Analysis of zz-www.sudokuwiki.org-0079-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=79

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=79

position: ....6...268.1.2.4....4..5.......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... initial

Autosolve

position: ....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F5: 7,8 => CTR => F5: 6
* DIS # G1: 3,7 => CTR => G1: 1,8
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* PRF # I5: 3,7 => SOL
* CNT   6 HDP CHAINS /  39 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 # F5: 7,8 => CTR => F5: 6
* DIS F5: 6 # G1: 3,7 => CTR => G1: 1,8
* DIS F5: 6 + G1: 1,8 # G4: 3,7 => CTR => G4: 1,2,4,6
* DIS F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 8 => CTR => G8: 3,7
* PRF F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I5: 3,7 => SOL
* STA F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 + I5: 3,7
* CNT   5 HDP CHAINS /  37 HYP OPENED

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

Details

Positions

....6...268.1.2.4....4..5.......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... initial
....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... autosolve
493765812685192347127438569762349185541826973938517624874653291319284756256971438 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
F3: 7,8
G2: 3,7
D4: 3,7
H5: 3,7
E7: 1,5
E8: 8,9
F9: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  => 12 pairs (_) / A3 = 1  =>  7 pairs (_)
E7,F9: 1.. / E7 = 1  => 13 pairs (_) / F9 = 1  =>  9 pairs (_)
A3,I3: 1.. / A3 = 1  =>  7 pairs (_) / I3 = 1  => 12 pairs (_)
F6,F9: 1.. / F6 = 1  => 13 pairs (_) / F9 = 1  =>  9 pairs (_)
B3,C3: 2.. / B3 = 2  =>  7 pairs (_) / C3 = 2  =>  8 pairs (_)
G7,H7: 2.. / G7 = 2  =>  7 pairs (_) / H7 = 2  => 10 pairs (_)
B3,B4: 2.. / B3 = 2  =>  7 pairs (_) / B4 = 2  =>  8 pairs (_)
H6,H7: 2.. / H6 = 2  =>  7 pairs (_) / H7 = 2  => 10 pairs (_)
A1,B1: 4.. / A1 = 4  =>  9 pairs (_) / B1 = 4  =>  7 pairs (_)
E4,E6: 4.. / E4 = 4  => 11 pairs (_) / E6 = 4  =>  9 pairs (_)
G9,I9: 4.. / G9 = 4  =>  7 pairs (_) / I9 = 4  => 11 pairs (_)
F1,E2: 5.. / F1 = 5  =>  9 pairs (_) / E2 = 5  => 13 pairs (_)
I4,I5: 5.. / I4 = 5  =>  8 pairs (_) / I5 = 5  =>  8 pairs (_)
E7,F9: 5.. / E7 = 5  =>  9 pairs (_) / F9 = 5  => 13 pairs (_)
C2,E2: 5.. / C2 = 5  =>  9 pairs (_) / E2 = 5  => 13 pairs (_)
E2,E7: 5.. / E2 = 5  => 13 pairs (_) / E7 = 5  =>  9 pairs (_)
F1,F9: 5.. / F1 = 5  =>  9 pairs (_) / F9 = 5  => 13 pairs (_)
F5,F6: 6.. / F5 = 6  =>  7 pairs (_) / F6 = 6  =>  0 pairs (X)
G4,G6: 6.. / G4 = 6  =>  7 pairs (_) / G6 = 6  =>  7 pairs (_)
D7,D9: 6.. / D7 = 6  =>  8 pairs (_) / D9 = 6  =>  9 pairs (_)
B5,F5: 6.. / B5 = 6  =>  0 pairs (X) / F5 = 6  =>  7 pairs (_)
B7,D7: 6.. / B7 = 6  =>  9 pairs (_) / D7 = 6  =>  8 pairs (_)
G1,I3: 8.. / G1 = 8  => 11 pairs (_) / I3 = 8  => 10 pairs (_)
A6,C6: 9.. / A6 = 9  =>  7 pairs (_) / C6 = 9  =>  7 pairs (_)
* DURATION: 0:00:26.268704  START: 04:50:44.421450  END: 04:51:10.690154 2017-05-01
* CP COUNT: (24)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E8,F3,F9,G2,H5)
* ....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7....
* PAIR F3: 7,8 BLK 2
D1: 7,8,3,9                              # reduction candidate for 7,8
D1: 7,8                                  # 18 pairs
F1: 7,8,5                                # reduction candidate for 7,8
F1: 7,8                                  # 13 pairs
* PAIR F3: 7,8 ROW 3
I3: 7,8,1,3,9                            # reduction candidate for 7,8
I3: 1,3,9                                # 11 pairs
I3: 7,8                                  # 10 pairs
* PAIR F3: 7,8 COL F
F5: 7,8,6                                # reduction candidate for 7,8
F5: 7,8 => CTR
* ...96581268513274....4..56....3.968..61.2.93..3.5.6.....4653....1.2.4.56256.71.9.
F5: 6                                    #  7 pairs
F6: 7,8,1,6                              # reduction candidate for 7,8
F6: 7,8                                  # 11 pairs
* PAIR G2: 3,7 BLK 3
G1: 3,7,1,8                              # reduction candidate for 3,7
G1: 3,7 => CTR
* 4..968.1268.152.49129437568752349.8.8.1.269...3.581.24564813297.1.294856298675431
G1: 1,8                                  #  8 pairs
H1: 3,7,1,9                              # reduction candidate for 3,7
H1: 3,7                                  # 13 pairs
I2: 3,7,9                                # reduction candidate for 3,7
I2: 3,7                                  # 12 pairs
I3: 3,7,1,8,9                            # reduction candidate for 3,7
I3: 3,7                                  # 15 pairs
* PAIR G2: 3,7 ROW 2
C2: 3,7,5,9                              # reduction candidate for 3,7
C2: 3,7                                  # 15 pairs
C2: 5,9                                  #  8 pairs
* PAIR G2: 3,7 COL G
G4: 3,7,1,2,4,6                          # reduction candidate for 3,7
G4: 3,7 => CTR
* ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413
G4: 1,2,4,6                              #  7 pairs
G8: 3,7,8                                # reduction candidate for 3,7
G8: 3,7                                  #  9 pairs
* PAIR D4: 3,7 BLK 5
D5: 3,7,8                                # reduction candidate for 3,7
D5: 8                                    # 17 pairs
D5: 3,7                                  # 12 pairs
* PAIR D4: 3,7 ROW 4
G4: 3,7,1,2,4,6                          # reduction candidate for 3,7
G4: 3,7 => CTR
* ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413
G4: 1,2,4,6                              #  7 pairs
I4: 3,7,1,4,5                            # reduction candidate for 3,7
I4: 3,7                                  # 14 pairs
* PAIR D4: 3,7 COL D
D1: 3,7,8,9                              # reduction candidate for 3,7
D1: 3,7                                  # 17 pairs
D1: 8,9                                  # 12 pairs
* PAIR H5: 3,7 BLK 6
G4: 3,7,1,2,4,6                          # reduction candidate for 3,7
G4: 3,7 => CTR
* ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413
G4: 1,2,4,6                              #  7 pairs
I4: 3,7,1,4,5                            # reduction candidate for 3,7
I4: 3,7                                  # 14 pairs
I5: 3,7,4,5                              # reduction candidate for 3,7
I5: 3,7 => SOLVED
* 493765812685192347127438569762349185541826973938517624874653291319284756256971438
I5: 4,5                                  #  8 pairs
* PAIR H5: 3,7 ROW 5
D5: 3,7,8                                # reduction candidate for 3,7
D5: 8                                    # 17 pairs
D5: 3,7                                  # 12 pairs
* PAIR H5: 3,7 COL H
H1: 3,7,1,9                              # reduction candidate for 3,7
H1: 3,7                                  # 13 pairs
H1: 1,9                                  #  8 pairs
* PAIR E8: 8,9 BLK 8
D7: 8,9,6                                # reduction candidate for 8,9
D7: 8,9                                  #  9 pairs
D9: 8,9,6                                # reduction candidate for 8,9
D9: 8,9                                  #  8 pairs
* PAIR E8: 8,9 ROW 8
A8: 8,9,3,7                              # reduction candidate for 8,9
A8: 8,9                                  # 13 pairs
C8: 8,9,3,7                              # reduction candidate for 8,9
C8: 8,9                                  # 11 pairs
* PAIR E8: 8,9 COL E
E3: 8,9,3                                # reduction candidate for 8,9
E3: 8,9                                  # 10 pairs
E3: 3                                    #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0079-base-pr-000.dot
* REASONING
* DIS # F5: 7,8 => CTR => F5: 6
* DIS # G1: 3,7 => CTR => G1: 1,8
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* PRF # I5: 3,7 => SOL
* CNT   6 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E8,F3,F9,G2,H5)
* ....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7....
* PAIR F3: 7,8 BLK 2
D1: 7,8,3,9                              # reduction candidate for 7,8
D1: 7,8                                  # 18 pairs
F1: 7,8,5                                # reduction candidate for 7,8
F1: 7,8                                  # 13 pairs
* PAIR F3: 7,8 ROW 3
I3: 7,8,1,3,9                            # reduction candidate for 7,8
I3: 1,3,9                                # 11 pairs
I3: 7,8                                  # 10 pairs
* PAIR F3: 7,8 COL F
F5: 7,8,6                                # reduction candidate for 7,8
F5: 7,8 => CTR
* ...96581268513274....4..56....3.968..61.2.93..3.5.6.....4653....1.2.4.56256.71.9.
F6: 7,8,1                                # reduction candidate for 7,8
F6: 7,8                                  # 11 pairs
* RESTART
* PAIR F3: 7,8 COL F
F6: 7,8,1                                # reduction candidate for 7,8
F6: 1                                    # 13 pairs
F6: 7,8                                  # 11 pairs
* PAIR RESTART
* PAIR F3: 7,8 BLK 2
D1: 7,8,3,9                              # reduction candidate for 7,8
D1: 7,8                                  # 20 pairs
F1: 7,8,5                                # reduction candidate for 7,8
F1: 7,8                                  # 13 pairs
* PAIR F3: 7,8 ROW 3
I3: 7,8,1,3,9                            # reduction candidate for 7,8
I3: 1,3,9                                # 11 pairs
I3: 7,8                                  # 10 pairs
* PAIR F3: 7,8 COL F
F6: 7,8,1                                # reduction candidate for 7,8
F6: 1                                    # 13 pairs
F6: 7,8                                  # 11 pairs
* PAIR G2: 3,7 BLK 3
G1: 3,7,1,8                              # reduction candidate for 3,7
G1: 3,7 => CTR
* 4..968.1268.152.49129437568..2.49.8.8.1.269...3.581.24.64813297.1.294856298675431
H1: 3,7,1,9                              # reduction candidate for 3,7
H1: 3,7                                  # 13 pairs
I2: 3,7,9                                # reduction candidate for 3,7
I2: 3,7                                  # 12 pairs
I3: 3,7,1,8,9                            # reduction candidate for 3,7
I3: 3,7                                  # 15 pairs
* PAIR G2: 3,7 ROW 2
C2: 3,7,5,9                              # reduction candidate for 3,7
C2: 3,7                                  # 16 pairs
C2: 5,9                                  #  9 pairs
* PAIR G2: 3,7 COL G
G4: 3,7,1,2,4,6                          # reduction candidate for 3,7
G4: 3,7 => CTR
* ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413
G8: 3,7,8                                # reduction candidate for 3,7
G8: 3,7                                  #  9 pairs
* RESTART
* PAIR G2: 3,7 COL G
G8: 3,7,8                                # reduction candidate for 3,7
G8: 8 => CTR
* 4.39681726871523491..437568...349.81841726935.3.581724564813297.1.294856298675413
* PAIR RESTART
* PAIR G2: 3,7 BLK 3
H1: 3,7,1,9                              # reduction candidate for 3,7
H1: 3,7                                  # 14 pairs
I2: 3,7,9                                # reduction candidate for 3,7
I2: 3,7                                  # 13 pairs
I3: 3,7,1,8,9                            # reduction candidate for 3,7
I3: 3,7                                  # 15 pairs
* PAIR G2: 3,7 ROW 2
C2: 3,7,5,9                              # reduction candidate for 3,7
C2: 3,7                                  # 18 pairs
C2: 5,9                                  # 10 pairs
* PAIR D4: 3,7 BLK 5
D5: 3,7,8                                # reduction candidate for 3,7
D5: 8                                    # 20 pairs
D5: 3,7                                  # 15 pairs
* PAIR D4: 3,7 ROW 4
I4: 3,7,1,4,5                            # reduction candidate for 3,7
I4: 3,7                                  # 16 pairs
I4: 1,4,5                                # 10 pairs
* PAIR D4: 3,7 COL D
D1: 3,7,8,9                              # reduction candidate for 3,7
D1: 3,7                                  # 20 pairs
D1: 8,9                                  # 15 pairs
* PAIR H5: 3,7 BLK 6
I4: 3,7,1,4,5                            # reduction candidate for 3,7
I4: 3,7                                  # 16 pairs
I5: 3,7,4,5                              # reduction candidate for 3,7
I5: 3,7 => SOLVED
* 493765812685192347127438569762349185541826973938517624874653291319284756256971438
* DURATION: 0:00:28.036762  START: 04:51:36.561488  END: 04:52:04.598250 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0079-base-pr-001.dot
* REASONING
* DIS # F5: 7,8 => CTR => F5: 6
* DIS F5: 6 # G1: 3,7 => CTR => G1: 1,8
* DIS F5: 6 + G1: 1,8 # G4: 3,7 => CTR => G4: 1,2,4,6
* DIS F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 8 => CTR => G8: 3,7
* PRF F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I5: 3,7 => SOL
* STA F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 + I5: 3,7
* CNT   5 HDP CHAINS /  37 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=79

Solution

position: 493765812685192347127438569762349185541826973938517624874653291319284756256971438 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 # D1: 7,8 => UNS
* INC # F1: 7,8 => UNS
* INC # I3: 7,8 => UNS
* INC # I3: 1,3,9 => UNS
* DIS # F5: 7,8 => CTR => F5: 6
* INC # F5: 6 => UNS
* INC # F6: 7,8 => UNS
* DIS # G1: 3,7 => CTR => G1: 1,8
* INC # G1: 1,8 => UNS
* INC # H1: 3,7 => UNS
* INC # I2: 3,7 => UNS
* INC # I3: 3,7 => UNS
* INC # C2: 3,7 => UNS
* INC # C2: 5,9 => UNS
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* INC # G4: 1,2,4,6 => UNS
* INC # G8: 3,7 => UNS
* INC # D5: 3,7 => UNS
* INC # D5: 8 => UNS
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* INC # G4: 1,2,4,6 => UNS
* INC # I4: 3,7 => UNS
* INC # D1: 3,7 => UNS
* INC # D1: 8,9 => UNS
* DIS # G4: 3,7 => CTR => G4: 1,2,4,6
* INC # G4: 1,2,4,6 => UNS
* INC # I4: 3,7 => UNS
* PRF # I5: 3,7 => SOL
* INC # I5: 4,5 => UNS
* INC # D5: 3,7 => UNS
* INC # D5: 8 => UNS
* INC # H1: 3,7 => UNS
* INC # H1: 1,9 => UNS
* INC # D7: 8,9 => UNS
* INC # D9: 8,9 => UNS
* INC # A8: 8,9 => UNS
* INC # C8: 8,9 => UNS
* INC # E3: 8,9 => UNS
* INC # E3: 3 => UNS
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 7,8 => UNS
* INC # F1: 7,8 => UNS
* INC # I3: 7,8 => UNS
* INC # I3: 1,3,9 => UNS
* DIS # F5: 7,8 => CTR => F5: 6
* INC F5: 6 # F6: 7,8 => UNS
* INC F5: 6 # F6: 7,8 => UNS
* INC F5: 6 # F6: 1 => UNS
* INC F5: 6 # D1: 7,8 => UNS
* INC F5: 6 # F1: 7,8 => UNS
* INC F5: 6 # I3: 7,8 => UNS
* INC F5: 6 # I3: 1,3,9 => UNS
* INC F5: 6 # F6: 7,8 => UNS
* INC F5: 6 # F6: 1 => UNS
* DIS F5: 6 # G1: 3,7 => CTR => G1: 1,8
* INC F5: 6 + G1: 1,8 # H1: 3,7 => UNS
* INC F5: 6 + G1: 1,8 # I2: 3,7 => UNS
* INC F5: 6 + G1: 1,8 # I3: 3,7 => UNS
* INC F5: 6 + G1: 1,8 # C2: 3,7 => UNS
* INC F5: 6 + G1: 1,8 # C2: 5,9 => UNS
* DIS F5: 6 + G1: 1,8 # G4: 3,7 => CTR => G4: 1,2,4,6
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 3,7 => UNS
* DIS F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 8 => CTR => G8: 3,7
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # H1: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I2: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I3: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # C2: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # C2: 5,9 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D5: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D5: 8 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I4: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I4: 1,4,5 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D1: 3,7 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D1: 8,9 => UNS
* INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I4: 3,7 => UNS
* PRF F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I5: 3,7 => SOL
* STA F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 + I5: 3,7
* CNT  37 HDP CHAINS /  37 HYP OPENED