Analysis of zz-www.sudokuwiki.org-0102-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=102

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=102

position: 52....6..3.7..8.......7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9....57 initial

Autosolve

position: 528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 1,6 => CTR => B3: 9
* DIS # I1: 3 => CTR => I1: 4,9
* DIS # F3: 3,9 => CTR => F3: 2,5,6
* DIS # B7: 7,8 => CTR => B7: 3,4,5
* DIS # A8: 7,8 => CTR => A8: 2
* DIS # B9: 6,8 => CTR => B9: 3,4
* DIS # D9: 3,4 => CTR => D9: 1,8
* DIS # B9: 6,8 => CTR => B9: 3,4
* CNT   8 HDP CHAINS /  45 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 # B3: 1,6 => CTR => B3: 9
* DIS B3: 9 # E2: 6 => CTR => E2: 4,9
* PRF B3: 9 + E2: 4,9 # G6: 1 => SOL
* STA B3: 9 + E2: 4,9 + G6: 1
* CNT   3 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

52....6..3.7..8.......7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9....57 initial
528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257 autosolve
528319674367248519194576823932861745715432968486957132851724396273695481649183257 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A3: 1,6
D2: 2,4
H2: 1,2
I2: 4,9
H3: 1,2
I3: 3,9
G4: 3,7
I5: 6,8
A7: 7,8
A9: 6,8
F9: 3,4
G7: 3,9
I7: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,E1: 1.. / D1 = 1  => 14 pairs (_) / E1 = 1  => 15 pairs (_)
H2,H3: 1.. / H2 = 1  => 14 pairs (_) / H3 = 1  =>  0 pairs (X)
G5,G6: 1.. / G5 = 1  => 22 pairs (_) / G6 = 1  => 14 pairs (_)
D9,E9: 1.. / D9 = 1  => 15 pairs (_) / E9 = 1  => 14 pairs (_)
B2,H2: 1.. / B2 = 1  =>  0 pairs (X) / H2 = 1  => 14 pairs (_)
B6,G6: 1.. / B6 = 1  => 22 pairs (_) / G6 = 1  => 14 pairs (_)
A3,A5: 1.. / A3 = 1  => 14 pairs (_) / A5 = 1  =>  0 pairs (X)
D1,D9: 1.. / D1 = 1  => 14 pairs (_) / D9 = 1  => 15 pairs (_)
E1,E9: 1.. / E1 = 1  => 15 pairs (_) / E9 = 1  => 14 pairs (_)
H2,H3: 2.. / H2 = 2  =>  0 pairs (X) / H3 = 2  => 14 pairs (_)
A8,C8: 2.. / A8 = 2  => 14 pairs (_) / C8 = 2  =>  0 pairs (X)
D2,H2: 2.. / D2 = 2  => 14 pairs (_) / H2 = 2  =>  0 pairs (X)
C4,D4: 2.. / C4 = 2  => 15 pairs (_) / D4 = 2  =>  0 pairs (X)
A5,A8: 2.. / A5 = 2  =>  0 pairs (X) / A8 = 2  => 14 pairs (_)
F3,F5: 2.. / F3 = 2  =>  0 pairs (X) / F5 = 2  => 15 pairs (_)
I1,I3: 3.. / I1 = 3  =>  0 pairs (X) / I3 = 3  => 14 pairs (_)
I1,I2: 4.. / I1 = 4  => 17 pairs (_) / I2 = 4  => 15 pairs (_)
H4,H5: 4.. / H4 = 4  => 14 pairs (_) / H5 = 4  => 13 pairs (_)
B7,B9: 4.. / B7 = 4  => 16 pairs (_) / B9 = 4  => 17 pairs (_)
D3,F3: 5.. / D3 = 5  => 13 pairs (_) / F3 = 5  =>  0 pairs (X)
E6,E8: 5.. / E6 = 5  => 16 pairs (_) / E8 = 5  =>  0 pairs (X)
E2,F3: 6.. / E2 = 6  => 16 pairs (_) / F3 = 6  => 14 pairs (_)
A9,B9: 6.. / A9 = 6  => 14 pairs (_) / B9 = 6  =>  0 pairs (X)
H7,I7: 6.. / H7 = 6  => 17 pairs (_) / I7 = 6  => 12 pairs (_)
B2,E2: 6.. / B2 = 6  => 14 pairs (_) / E2 = 6  => 16 pairs (_)
A3,A9: 6.. / A3 = 6  =>  0 pairs (X) / A9 = 6  => 14 pairs (_)
I5,I7: 6.. / I5 = 6  => 17 pairs (_) / I7 = 6  => 12 pairs (_)
I5,I7: 8.. / I5 = 8  => 12 pairs (_) / I7 = 8  => 17 pairs (_)
B2,B3: 9.. / B2 = 9  =>  0 pairs (X) / B3 = 9  => 15 pairs (_)
G5,H5: 9.. / G5 = 9  => 13 pairs (_) / H5 = 9  => 16 pairs (_)
G5,G7: 9.. / G5 = 9  => 13 pairs (_) / G7 = 9  => 16 pairs (_)
* DURATION: 0:00:45.806012  START: 05:16:44.601953  END: 05:17:30.407965 2017-05-01
* CP COUNT: (31)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,D2,F9,G4,G7,H2,H3,I2,I3,I5,I7)
* 528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257
* PAIR A3: 1,6 BLK 1
B2: 1,6,9                                # reduction candidate for 1,6
B2: 1,6                                  # 15 pairs
B3: 1,6,9                                # reduction candidate for 1,6
B3: 1,6 => CTR
* 528...67.397268514..4.7.82.932..1765..67329484..9.6.32..1.2.3.62.36..4.1..9...257
B3: 9                                    # 15 pairs
* PAIR D2: 2,4 COL D
D4: 2,4,7,8                              # reduction candidate for 2,4
D4: 2,4                                  # 16 pairs
D5: 2,4,5,7,8                            # reduction candidate for 2,4
D5: 2,4                                  # 21 pairs
* PAIR I2: 4,9 BLK 3
I1: 4,9,3                                # reduction candidate for 4,9
I1: 3 => CTR
* 528...673397268514..4.7.829932..1765..6.32.484..9.6.32..1.2.3.62.36..4.1..9...257
I1: 4,9                                  # 14 pairs
* PAIR I2: 4,9 ROW 2
E2: 4,9,6                                # reduction candidate for 4,9
E2: 6                                    # 16 pairs
E2: 4,9                                  # 14 pairs
* PAIR I3: 3,9 BLK 3
I1: 3,9,4                                # reduction candidate for 3,9
I1: 4                                    # 17 pairs
I1: 3,9                                  # 15 pairs
* PAIR I3: 3,9 ROW 3
F3: 3,9,2,5,6                            # reduction candidate for 3,9
F3: 3,9 => CTR
* 528...67.3.7268514..457.82.9.2..1.65..6.32.484..956.32..1.2....2..6..4.1..9...257
F3: 2,5,6                                # 13 pairs
* PAIR G4: 3,7 BLK 6
G6: 3,7,1                                # reduction candidate for 3,7
G6: 3,7                                  # 22 pairs
G6: 1                                    # 14 pairs
* PAIR G4: 3,7 ROW 4
B4: 3,7,8                                # reduction candidate for 3,7
B4: 3,7                                  # 15 pairs
B4: 8                                    # 14 pairs
* PAIR I5: 6,8 BLK 6
H4: 6,8,3,4                              # reduction candidate for 6,8
H4: 6,8                                  # 15 pairs
H5: 6,8,4,9                              # reduction candidate for 6,8
H5: 6,8                                  # 18 pairs
H6: 6,8,3                                # reduction candidate for 6,8
H6: 6,8                                  # 16 pairs
* PAIR A7: 7,8 BLK 7
B7: 7,8,3,4,5                            # reduction candidate for 7,8
B7: 7,8 => CTR
* 528...67.3.72.851.1.4.7.82.9.2..1..5....32..848.956..2..1.2....2..697481649..3257
B7: 3,4,5                                # 13 pairs
A8: 7,8,2                                # reduction candidate for 7,8
A8: 7,8 => CTR
* 528...67.3.7..85..1.4.728..9....1..52...3....4..9....2..1.2......26..4.1..9...257
A8: 2                                    # 14 pairs
B8: 7,8,3,5                              # reduction candidate for 7,8
B8: 7,8                                  # 19 pairs
* PAIR A7: 7,8 ROW 7
D7: 7,8,3,4,5                            # reduction candidate for 7,8
D7: 7,8                                  # 18 pairs
D7: 3,4,5                                # 16 pairs
* PAIR A7: 7,8 COL A
A5: 7,8,1,2                              # reduction candidate for 7,8
A5: 1,2                                  # 15 pairs
A5: 7,8                                  # 14 pairs
* PAIR A9: 6,8 BLK 7
B9: 6,8,3,4                              # reduction candidate for 6,8
B9: 6,8 => CTR
* 528.9.67.3.7.685....4.7.8..9...41..5.5..329464.3956.82741.2...8235687491..9...257
B9: 3,4                                  # 18 pairs
* PAIR F9: 3,4 BLK 8
D7: 3,4,5,7,8                            # reduction candidate for 3,4
D7: 3,4                                  # 22 pairs
F7: 3,4,5,7,9                            # reduction candidate for 3,4
F7: 3,4                                  # 27 pairs
D9: 3,4,1,8                              # reduction candidate for 3,4
D9: 3,4 => CTR
* 5281..67.3.7.685....4.7.8..9...41..5....329464.3956.82741.2...82..687491..9.1.257
D9: 1,8                                  # 14 pairs
* PAIR F9: 3,4 ROW 9
B9: 3,4,6,8                              # reduction candidate for 3,4
B9: 6,8 => CTR
* 528.9.67.3.7.685....4.7.8..9...41..5.5..329464.3956.82741.2...8235687491..9...257
B9: 3,4                                  # 18 pairs
* PAIR F9: 3,4 COL F
F1: 3,4,9                                # reduction candidate for 3,4
F1: 9                                    # 19 pairs
F1: 3,4                                  # 14 pairs
* PAIR G7: 3,9 BLK 9
H7: 3,9,6,8                              # reduction candidate for 3,9
H7: 3,9                                  # 15 pairs
H8: 3,9,8                                # reduction candidate for 3,9
H8: 3,9                                  # 18 pairs
* PAIR G7: 3,9 ROW 7
F7: 3,9,4,5,7                            # reduction candidate for 3,9
F7: 3,9                                  # 21 pairs
F7: 4,5,7                                # 14 pairs
* PAIR I7: 6,8 BLK 9
H7: 6,8,3,9                              # reduction candidate for 6,8
H7: 6,8                                  # 18 pairs
H7: 3,9                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0102-base-pr-000.dot
* REASONING
* DIS # B3: 1,6 => CTR => B3: 9
* DIS # I1: 3 => CTR => I1: 4,9
* DIS # F3: 3,9 => CTR => F3: 2,5,6
* DIS # B7: 7,8 => CTR => B7: 3,4,5
* DIS # A8: 7,8 => CTR => A8: 2
* DIS # B9: 6,8 => CTR => B9: 3,4
* DIS # D9: 3,4 => CTR => D9: 1,8
* DIS # B9: 6,8 => CTR => B9: 3,4
* CNT   8 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,D2,F9,G4,G7,H2,H3,I2,I3,I5,I7)
* 528...67.3.7..85....4.7.8..9....1..5....3....4..9....2..1.2.......6..4.1..9...257
* PAIR A3: 1,6 BLK 1
B2: 1,6,9                                # reduction candidate for 1,6
B2: 1,6                                  # 15 pairs
B3: 1,6,9                                # reduction candidate for 1,6
B3: 1,6 => CTR
* 528...67.397268514..4.7.82.932..1765..67329484..9.6.32..1.2.3.62.36..4.1..9...257
* RESTART
* PAIR D2: 2,4 COL D
D4: 2,4,7,8                              # reduction candidate for 2,4
D4: 2,4                                  # 21 pairs
D5: 2,4,5,7,8                            # reduction candidate for 2,4
D5: 2,4                                  # 25 pairs
* PAIR I2: 4,9 ROW 2
E2: 4,9,6                                # reduction candidate for 4,9
E2: 6 => CTR
* 528.93674317468529694.7.8139...41..51...32946473956182741.2...82..687491869...257
* PAIR RESTART
* PAIR G4: 3,7 BLK 6
G6: 3,7,1                                # reduction candidate for 3,7
G6: 1 => SOLVED
* 528319674367248519194576823932861745715432968486957132851724396273695481649183257
* DURATION: 0:00:09.523924  START: 05:18:05.550706  END: 05:18:15.074630 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0102-base-pr-001.dot
* REASONING
* DIS # B3: 1,6 => CTR => B3: 9
* DIS B3: 9 # E2: 6 => CTR => E2: 4,9
* PRF B3: 9 + E2: 4,9 # G6: 1 => SOL
* STA B3: 9 + E2: 4,9 + G6: 1
* CNT   3 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=102

Solution

position: 528319674367248519194576823932861745715432968486957132851724396273695481649183257 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 # B2: 1,6 => UNS
* DIS # B3: 1,6 => CTR => B3: 9
* INC # B3: 9 => UNS
* INC # D4: 2,4 => UNS
* INC # D5: 2,4 => UNS
* INC # I1: 4,9 => UNS
* DIS # I1: 3 => CTR => I1: 4,9
* INC # E2: 4,9 => UNS
* INC # E2: 6 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 4 => UNS
* DIS # F3: 3,9 => CTR => F3: 2,5,6
* INC # F3: 2,5,6 => UNS
* INC # G6: 3,7 => UNS
* INC # G6: 1 => UNS
* INC # B4: 3,7 => UNS
* INC # B4: 8 => UNS
* INC # H4: 6,8 => UNS
* INC # H5: 6,8 => UNS
* INC # H6: 6,8 => UNS
* DIS # B7: 7,8 => CTR => B7: 3,4,5
* INC # B7: 3,4,5 => UNS
* DIS # A8: 7,8 => CTR => A8: 2
* INC # A8: 2 => UNS
* INC # B8: 7,8 => UNS
* INC # D7: 7,8 => UNS
* INC # D7: 3,4,5 => UNS
* INC # A5: 7,8 => UNS
* INC # A5: 1,2 => UNS
* DIS # B9: 6,8 => CTR => B9: 3,4
* INC # B9: 3,4 => UNS
* INC # D7: 3,4 => UNS
* INC # F7: 3,4 => UNS
* DIS # D9: 3,4 => CTR => D9: 1,8
* INC # D9: 1,8 => UNS
* INC # B9: 3,4 => UNS
* DIS # B9: 6,8 => CTR => B9: 3,4
* INC # F1: 3,4 => UNS
* INC # F1: 9 => UNS
* INC # H7: 3,9 => UNS
* INC # H8: 3,9 => UNS
* INC # F7: 3,9 => UNS
* INC # F7: 4,5,7 => UNS
* INC # H7: 6,8 => UNS
* INC # H7: 3,9 => UNS
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,6 => UNS
* DIS # B3: 1,6 => CTR => B3: 9
* INC B3: 9 # D4: 2,4 => UNS
* INC B3: 9 # D5: 2,4 => UNS
* INC B3: 9 # E2: 4,9 => UNS
* DIS B3: 9 # E2: 6 => CTR => E2: 4,9
* INC B3: 9 + E2: 4,9 # G6: 3,7 => UNS
* PRF B3: 9 + E2: 4,9 # G6: 1 => SOL
* STA B3: 9 + E2: 4,9 + G6: 1
* CNT   8 HDP CHAINS /   8 HYP OPENED