Analysis of zz-www.sudokuwiki.org-0133-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=133

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=133

position: 6..7.4....3..9..8...96....11.........4.3...9.........27....14......3..5....4.7..6 initial

Autosolve

position: 6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 2,5 => CTR => E1: 1,8
* PRF # D2: 2,5 => SOL
* DIS # D2: 1 => CTR => D2: 2,5
* DIS # E3: 2,5 => CTR => E3: 8
* DIS # A2: 2,5 => CTR => A2: 4
* PRF # A2: 4 => SOL
* DIS # C2: 2,5 => CTR => C2: 1,4,7
* DIS # I2: 5 => CTR => I2: 4,7
* DIS # D7: 2,5 => CTR => D7: 8,9
* PRF # E7: 2,5 => SOL
* DIS # E7: 6 => CTR => E7: 2,5
* DIS # A9: 2,5 => CTR => A9: 3,8,9
* DIS # E1: 2,5 => CTR => E1: 1,8
* DIS # E3: 2,5 => CTR => E3: 8
* DIS # E4: 2,5 => CTR => E4: 4,6,7
* DIS # E5: 2,5 => CTR => E5: 1,6,7
* DIS # G9: 2,3 => CTR => G9: 8,9
* CNT  17 HDP CHAINS /  38 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: 2,5 => CTR => E1: 1,8
* PRF E1: 1,8 # D2: 2,5 => SOL
* STA E1: 1,8 + D2: 2,5
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

6..7.4....3..9..8...96....11.........4.3...9.........27....14......3..5....4.7..6 initial
6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16 autosolve
682714539431295687579683241123579864847362195965148372796851423214936758358427916 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
F2: 2,5
H1: 2,3
H3: 4,7
E9: 2,5
H7: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D2: 1.. / E1 = 1  =>  0 pairs (*) / D2 = 1  =>  0 pairs (X)
G5,G6: 1.. / G5 = 1  =>  5 pairs (_) / G6 = 1  =>  0 pairs (X)
B8,C8: 1.. / B8 = 1  =>  5 pairs (_) / C8 = 1  =>  0 pairs (X)
C2,D2: 1.. / C2 = 1  =>  0 pairs (*) / D2 = 1  =>  0 pairs (X)
E5,G5: 1.. / E5 = 1  =>  0 pairs (X) / G5 = 1  =>  5 pairs (_)
B1,B8: 1.. / B1 = 1  =>  0 pairs (X) / B8 = 1  =>  5 pairs (_)
D2,D6: 1.. / D2 = 1  =>  0 pairs (X) / D6 = 1  =>  0 pairs (_)
H1,H7: 2.. / H1 = 2  =>  7 pairs (_) / H7 = 2  =>  5 pairs (_)
A6,A9: 3.. / A6 = 3  =>  5 pairs (_) / A9 = 3  =>  5 pairs (_)
H1,H7: 3.. / H1 = 3  =>  5 pairs (_) / H7 = 3  =>  7 pairs (_)
I2,H3: 4.. / I2 = 4  =>  0 pairs (X) / H3 = 4  =>  8 pairs (_)
E4,E6: 4.. / E4 = 4  =>  0 pairs (X) / E6 = 4  =>  6 pairs (_)
A8,C8: 4.. / A8 = 4  =>  0 pairs (X) / C8 = 4  =>  0 pairs (_)
A3,H3: 4.. / A3 = 4  =>  0 pairs (X) / H3 = 4  =>  8 pairs (_)
E6,H6: 4.. / E6 = 4  =>  6 pairs (_) / H6 = 4  =>  0 pairs (X)
C2,C8: 4.. / C2 = 4  =>  0 pairs (X) / C8 = 4  =>  0 pairs (_)
I2,I4: 4.. / I2 = 4  =>  0 pairs (X) / I4 = 4  =>  8 pairs (_)
H4,H6: 6.. / H4 = 6  =>  6 pairs (_) / H6 = 6  =>  6 pairs (_)
E7,F8: 6.. / E7 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
C2,B3: 7.. / C2 = 7  =>  0 pairs (X) / B3 = 7  =>  9 pairs (_)
G8,I8: 7.. / G8 = 7  =>  8 pairs (_) / I8 = 7  =>  0 pairs (X)
C2,I2: 7.. / C2 = 7  =>  0 pairs (X) / I2 = 7  =>  9 pairs (_)
E1,E3: 8.. / E1 = 8  =>  0 pairs (X) / E3 = 8  =>  5 pairs (_)
G1,I1: 9.. / G1 = 9  =>  8 pairs (_) / I1 = 9  =>  7 pairs (_)
* DURATION: 0:00:35.854877  START: 06:00:18.704757  END: 06:00:54.559634 2017-05-01
* CP COUNT: (24)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E9,F2,H1,H3,H7)
* 6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16
* PAIR F2: 2,5 BLK 2
E1: 2,5,1,8                              # reduction candidate for 2,5
E1: 2,5 => CTR
* 6..7.4....3419.687.79683.411.......484.3...95....4.1.27...614..4...3.75....4.7.16
E1: 1,8                                  #  6 pairs
D2: 2,5,1                                # reduction candidate for 2,5
D2: 2,5 => SOLVED
* 682714539431295687579683241123579864847362195965148372796851423214936758358427916
D2: 1 => CTR
* 6..7.4...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16
E3: 2,5,8                                # reduction candidate for 2,5
E3: 2,5 => CTR
* 6..784...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16
E3: 8                                    #  5 pairs
* PAIR F2: 2,5 ROW 2
A2: 2,5,4                                # reduction candidate for 2,5
A2: 2,5 => CTR
* 6..7.4...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16
A2: 4 => SOLVED
* 682714539431295687579683241123579864847362195965148372796851423214936758358427916
C2: 2,5,1,4,7                            # reduction candidate for 2,5
C2: 2,5 => CTR
* 6.17.4...43.19.687.796.3.411.....3.4.4.31..9.....4.1.27....14...14.3675....4.7.16
C2: 1,4,7                                #  5 pairs
* PAIR F2: 2,5 COL F
F4: 2,5,6,8,9                            # reduction candidate for 2,5
F4: 2,5                                  #  7 pairs
F5: 2,5,6,8                              # reduction candidate for 2,5
F5: 2,5                                  #  6 pairs
* PAIR H1: 2,3 BLK 3
G1: 2,3,5,9                              # reduction candidate for 2,3
G1: 2,3                                  #  9 pairs
G1: 5,9                                  #  6 pairs
* PAIR H3: 4,7 BLK 3
I2: 4,7,5                                # reduction candidate for 4,7
I2: 5 => CTR
* 6.17.4...437192685..96.37411.....3.4.4.31.59.....4.1.27....14....4.3..5....4.7.16
I2: 4,7                                  #  7 pairs
* PAIR H3: 4,7 COL H
H4: 4,7,6                                # reduction candidate for 4,7
H4: 4,7                                  #  6 pairs
H6: 4,7,6                                # reduction candidate for 4,7
H6: 4,7                                  #  6 pairs
* PAIR E9: 2,5 BLK 8
D7: 2,5,8,9                              # reduction candidate for 2,5
D7: 2,5 => CTR
* 6..7.4....3719.68...96.3..11.........4.3...9.........27....14....4.3.257...4.7.16
D7: 8,9                                  # 10 pairs
E7: 2,5,6                                # reduction candidate for 2,5
E7: 2,5 => SOLVED
* 682714539431295687579683241123579864847362195965148372796851423214936758358427916
E7: 6 => CTR
* 6..7.4...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16
* PAIR E9: 2,5 ROW 9
A9: 2,5,3,8,9                            # reduction candidate for 2,5
A9: 2,5 => CTR
* 6..7.4.29.3719.68...96.3..11..2......4.3...9.3..5....27..9.1438914836257.834.7916
A9: 3,8,9                                #  5 pairs
B9: 2,5,8,9                              # reduction candidate for 2,5
B9: 2,5                                  #  7 pairs
C9: 2,5,3,8                              # reduction candidate for 2,5
C9: 2,5                                  #  7 pairs
* PAIR E9: 2,5 COL E
E1: 2,5,1,8                              # reduction candidate for 2,5
E1: 2,5 => CTR
* 6..7.4....3419.687.79683.411.......484.3...95....4.1.27...614..4...3.75....4.7.16
E1: 1,8                                  #  6 pairs
E3: 2,5,8                                # reduction candidate for 2,5
E3: 2,5 => CTR
* 6..784...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16
E3: 8                                    #  5 pairs
E4: 2,5,4,6,7                            # reduction candidate for 2,5
E4: 2,5 => CTR
* 6..714....31.9.687.79683.411.......4.4.37.19....14...27...614...1..3..5....4.7.16
E4: 4,6,7                                #  5 pairs
E5: 2,5,1,6,7                            # reduction candidate for 2,5
E5: 2,5 => CTR
* 6..714....31.9.687.79683.411.......4.473.619....14...27...614...1..3..5....4.7.16
E5: 1,6,7                                #  5 pairs
* PAIR H7: 2,3 BLK 9
G9: 2,3,8,9                              # reduction candidate for 2,3
G9: 2,3 => CTR
* 6..7.4923.3..9.6875796.3.411.......4.4.3...95....4...27....143.....3.75....4.7216
G9: 8,9                                  #  6 pairs
* PAIR H7: 2,3 ROW 7
C7: 2,3,5,6,8                            # reduction candidate for 2,3
C7: 2,3                                  #  8 pairs
C7: 5,6,8                                #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0133-base-pr-000.dot
* REASONING
* DIS # E1: 2,5 => CTR => E1: 1,8
* PRF # D2: 2,5 => SOL
* DIS # D2: 1 => CTR => D2: 2,5
* DIS # E3: 2,5 => CTR => E3: 8
* DIS # A2: 2,5 => CTR => A2: 4
* PRF # A2: 4 => SOL
* DIS # C2: 2,5 => CTR => C2: 1,4,7
* DIS # I2: 5 => CTR => I2: 4,7
* DIS # D7: 2,5 => CTR => D7: 8,9
* PRF # E7: 2,5 => SOL
* DIS # E7: 6 => CTR => E7: 2,5
* DIS # A9: 2,5 => CTR => A9: 3,8,9
* DIS # E1: 2,5 => CTR => E1: 1,8
* DIS # E3: 2,5 => CTR => E3: 8
* DIS # E4: 2,5 => CTR => E4: 4,6,7
* DIS # E5: 2,5 => CTR => E5: 1,6,7
* DIS # G9: 2,3 => CTR => G9: 8,9
* CNT  17 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E9,F2,H1,H3,H7)
* 6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16
* PAIR F2: 2,5 BLK 2
E1: 2,5,1,8                              # reduction candidate for 2,5
E1: 2,5 => CTR
* 6..7.4....3419.687.79683.411.......484.3...95....4.1.27...614..4...3.75....4.7.16
D2: 2,5,1                                # reduction candidate for 2,5
D2: 2,5 => SOLVED
* 682714539431295687579683241123579864847362195965148372796851423214936758358427916
* DURATION: 0:00:03.682255  START: 06:01:23.340140  END: 06:01:27.022395 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0133-base-pr-001.dot
* REASONING
* DIS # E1: 2,5 => CTR => E1: 1,8
* PRF E1: 1,8 # D2: 2,5 => SOL
* STA E1: 1,8 + D2: 2,5
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=133

Solution

position: 682714539431295687579683241123579864847362195965148372796851423214936758358427916 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:

* DIS # E1: 2,5 => CTR => E1: 1,8
* INC # E1: 1,8 => UNS
* PRF # D2: 2,5 => SOL
* DIS # D2: 1 => CTR => D2: 2,5
* DIS # E3: 2,5 => CTR => E3: 8
* INC # E3: 8 => UNS
* DIS # A2: 2,5 => CTR => A2: 4
* PRF # A2: 4 => SOL
* DIS # C2: 2,5 => CTR => C2: 1,4,7
* INC # C2: 1,4,7 => UNS
* INC # F4: 2,5 => UNS
* INC # F5: 2,5 => UNS
* INC # G1: 2,3 => UNS
* INC # G1: 5,9 => UNS
* INC # I2: 4,7 => UNS
* DIS # I2: 5 => CTR => I2: 4,7
* INC # H4: 4,7 => UNS
* INC # H6: 4,7 => UNS
* DIS # D7: 2,5 => CTR => D7: 8,9
* INC # D7: 8,9 => UNS
* PRF # E7: 2,5 => SOL
* DIS # E7: 6 => CTR => E7: 2,5
* DIS # A9: 2,5 => CTR => A9: 3,8,9
* INC # A9: 3,8,9 => UNS
* INC # B9: 2,5 => UNS
* INC # C9: 2,5 => UNS
* DIS # E1: 2,5 => CTR => E1: 1,8
* INC # E1: 1,8 => UNS
* DIS # E3: 2,5 => CTR => E3: 8
* INC # E3: 8 => UNS
* DIS # E4: 2,5 => CTR => E4: 4,6,7
* INC # E4: 4,6,7 => UNS
* DIS # E5: 2,5 => CTR => E5: 1,6,7
* INC # E5: 1,6,7 => UNS
* DIS # G9: 2,3 => CTR => G9: 8,9
* INC # G9: 8,9 => UNS
* INC # C7: 2,3 => UNS
* INC # C7: 5,6,8 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E1: 2,5 => CTR => E1: 1,8
* PRF E1: 1,8 # D2: 2,5 => SOL
* STA E1: 1,8 + D2: 2,5
* CNT   2 HDP CHAINS /   2 HYP OPENED