D5: 1,8
* DIS # E4: 2,7 => CTR => E4: 1,5,8
* DIS # C9: 5,8 => CTR => C9: 3,9
* DIS # A1: 5,8 => CTR => A1: 1,2,7
* DIS # C9: 5,9 => CTR => C9: 3,8
* CNT  10 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,C5,F5,F9,H2,H3)
* ....6..4......17.89....82.6.....4.3.35..9...4.8...3.....23....5..12......7..4..62
* PAIR B1: 1,2 BLK 1
A1: 1,2,5,7,8                            # reduction candidate for 1,2
A1: 1,2 => CTR
* ..8.6.543...421798947538216..9.54.3.356.92..4284..3.5...23....5..12......7..4..62
* PAIR H2: 5,9 BLK 3
G1: 5,9,1,3                              # reduction candidate for 5,9
G1: 5,9 => SOLVED
* 718962543265431798934758216129584637356197824487623951892316475641275389573849162
* DURATION: 0:00:04.132985  START: 04:00:55.619281  END: 04:00:59.752266 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0031-base-pr-001.dot
* REASONING
* DIS # A1: 1,2 => CTR => A1: 5,7,8
* PRF A1: 5,7,8 # G1: 5,9 => SOL
* STA A1: 5,7,8 + G1: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=31

Solution

position: 718962543265431798934758216129584637356197824487623951892316475641275389573849162 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:

* DIS # A1: 1,2 => CTR => A1: 5,7,8
* INC # A1: 5,7,8 => UNS
* INC # B4: 1,2 => UNS
* INC # B4: 6,9 => UNS
* INC # G1: 5,9 => UNS
* INC # G1: 1,3 => UNS
* INC # D2: 5,9 => UNS
* INC # D2: 4 => UNS
* PRF # H6: 5,9 => SOL
* INC # H6: 1,2,7 => UNS
* PRF # G1: 1,5 => SOL
* INC # G1: 3,9 => UNS
* PRF # H6: 1,5 => SOL
* INC # H6: 2,7,9 => UNS
* INC # A4: 6,7 => UNS
* INC # C4: 6,7 => UNS
* INC # A6: 6,7 => UNS
* PRF # C6: 6,7 => SOL
* INC # C6: 4,9 => UNS
* DIS # D5: 6,7 => CTR => D5: 1,8
* INC # D5: 1,8 => UNS
* DIS # E4: 2,7 => CTR => E4: 1,5,8
* INC # E4: 1,5,8 => UNS
* INC # E6: 2,7 => UNS
* INC # H5: 2,7 => UNS
* INC # H5: 1,8 => UNS
* INC # F1: 2,7 => UNS
* INC # F1: 5,9 => UNS
* INC # A8: 5,8 => UNS
* DIS # C9: 5,8 => CTR => C9: 3,9
* INC # C9: 3,9 => UNS
* INC # D9: 5,8 => UNS
* INC # D9: 1,9 => UNS
* DIS # A1: 5,8 => CTR => A1: 1,2,7
* INC # A1: 1,2,7 => UNS
* INC # F8: 5,9 => UNS
* INC # D9: 5,9 => UNS
* DIS # C9: 5,9 => CTR => C9: 3,8
* INC # C9: 3,8 => UNS
* INC # F1: 5,9 => UNS
* INC # F1: 2,7 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 1,2 => CTR => A1: 5,7,8
* PRF A1: 5,7,8 # G1: 5,9 => SOL
* STA A1: 5,7,8 + G1: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED