Analysis of zz-www.sudokuwiki.org-0020-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=20

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=20

position: .8.9...1......3.....21.48.38.....5...9..6..7...7.....21.83.57.....8......2...9.4. initial

Autosolve

position: .8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 2 => CTR => E1: 5,7
* DIS # A3: 5,7 => CTR => A3: 6,9
* DIS # H4: 6 => CTR => H4: 3,9
* DIS # G6: 4,6 => CTR => G6: 3,9
* DIS # B8: 4,6 => CTR => B8: 3,7
* DIS # C8: 4,6 => CTR => C8: 3,9
* DIS # E8: 1,7 => CTR => E8: 2,4
* DIS # F8: 2 => CTR => F8: 6,7
* PRF # D2: 2 => SOL
* DIS # E8: 1,7 => CTR => E8: 2,4
* DIS # H7: 6,9 => CTR => H7: 2
* CNT  11 HDP CHAINS /  43 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: 2 => CTR => E1: 5,7
* DIS E1: 5,7 # A3: 5,7 => CTR => A3: 6,9
* DIS E1: 5,7 + A3: 6,9 # B3: 6 => CTR => B3: 5,7
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 6 => CTR => H4: 3,9
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 # C5: 4,5 => CTR => C5: 1,3
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 6 => CTR => G6: 3,9
* PRF E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 # A8: 4,6 => SOL
* STA E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 + A8: 4,6
* CNT   7 HDP CHAINS /  12 HYP OPENED

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

Details

Positions

.8.9...1......3.....21.48.38.....5...9..6..7...7.....21.83.57.....8......2...9.4. initial
.8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48 autosolve
384976215516283497972154863841792536293568174657431982168345729439827651725619348 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
E3: 5,7
D4: 2,7
E4: 3,9
F4: 2,7
D5: 4,5
D6: 4,5
E6: 3,9
I5: 1,4
B7: 4,6
E7: 2,4
D9: 6,7
E9: 1,7
I7: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 1.. / B2 = 1  => 13 pairs (_) / C2 = 1  => 13 pairs (_)
E8,E9: 1.. / E8 = 1  =>  0 pairs (X) / E9 = 1  => 13 pairs (_)
E9,G9: 1.. / E9 = 1  => 13 pairs (_) / G9 = 1  =>  0 pairs (X)
B2,B4: 1.. / B2 = 1  => 13 pairs (_) / B4 = 1  => 13 pairs (_)
D4,F4: 2.. / D4 = 2  => 15 pairs (_) / F4 = 2  =>  0 pairs (*)
E7,H7: 2.. / E7 = 2  =>  0 pairs (X) / H7 = 2  => 14 pairs (_)
D2,D4: 2.. / D2 = 2  =>  0 pairs (*) / D4 = 2  =>  0 pairs (X)
A1,C1: 3.. / A1 = 3  => 13 pairs (_) / C1 = 3  => 19 pairs (_)
E4,E6: 3.. / E4 = 3  =>  0 pairs (X) / E6 = 3  => 12 pairs (_)
C5,G5: 3.. / C5 = 3  => 15 pairs (_) / G5 = 3  => 18 pairs (_)
H4,H8: 3.. / H4 = 3  => 15 pairs (_) / H8 = 3  => 18 pairs (_)
D5,D6: 4.. / D5 = 4  =>  0 pairs (X) / D6 = 4  => 11 pairs (_)
E7,E8: 4.. / E7 = 4  => 14 pairs (_) / E8 = 4  =>  0 pairs (X)
B7,E7: 4.. / B7 = 4  =>  0 pairs (X) / E7 = 4  => 14 pairs (_)
E1,E3: 5.. / E1 = 5  => 17 pairs (_) / E3 = 5  => 15 pairs (_)
D5,D6: 5.. / D5 = 5  => 11 pairs (_) / D6 = 5  =>  0 pairs (X)
A9,C9: 5.. / A9 = 5  => 15 pairs (_) / C9 = 5  => 11 pairs (_)
H8,I8: 5.. / H8 = 5  => 16 pairs (_) / I8 = 5  => 14 pairs (_)
C5,D5: 5.. / C5 = 5  =>  0 pairs (X) / D5 = 5  => 11 pairs (_)
F1,D2: 6.. / F1 = 6  => 17 pairs (_) / D2 = 6  => 14 pairs (_)
F8,D9: 6.. / F8 = 6  => 14 pairs (_) / D9 = 6  => 17 pairs (_)
D2,D9: 6.. / D2 = 6  => 14 pairs (_) / D9 = 6  => 17 pairs (_)
F1,F8: 6.. / F1 = 6  => 17 pairs (_) / F8 = 6  => 14 pairs (_)
I1,I2: 7.. / I1 = 7  => 15 pairs (_) / I2 = 7  => 14 pairs (_)
D4,F4: 7.. / D4 = 7  =>  0 pairs (*) / F4 = 7  =>  0 pairs (X)
E4,E6: 9.. / E4 = 9  => 12 pairs (_) / E6 = 9  =>  0 pairs (X)
A8,C8: 9.. / A8 = 9  =>  0 pairs (X) / C8 = 9  => 13 pairs (_)
H7,I7: 9.. / H7 = 9  =>  0 pairs (X) / I7 = 9  => 13 pairs (_)
A3,H3: 9.. / A3 = 9  => 14 pairs (_) / H3 = 9  =>  0 pairs (X)
E6,G6: 9.. / E6 = 9  =>  0 pairs (X) / G6 = 9  => 12 pairs (_)
C2,C8: 9.. / C2 = 9  =>  0 pairs (X) / C8 = 9  => 13 pairs (_)
G2,G6: 9.. / G2 = 9  =>  0 pairs (X) / G6 = 9  => 12 pairs (_)
* DURATION: 0:00:46.264106  START: 03:45:41.841693  END: 03:46:28.105799 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,D4,D5,D6,D9,E3,E4,E6,E7,E9,F4,I5,I7)
* .8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48
* PAIR E3: 5,7 BLK 2
E1: 5,7,2                                # reduction candidate for 5,7
E1: 2 => CTR
* .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48
E1: 5,7                                  # 18 pairs
* PAIR E3: 5,7 ROW 3
A3: 5,7,6,9                              # reduction candidate for 5,7
A3: 5,7 => CTR
* 38.9...1.47..83....621.48938...9.536293568.7.657431982148325769.3.84.....2..19348
A3: 6,9                                  # 14 pairs
B3: 5,7,6                                # reduction candidate for 5,7
B3: 5,7                                  # 16 pairs
* PAIR D4: 2,7 COL D
D2: 2,7,6                                # reduction candidate for 2,7
D2: 2,7                                  # 17 pairs
D2: 6                                    # 14 pairs
* PAIR E4: 3,9 ROW 4
H4: 3,9,6                                # reduction candidate for 3,9
H4: 6 => CTR
* .8.9...1.....83.....21.48.38.....56.29..6837...7..1.82148325796.7.846.35.2...9.48
H4: 3,9                                  # 14 pairs
* PAIR F4: 2,7 COL F
F1: 2,7,6                                # reduction candidate for 2,7
F1: 2,7                                  # 14 pairs
F8: 2,7,6                                # reduction candidate for 2,7
F8: 2,7                                  # 17 pairs
* PAIR D5: 4,5 ROW 5
C5: 4,5,1,3                              # reduction candidate for 4,5
C5: 4,5                                  # 18 pairs
C5: 1,3                                  # 12 pairs
* PAIR D6: 4,5 ROW 6
A6: 4,5,3,6                              # reduction candidate for 4,5
A6: 4,5                                  # 15 pairs
B6: 4,5,3,6                              # reduction candidate for 4,5
B6: 4,5                                  # 15 pairs
* PAIR E6: 3,9 ROW 6
G6: 3,9,4,6                              # reduction candidate for 3,9
G6: 4,6 => CTR
* .8.95..1....68392.9.21748538..23756929..6837..37.91.821.83.57....98...35.2..19648
G6: 3,9                                  # 14 pairs
* PAIR I5: 1,4 BLK 6
I4: 1,4,6,9                              # reduction candidate for 1,4
I4: 1,4                                  # 21 pairs
G5: 1,4,3                                # reduction candidate for 1,4
G5: 1,4                                  # 15 pairs
* PAIR I5: 1,4 ROW 5
C5: 1,4,3,5                              # reduction candidate for 1,4
C5: 1,4                                  # 21 pairs
C5: 3,5                                  # 14 pairs
* PAIR B7: 4,6 BLK 7
A8: 4,6,3,7,9                            # reduction candidate for 4,6
A8: 4,6                                  # 16 pairs
B8: 4,6,3,7                              # reduction candidate for 4,6
B8: 4,6 => CTR
* .8.9..21.4..2839579721548638.4...59629..683716.7.914821683457297498...35.2...9.48
B8: 3,7                                  # 14 pairs
C8: 4,6,3,9                              # reduction candidate for 4,6
C8: 4,6 => CTR
* .8.9...1..19.83.....21.48938...9.5..29..68.7...7.319821483257699.6847...725619348
C8: 3,9                                  # 14 pairs
* PAIR B7: 4,6 COL B
B2: 4,6,1,5,7                            # reduction candidate for 4,6
B2: 4,6                                  # 19 pairs
B4: 4,6,1,3                              # reduction candidate for 4,6
B4: 4,6                                  # 19 pairs
B6: 4,6,3,5                              # reduction candidate for 4,6
B6: 4,6                                  # 19 pairs
* PAIR E7: 2,4 BLK 8
E8: 2,4,1,7                              # reduction candidate for 2,4
E8: 1,7 => CTR
* .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48
E8: 2,4                                  # 18 pairs
* PAIR D9: 6,7 BLK 8
F8: 6,7,2                                # reduction candidate for 6,7
F8: 2 => CTR
* .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48
F8: 6,7                                  # 18 pairs
* PAIR D9: 6,7 ROW 9
A9: 6,7,3,5                              # reduction candidate for 6,7
A9: 6,7                                  # 16 pairs
A9: 3,5                                  # 15 pairs
* PAIR D9: 6,7 COL D
D2: 6,7,2                                # reduction candidate for 6,7
D2: 2 => SOLVED
* 384976215516283497972154863841792536293568174657431982168345729439827651725619348
D2: 6,7                                  # 15 pairs
* PAIR E9: 1,7 BLK 8
E8: 1,7,2,4                              # reduction candidate for 1,7
E8: 1,7 => CTR
* .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48
E8: 2,4                                  # 18 pairs
* PAIR I7: 6,9 BLK 9
H7: 6,9,2                                # reduction candidate for 6,9
H7: 6,9 => CTR
* 38.9...1.4.1.83.9.962174853814.9.536293568.7...7431982148325769.3.84.....2..19348
H7: 2                                    # 14 pairs
* PAIR I7: 6,9 COL I
I2: 6,9,4,5,7                            # reduction candidate for 6,9
I2: 6,9                                  # 23 pairs
I4: 6,9,1,4                              # reduction candidate for 6,9
I4: 6,9                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0020-base-pr-000.dot
* REASONING
* DIS # E1: 2 => CTR => E1: 5,7
* DIS # A3: 5,7 => CTR => A3: 6,9
* DIS # H4: 6 => CTR => H4: 3,9
* DIS # G6: 4,6 => CTR => G6: 3,9
* DIS # B8: 4,6 => CTR => B8: 3,7
* DIS # C8: 4,6 => CTR => C8: 3,9
* DIS # E8: 1,7 => CTR => E8: 2,4
* DIS # F8: 2 => CTR => F8: 6,7
* PRF # D2: 2 => SOL
* DIS # E8: 1,7 => CTR => E8: 2,4
* DIS # H7: 6,9 => CTR => H7: 2
* CNT  11 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,D4,D5,D6,D9,E3,E4,E6,E7,E9,F4,I5,I7)
* .8.9...1.....83.....21.48.38.....5..29..68.7...7..1.821.83.57.....8......2...9.48
* PAIR E3: 5,7 BLK 2
E1: 5,7,2                                # reduction candidate for 5,7
E1: 2 => CTR
* .8.926417..67832.59721548638..297536293568174657431982168345729.398.2651.256.9.48
* PAIR E3: 5,7 ROW 3
A3: 5,7,6,9                              # reduction candidate for 5,7
A3: 5,7 => CTR
* 38.9...1.47..83....621.48938...9.536293568.7.657431982148325769.3.84.....2..19348
B3: 5,7,6                                # reduction candidate for 5,7
B3: 5,7                                  # 21 pairs
* RESTART
* PAIR E3: 5,7 ROW 3
B3: 5,7,6                                # reduction candidate for 5,7
B3: 6 => CTR
* 38495..17.71.83..4962174853816...53.293568471.574319821483257...3984.125.2..19348
* PAIR RESTART
* PAIR E4: 3,9 ROW 4
H4: 3,9,6                                # reduction candidate for 3,9
H4: 6 => CTR
* .8.9...1....683.5.6.21.48938..2.756.29..68.7..67..19821483257.....8...35.2..19648
* PAIR RESTART
* PAIR D5: 4,5 ROW 5
C5: 4,5,1,3                              # reduction candidate for 4,5
C5: 4,5 => CTR
* .8.9...1....683.5...21.48638..23759629..68371.37.914821.83.57.....8..135.2..19648
* PAIR RESTART
* PAIR E6: 3,9 ROW 6
G6: 3,9,6                                # reduction candidate for 3,9
G6: 6 => CTR
* .8.9...1.....839..9.21.48638.....59.29.568374..74916821.83.57.....8......2..19.48
* PAIR RESTART
* PAIR B7: 4,6 BLK 7
A8: 4,6,7,9                              # reduction candidate for 4,6
A8: 4,6 => SOLVED
* 384976215516283497972154863841792536293568174657431982168345729439827651725619348
* DURATION: 0:00:14.429251  START: 03:47:03.620694  END: 03:47:18.049945 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0020-base-pr-001.dot
* REASONING
* DIS # E1: 2 => CTR => E1: 5,7
* DIS E1: 5,7 # A3: 5,7 => CTR => A3: 6,9
* DIS E1: 5,7 + A3: 6,9 # B3: 6 => CTR => B3: 5,7
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 6 => CTR => H4: 3,9
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 # C5: 4,5 => CTR => C5: 1,3
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 6 => CTR => G6: 3,9
* PRF E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 # A8: 4,6 => SOL
* STA E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 + A8: 4,6
* CNT   7 HDP CHAINS /  12 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=20

Solution

position: 384976215516283497972154863841792536293568174657431982168345729439827651725619348 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 # E1: 5,7 => UNS
* DIS # E1: 2 => CTR => E1: 5,7
* DIS # A3: 5,7 => CTR => A3: 6,9
* INC # A3: 6,9 => UNS
* INC # B3: 5,7 => UNS
* INC # D2: 2,7 => UNS
* INC # D2: 6 => UNS
* INC # H4: 3,9 => UNS
* DIS # H4: 6 => CTR => H4: 3,9
* INC # F1: 2,7 => UNS
* INC # F8: 2,7 => UNS
* INC # C5: 4,5 => UNS
* INC # C5: 1,3 => UNS
* INC # A6: 4,5 => UNS
* INC # B6: 4,5 => UNS
* INC # G6: 3,9 => UNS
* DIS # G6: 4,6 => CTR => G6: 3,9
* INC # I4: 1,4 => UNS
* INC # G5: 1,4 => UNS
* INC # C5: 1,4 => UNS
* INC # C5: 3,5 => UNS
* INC # A8: 4,6 => UNS
* DIS # B8: 4,6 => CTR => B8: 3,7
* INC # B8: 3,7 => UNS
* DIS # C8: 4,6 => CTR => C8: 3,9
* INC # C8: 3,9 => UNS
* INC # B2: 4,6 => UNS
* INC # B4: 4,6 => UNS
* INC # B6: 4,6 => UNS
* INC # E8: 2,4 => UNS
* DIS # E8: 1,7 => CTR => E8: 2,4
* INC # F8: 6,7 => UNS
* DIS # F8: 2 => CTR => F8: 6,7
* INC # A9: 6,7 => UNS
* INC # A9: 3,5 => UNS
* INC # D2: 6,7 => UNS
* PRF # D2: 2 => SOL
* DIS # E8: 1,7 => CTR => E8: 2,4
* INC # E8: 2,4 => UNS
* DIS # H7: 6,9 => CTR => H7: 2
* INC # H7: 2 => UNS
* INC # I2: 6,9 => UNS
* INC # I4: 6,9 => UNS
* CNT  43 HDP CHAINS /  43 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 5,7 => UNS
* DIS # E1: 2 => CTR => E1: 5,7
* DIS E1: 5,7 # A3: 5,7 => CTR => A3: 6,9
* INC E1: 5,7 + A3: 6,9 # B3: 5,7 => UNS
* INC E1: 5,7 + A3: 6,9 # B3: 5,7 => UNS
* DIS E1: 5,7 + A3: 6,9 # B3: 6 => CTR => B3: 5,7
* INC E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 3,9 => UNS
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 # H4: 6 => CTR => H4: 3,9
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 # C5: 4,5 => CTR => C5: 1,3
* INC E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 3,9 => UNS
* DIS E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 # G6: 6 => CTR => G6: 3,9
* PRF E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 # A8: 4,6 => SOL
* STA E1: 5,7 + A3: 6,9 + B3: 5,7 + H4: 3,9 + C5: 1,3 + G6: 3,9 + A8: 4,6
* CNT  12 HDP CHAINS /  12 HYP OPENED