Analysis of zz-www.sudokuwiki.org-0108-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=108

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=108

position: .....6..42.7...1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... initial

Autosolve

position: .....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 3,8 => CTR => C1: 5,9
* DIS # I7: 3,9 => CTR => I7: 1,6
* DIS # H1: 3,9 => CTR => H1: 2,7,8
* PRF # H9: 3 => SOL
* DIS # B8: 6 => CTR => B8: 2,4
* CNT   5 HDP CHAINS /  30 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 # C1: 3,8 => CTR => C1: 5,9
* DIS C1: 5,9 # I7: 3,9 => CTR => I7: 1,6
* DIS C1: 5,9 + I7: 1,6 # H1: 3,9 => CTR => H1: 2,7,8
* PRF C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 3 => SOL
* STA C1: 5,9 + I7: 1,6 + H1: 2,7,8 + H9: 3
* CNT   4 HDP CHAINS /  34 HYP OPENED

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

Details

Positions

.....6..42.7...1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... initial
.....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6..... autosolve
135786924297435186864291753476928315319574268582163479753842691621359847948617532 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
G3: 6,7
G6: 4,5
C7: 3,8
A8: 4,6
D8: 3,9
E8: 3,5
G7: 6,9
H7: 3,9
H8: 2,4
G9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  => 11 pairs (_) / A3 = 1  => 10 pairs (_)
I7,I9: 1.. / I7 = 1  => 14 pairs (_) / I9 = 1  => 14 pairs (_)
A3,F3: 1.. / A3 = 1  => 10 pairs (_) / F3 = 1  => 11 pairs (_)
D7,I7: 1.. / D7 = 1  => 14 pairs (_) / I7 = 1  => 14 pairs (_)
G1,H1: 2.. / G1 = 2  => 11 pairs (_) / H1 = 2  =>  0 pairs (*)
E4,E5: 2.. / E4 = 2  => 10 pairs (_) / E5 = 2  => 12 pairs (_)
B8,B9: 2.. / B8 = 2  =>  7 pairs (_) / B9 = 2  => 16 pairs (_)
E4,I4: 2.. / E4 = 2  => 10 pairs (_) / I4 = 2  => 12 pairs (_)
B8,H8: 2.. / B8 = 2  =>  7 pairs (_) / H8 = 2  => 16 pairs (_)
G1,G5: 2.. / G1 = 2  => 11 pairs (_) / G5 = 2  =>  0 pairs (*)
G6,H6: 4.. / G6 = 4  =>  8 pairs (_) / H6 = 4  =>  0 pairs (X)
G6,G9: 4.. / G6 = 4  =>  8 pairs (_) / G9 = 4  =>  0 pairs (X)
A1,C1: 5.. / A1 = 5  => 22 pairs (_) / C1 = 5  => 10 pairs (_)
E2,F2: 5.. / E2 = 5  => 10 pairs (_) / F2 = 5  => 11 pairs (_)
E8,F8: 5.. / E8 = 5  => 11 pairs (_) / F8 = 5  => 10 pairs (_)
G9,I9: 5.. / G9 = 5  =>  8 pairs (_) / I9 = 5  =>  0 pairs (X)
C1,C4: 5.. / C1 = 5  => 10 pairs (_) / C4 = 5  => 22 pairs (_)
E2,E8: 5.. / E2 = 5  => 10 pairs (_) / E8 = 5  => 11 pairs (_)
F2,F8: 5.. / F2 = 5  => 11 pairs (_) / F8 = 5  => 10 pairs (_)
G6,G9: 5.. / G6 = 5  =>  0 pairs (X) / G9 = 5  =>  8 pairs (_)
E4,E6: 6.. / E4 = 6  =>  0 pairs (X) / E6 = 6  => 10 pairs (_)
A8,B8: 6.. / A8 = 6  => 10 pairs (_) / B8 = 6  =>  0 pairs (X)
G7,I7: 6.. / G7 = 6  =>  9 pairs (_) / I7 = 6  => 20 pairs (_)
B2,I2: 6.. / B2 = 6  => 20 pairs (_) / I2 = 6  => 12 pairs (_)
C3,C4: 6.. / C3 = 6  => 13 pairs (_) / C4 = 6  => 12 pairs (_)
G3,G7: 6.. / G3 = 6  => 20 pairs (_) / G7 = 6  =>  9 pairs (_)
G5,H6: 7.. / G5 = 7  => 20 pairs (_) / H6 = 7  => 10 pairs (_)
A7,B9: 7.. / A7 = 7  => 12 pairs (_) / B9 = 7  => 15 pairs (_)
F3,G3: 7.. / F3 = 7  => 20 pairs (_) / G3 = 7  =>  9 pairs (_)
A7,D7: 7.. / A7 = 7  => 12 pairs (_) / D7 = 7  => 15 pairs (_)
H1,H6: 7.. / H1 = 7  => 20 pairs (_) / H6 = 7  => 10 pairs (_)
D8,F8: 9.. / D8 = 9  => 11 pairs (_) / F8 = 9  => 10 pairs (_)
* DURATION: 0:00:46.115258  START: 05:24:45.088098  END: 05:25:31.203356 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C7,D8,E8,G3,G6,G7,G9,H7,H8)
* .....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6.....
* PAIR C7: 3,8 BLK 7
A7: 3,8,7                                # reduction candidate for 3,8
A7: 3,8                                  # 15 pairs
B9: 3,8,2,4,7                            # reduction candidate for 3,8
B9: 3,8                                  # 10 pairs
C9: 3,8,4                                # reduction candidate for 3,8
C9: 3,8                                  # 18 pairs
* PAIR C7: 3,8 COL C
C1: 3,8,5,9                              # reduction candidate for 3,8
C1: 3,8 => CTR
* 5...169242974..186146298753465827319719534268..2169475.5.74269162195.8479.4681532
C1: 5,9                                  # 11 pairs
C3: 3,8,4,6                              # reduction candidate for 3,8
C3: 3,8                                  # 10 pairs
C5: 3,8,9                                # reduction candidate for 3,8
C5: 3,8                                  # 16 pairs
* PAIR A8: 4,6 BLK 7
B8: 4,6,2                                # reduction candidate for 4,6
B8: 4,6                                  # 16 pairs
B8: 2                                    #  7 pairs
* PAIR A8: 4,6 COL A
A3: 4,6,1,3,8                            # reduction candidate for 4,6
A3: 4,6                                  # 12 pairs
A4: 4,6,5,7,8                            # reduction candidate for 4,6
A4: 4,6                                  # 11 pairs
* PAIR D8: 3,9 BLK 8
F8: 3,9,5                                # reduction candidate for 3,9
F8: 3,9                                  # 11 pairs
F8: 5                                    # 10 pairs
* PAIR D8: 3,9 COL D
D6: 3,9,1,7,8                            # reduction candidate for 3,9
D6: 3,9                                  # 12 pairs
D6: 1,7,8                                # 10 pairs
* PAIR E8: 3,5 BLK 8
F8: 3,5,9                                # reduction candidate for 3,5
F8: 3,5                                  # 11 pairs
F8: 9                                    # 10 pairs
* PAIR E8: 3,5 COL E
E2: 3,5,8                                # reduction candidate for 3,5
E2: 8                                    # 16 pairs
E2: 3,5                                  # 11 pairs
* PAIR G7: 6,9 BLK 9
I7: 6,9,1,3                              # reduction candidate for 6,9
I7: 6,9                                  # 15 pairs
I7: 1,3                                  # 12 pairs
* PAIR H7: 3,9 BLK 9
I7: 3,9,1,6                              # reduction candidate for 3,9
I7: 3,9 => CTR
* ...7162.42.74..1..1..29.75..7..2.31.8135749625923614787581426....19..8.79346875.1
I7: 1,6                                  # 11 pairs
* PAIR H7: 3,9 COL H
H1: 3,9,2,7,8                            # reduction candidate for 3,9
H1: 3,9 => CTR
* 3.5..62942974..186146298753479...31..1.5.496...2...47..5..42639..1...8.79346..521
H1: 2,7,8                                # 10 pairs
H2: 3,9,8                                # reduction candidate for 3,9
H2: 3,9                                  # 14 pairs
* PAIR H8: 2,4 BLK 9
H9: 2,4,3                                # reduction candidate for 2,4
H9: 3 => SOLVED
* 135786924297435186864291753476928315319574268582163479753842691621359847948617532
H9: 2,4                                  # 11 pairs
* PAIR H8: 2,4 ROW 8
B8: 2,4,6                                # reduction candidate for 2,4
B8: 6 => CTR
* .....62.42.74..1.6...29.753.74...31..1.574962.92...47.75.142639461...8279236...41
B8: 2,4                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0108-base-pr-000.dot
* REASONING
* DIS # C1: 3,8 => CTR => C1: 5,9
* DIS # I7: 3,9 => CTR => I7: 1,6
* DIS # H1: 3,9 => CTR => H1: 2,7,8
* PRF # H9: 3 => SOL
* DIS # B8: 6 => CTR => B8: 2,4
* CNT   5 HDP CHAINS /  30 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C7,D8,E8,G3,G6,G7,G9,H7,H8)
* .....6..42.74..1.....29..5.......31..1.5.4.6...2.......5..42.....1...8.79..6.....
* PAIR C7: 3,8 BLK 7
A7: 3,8,7                                # reduction candidate for 3,8
A7: 3,8                                  # 15 pairs
B9: 3,8,2,4,7                            # reduction candidate for 3,8
B9: 3,8                                  # 10 pairs
C9: 3,8,4                                # reduction candidate for 3,8
C9: 3,8                                  # 18 pairs
* PAIR C7: 3,8 COL C
C1: 3,8,5,9                              # reduction candidate for 3,8
C1: 3,8 => CTR
* 5...169242974..186146298753465827319719534268..2169475.5.74269162195.8479.4681532
C3: 3,8,4,6                              # reduction candidate for 3,8
C3: 3,8                                  # 10 pairs
C5: 3,8,9                                # reduction candidate for 3,8
C5: 3,8                                  # 16 pairs
* PAIR RESTART
* PAIR C7: 3,8 BLK 7
A7: 3,8,7                                # reduction candidate for 3,8
A7: 3,8                                  # 16 pairs
B9: 3,8,2,4,7                            # reduction candidate for 3,8
B9: 3,8                                  # 11 pairs
C9: 3,8,4                                # reduction candidate for 3,8
C9: 3,8                                  # 18 pairs
* PAIR C7: 3,8 COL C
C3: 3,8,4,6                              # reduction candidate for 3,8
C3: 3,8                                  # 10 pairs
C5: 3,8,9                                # reduction candidate for 3,8
C5: 3,8                                  # 16 pairs
* PAIR A8: 4,6 BLK 7
B8: 4,6,2                                # reduction candidate for 4,6
B8: 4,6                                  # 16 pairs
B8: 2                                    #  8 pairs
* PAIR A8: 4,6 COL A
A3: 4,6,1,3,8                            # reduction candidate for 4,6
A3: 4,6                                  # 12 pairs
A4: 4,6,5,7,8                            # reduction candidate for 4,6
A4: 4,6                                  # 12 pairs
* PAIR D8: 3,9 BLK 8
F8: 3,9,5                                # reduction candidate for 3,9
F8: 3,9                                  # 12 pairs
F8: 5                                    # 11 pairs
* PAIR D8: 3,9 COL D
D6: 3,9,1,7,8                            # reduction candidate for 3,9
D6: 3,9                                  # 13 pairs
D6: 1,7,8                                # 11 pairs
* PAIR E8: 3,5 BLK 8
F8: 3,5,9                                # reduction candidate for 3,5
F8: 3,5                                  # 12 pairs
F8: 9                                    # 11 pairs
* PAIR E8: 3,5 COL E
E2: 3,5,8                                # reduction candidate for 3,5
E2: 8                                    # 17 pairs
E2: 3,5                                  # 12 pairs
* PAIR G7: 6,9 BLK 9
I7: 6,9,1,3                              # reduction candidate for 6,9
I7: 6,9                                  # 16 pairs
I7: 1,3                                  # 13 pairs
* PAIR H7: 3,9 BLK 9
I7: 3,9,1,6                              # reduction candidate for 3,9
I7: 3,9 => CTR
* ...7162.42.74..1..1..29.75..7..2.31.8135749625923614787581426....19..8.79346875.1
* PAIR H7: 3,9 COL H
H1: 3,9,2,7,8                            # reduction candidate for 3,9
H1: 3,9 => CTR
* .....62342.74..189...29.756..6...31..1.5.496...2.6.47..5..426916.1...8.79..6..5.3
H2: 3,9,8                                # reduction candidate for 3,9
H2: 3,9                                  # 16 pairs
* RESTART
* PAIR H7: 3,9 COL H
H2: 3,9,8                                # reduction candidate for 3,9
H2: 8                                    # 17 pairs
H2: 3,9                                  # 16 pairs
* PAIR RESTART
* PAIR H7: 3,9 COL H
H2: 3,9,8                                # reduction candidate for 3,9
H2: 8                                    # 17 pairs
H2: 3,9                                  # 16 pairs
* PAIR H8: 2,4 BLK 9
H9: 2,4,3                                # reduction candidate for 2,4
H9: 3 => SOLVED
* 135786924297435186864291753476928315319574268582163479753842691621359847948617532
* DURATION: 0:00:29.264777  START: 05:25:54.903798  END: 05:26:24.168575 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0108-base-pr-001.dot
* REASONING
* DIS # C1: 3,8 => CTR => C1: 5,9
* DIS C1: 5,9 # I7: 3,9 => CTR => I7: 1,6
* DIS C1: 5,9 + I7: 1,6 # H1: 3,9 => CTR => H1: 2,7,8
* PRF C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 3 => SOL
* STA C1: 5,9 + I7: 1,6 + H1: 2,7,8 + H9: 3
* CNT   4 HDP CHAINS /  34 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=108

Solution

position: 135786924297435186864291753476928315319574268582163479753842691621359847948617532 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 # A7: 3,8 => UNS
* INC # B9: 3,8 => UNS
* INC # C9: 3,8 => UNS
* DIS # C1: 3,8 => CTR => C1: 5,9
* INC # C1: 5,9 => UNS
* INC # C3: 3,8 => UNS
* INC # C5: 3,8 => UNS
* INC # B8: 4,6 => UNS
* INC # B8: 2 => UNS
* INC # A3: 4,6 => UNS
* INC # A4: 4,6 => UNS
* INC # F8: 3,9 => UNS
* INC # F8: 5 => UNS
* INC # D6: 3,9 => UNS
* INC # D6: 1,7,8 => UNS
* INC # F8: 3,5 => UNS
* INC # F8: 9 => UNS
* INC # E2: 3,5 => UNS
* INC # E2: 8 => UNS
* INC # I7: 6,9 => UNS
* INC # I7: 1,3 => UNS
* DIS # I7: 3,9 => CTR => I7: 1,6
* INC # I7: 1,6 => UNS
* DIS # H1: 3,9 => CTR => H1: 2,7,8
* INC # H1: 2,7,8 => UNS
* INC # H2: 3,9 => UNS
* INC # H9: 2,4 => UNS
* PRF # H9: 3 => SOL
* INC # B8: 2,4 => UNS
* DIS # B8: 6 => CTR => B8: 2,4
* CNT  30 HDP CHAINS /  30 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A7: 3,8 => UNS
* INC # B9: 3,8 => UNS
* INC # C9: 3,8 => UNS
* DIS # C1: 3,8 => CTR => C1: 5,9
* INC C1: 5,9 # C3: 3,8 => UNS
* INC C1: 5,9 # C5: 3,8 => UNS
* INC C1: 5,9 # A7: 3,8 => UNS
* INC C1: 5,9 # B9: 3,8 => UNS
* INC C1: 5,9 # C9: 3,8 => UNS
* INC C1: 5,9 # C3: 3,8 => UNS
* INC C1: 5,9 # C5: 3,8 => UNS
* INC C1: 5,9 # B8: 4,6 => UNS
* INC C1: 5,9 # B8: 2 => UNS
* INC C1: 5,9 # A3: 4,6 => UNS
* INC C1: 5,9 # A4: 4,6 => UNS
* INC C1: 5,9 # F8: 3,9 => UNS
* INC C1: 5,9 # F8: 5 => UNS
* INC C1: 5,9 # D6: 3,9 => UNS
* INC C1: 5,9 # D6: 1,7,8 => UNS
* INC C1: 5,9 # F8: 3,5 => UNS
* INC C1: 5,9 # F8: 9 => UNS
* INC C1: 5,9 # E2: 3,5 => UNS
* INC C1: 5,9 # E2: 8 => UNS
* INC C1: 5,9 # I7: 6,9 => UNS
* INC C1: 5,9 # I7: 1,3 => UNS
* DIS C1: 5,9 # I7: 3,9 => CTR => I7: 1,6
* DIS C1: 5,9 + I7: 1,6 # H1: 3,9 => CTR => H1: 2,7,8
* INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 3,9 => UNS
* INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 3,9 => UNS
* INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 8 => UNS
* INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 3,9 => UNS
* INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H2: 8 => UNS
* INC C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 2,4 => UNS
* PRF C1: 5,9 + I7: 1,6 + H1: 2,7,8 # H9: 3 => SOL
* STA C1: 5,9 + I7: 1,6 + H1: 2,7,8 + H9: 3
* CNT  34 HDP CHAINS /  34 HYP OPENED