Analysis of zz-www.sudokuwiki.org-0103-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=103

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=103

position: ..92....862.........74.61.......7.4.1.8...7.9.7.8.......21.39.........517....83.. initial

Autosolve

position: ..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G1: 4,5 => CTR => G1: 6
* DIS # B9: 4,5 => CTR => B9: 1,6,9
* DIS # A6: 4,5 => CTR => A6: 2,3,9
* CNT   3 HDP CHAINS /  24 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 # G1: 4,5 => CTR => G1: 6
* DIS G1: 6 # I2: 3 => CTR => I2: 4,5
* DIS G1: 6 + I2: 4,5 # B7: 4,5 => CTR => B7: 6
* DIS G1: 6 + I2: 4,5 + B7: 6 # B9: 4,5 => CTR => B9: 1,9
* PRF G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 # C9: 4,5 => SOL
* STA G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 + C9: 4,5
* CNT   5 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

..92....862.........74.61.......7.4.1.8...7.9.7.8.......21.39.........517....83.. initial
..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83.. autosolve
459231678621789534387456192236917845148325769975864213562143987893672451714598326 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
F1: 1,5
G2: 4,5
A7: 4,5
H9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C2: 1.. / B1 = 1  => 10 pairs (_) / C2 = 1  => 10 pairs (_)
F1,F2: 1.. / F1 = 1  => 10 pairs (_) / F2 = 1  => 10 pairs (_)
B9,C9: 1.. / B9 = 1  => 10 pairs (_) / C9 = 1  => 10 pairs (_)
B1,F1: 1.. / B1 = 1  => 10 pairs (_) / F1 = 1  => 10 pairs (_)
C2,F2: 1.. / C2 = 1  => 10 pairs (_) / F2 = 1  => 10 pairs (_)
B1,B9: 1.. / B1 = 1  => 10 pairs (_) / B9 = 1  => 10 pairs (_)
C2,C9: 1.. / C2 = 1  => 10 pairs (_) / C9 = 1  => 10 pairs (_)
H3,I3: 2.. / H3 = 2  =>  0 pairs (X) / I3 = 2  =>  6 pairs (_)
A4,A6: 2.. / A4 = 2  =>  4 pairs (_) / A6 = 2  =>  0 pairs (X)
A4,I4: 2.. / A4 = 2  =>  4 pairs (_) / I4 = 2  =>  0 pairs (X)
G6,G8: 2.. / G6 = 2  =>  8 pairs (_) / G8 = 2  =>  8 pairs (_)
G8,I9: 4.. / G8 = 4  => 12 pairs (_) / I9 = 4  =>  8 pairs (_)
I2,I9: 4.. / I2 = 4  => 12 pairs (_) / I9 = 4  =>  8 pairs (_)
G1,H1: 6.. / G1 = 6  =>  8 pairs (_) / H1 = 6  =>  0 pairs (X)
B7,E7: 6.. / B7 = 6  =>  6 pairs (_) / E7 = 6  =>  9 pairs (_)
E1,D2: 7.. / E1 = 7  =>  7 pairs (_) / D2 = 7  => 10 pairs (_)
H1,H2: 7.. / H1 = 7  => 10 pairs (_) / H2 = 7  =>  7 pairs (_)
D8,E8: 7.. / D8 = 7  =>  7 pairs (_) / E8 = 7  => 10 pairs (_)
E1,H1: 7.. / E1 = 7  =>  7 pairs (_) / H1 = 7  => 10 pairs (_)
D2,H2: 7.. / D2 = 7  => 10 pairs (_) / H2 = 7  =>  7 pairs (_)
D2,D8: 7.. / D2 = 7  => 10 pairs (_) / D8 = 7  =>  7 pairs (_)
E1,E8: 7.. / E1 = 7  =>  7 pairs (_) / E8 = 7  => 10 pairs (_)
A3,B3: 8.. / A3 = 8  =>  5 pairs (_) / B3 = 8  =>  7 pairs (_)
A8,B8: 8.. / A8 = 8  =>  7 pairs (_) / B8 = 8  =>  5 pairs (_)
A3,A8: 8.. / A3 = 8  =>  5 pairs (_) / A8 = 8  =>  7 pairs (_)
B3,B8: 8.. / B3 = 8  =>  7 pairs (_) / B8 = 8  =>  5 pairs (_)
H2,H3: 9.. / H2 = 9  => 13 pairs (_) / H3 = 9  =>  7 pairs (_)
E3,H3: 9.. / E3 = 9  => 13 pairs (_) / H3 = 9  =>  7 pairs (_)
* DURATION: 0:00:33.138706  START: 05:18:30.366505  END: 05:19:03.505211 2017-05-01
* CP COUNT: (28)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,F1,G2,H9)
* ..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83..
* PAIR F1: 1,5 BLK 2
F2: 1,5,9                                # reduction candidate for 1,5
F2: 9                                    # 13 pairs
F2: 1,5                                  # 10 pairs
* PAIR F1: 1,5 ROW 1
B1: 1,5,3,4                              # reduction candidate for 1,5
B1: 3,4                                  # 11 pairs
B1: 1,5                                  #  8 pairs
* PAIR G2: 4,5 BLK 3
G1: 4,5,6                                # reduction candidate for 4,5
G1: 4,5 => CTR
* 439271568621.8.4738574361922953178461.8...7393748..21.5421639879837..651716..8324
G1: 6                                    #  8 pairs
I2: 4,5,3                                # reduction candidate for 4,5
I2: 4,5                                  # 12 pairs
* PAIR G2: 4,5 ROW 2
C2: 4,5,1,3                              # reduction candidate for 4,5
C2: 4,5                                  # 21 pairs
C2: 1,3                                  #  6 pairs
* PAIR A7: 4,5 BLK 7
B7: 4,5,6                                # reduction candidate for 4,5
B7: 4,5                                  #  9 pairs
B9: 4,5,1,6,9                            # reduction candidate for 4,5
B9: 4,5 => CTR
* .192.5..862..81..3..74.61.....31784.148..273937.849.1.4621.3987..3....517.1..83.4
B9: 1,6,9                                #  4 pairs
C9: 4,5,1,6                              # reduction candidate for 4,5
C9: 4,5                                  # 12 pairs
* PAIR A7: 4,5 ROW 7
E7: 4,5,6                                # reduction candidate for 4,5
E7: 6                                    #  9 pairs
E7: 4,5                                  #  6 pairs
* PAIR A7: 4,5 COL A
A1: 4,5,3                                # reduction candidate for 4,5
A1: 4,5                                  #  6 pairs
A6: 4,5,2,3,9                            # reduction candidate for 4,5
A6: 4,5 => CTR
* 3492.1678621789.3.85743619229.31784.138..57.9.7.892513562143987983....517....83..
A6: 2,3,9                                #  4 pairs
* PAIR H9: 2,6 BLK 9
G8: 2,6,4                                # reduction candidate for 2,6
G8: 2,6                                  #  8 pairs
I9: 2,6,4                                # reduction candidate for 2,6
I9: 2,6                                  # 12 pairs
* PAIR H9: 2,6 ROW 9
E9: 2,6,4,5,9                            # reduction candidate for 2,6
E9: 2,6                                  # 11 pairs
E9: 4,5,9                                #  8 pairs
* PAIR H9: 2,6 COL H
H5: 2,6,3                                # reduction candidate for 2,6
H5: 2,6                                  # 14 pairs
H5: 3                                    #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0103-base-pr-000.dot
* REASONING
* DIS # G1: 4,5 => CTR => G1: 6
* DIS # B9: 4,5 => CTR => B9: 1,6,9
* DIS # A6: 4,5 => CTR => A6: 2,3,9
* CNT   3 HDP CHAINS /  24 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,F1,G2,H9)
* ..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83..
* PAIR F1: 1,5 BLK 2
F2: 1,5,9                                # reduction candidate for 1,5
F2: 9                                    # 13 pairs
F2: 1,5                                  # 10 pairs
* PAIR F1: 1,5 ROW 1
B1: 1,5,3,4                              # reduction candidate for 1,5
B1: 3,4                                  # 11 pairs
B1: 1,5                                  #  8 pairs
* PAIR G2: 4,5 BLK 3
G1: 4,5,6                                # reduction candidate for 4,5
G1: 4,5 => CTR
* 439271568621.8.4738574361922953178461.8...7393748..21.5421639879837..651716..8324
I2: 4,5,3                                # reduction candidate for 4,5
I2: 4,5                                  # 12 pairs
* RESTART
* PAIR G2: 4,5 BLK 3
I2: 4,5,3                                # reduction candidate for 4,5
I2: 3 => CTR
* ..923.67862.78.493..7496125...31784.1.8..2739.74869512.62153987..36742517..928364
* PAIR A7: 4,5 BLK 7
B7: 4,5,6                                # reduction candidate for 4,5
B7: 4,5 => CTR
* 4192756386239814758574.61....5.1784.1.8.54729.748.2516542163987.86.49251791528364
B9: 4,5,1,9                              # reduction candidate for 4,5
B9: 4,5 => CTR
* .192.56.8623.81.....74.61......1784.1.8...7.9.7.8...1..621.3987..4...25175...83..
C9: 4,5,1                                # reduction candidate for 4,5
C9: 4,5 => SOLVED
* 459231678621789534387456192236917845148325769975864213562143987893672451714598326
* DURATION: 0:00:10.830818  START: 05:19:19.673560  END: 05:19:30.504378 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0103-base-pr-001.dot
* REASONING
* DIS # G1: 4,5 => CTR => G1: 6
* DIS G1: 6 # I2: 3 => CTR => I2: 4,5
* DIS G1: 6 + I2: 4,5 # B7: 4,5 => CTR => B7: 6
* DIS G1: 6 + I2: 4,5 + B7: 6 # B9: 4,5 => CTR => B9: 1,9
* PRF G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 # C9: 4,5 => SOL
* STA G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 + C9: 4,5
* CNT   5 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=103

Solution

position: 459231678621789534387456192236917845148325769975864213562143987893672451714598326 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 # F2: 1,5 => UNS
* INC # F2: 9 => UNS
* INC # B1: 1,5 => UNS
* INC # B1: 3,4 => UNS
* DIS # G1: 4,5 => CTR => G1: 6
* INC # G1: 6 => UNS
* INC # I2: 4,5 => UNS
* INC # C2: 4,5 => UNS
* INC # C2: 1,3 => UNS
* INC # B7: 4,5 => UNS
* DIS # B9: 4,5 => CTR => B9: 1,6,9
* INC # B9: 1,6,9 => UNS
* INC # C9: 4,5 => UNS
* INC # E7: 4,5 => UNS
* INC # E7: 6 => UNS
* INC # A1: 4,5 => UNS
* DIS # A6: 4,5 => CTR => A6: 2,3,9
* INC # A6: 2,3,9 => UNS
* INC # G8: 2,6 => UNS
* INC # I9: 2,6 => UNS
* INC # E9: 2,6 => UNS
* INC # E9: 4,5,9 => UNS
* INC # H5: 2,6 => UNS
* INC # H5: 3 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 1,5 => UNS
* INC # F2: 9 => UNS
* INC # B1: 1,5 => UNS
* INC # B1: 3,4 => UNS
* DIS # G1: 4,5 => CTR => G1: 6
* INC G1: 6 # I2: 4,5 => UNS
* INC G1: 6 # I2: 4,5 => UNS
* DIS G1: 6 # I2: 3 => CTR => I2: 4,5
* DIS G1: 6 + I2: 4,5 # B7: 4,5 => CTR => B7: 6
* DIS G1: 6 + I2: 4,5 + B7: 6 # B9: 4,5 => CTR => B9: 1,9
* PRF G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 # C9: 4,5 => SOL
* STA G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 + C9: 4,5
* CNT  11 HDP CHAINS /  11 HYP OPENED