Analysis of zz-www.sudokuwiki.org-0083-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=83

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=83

position: 6....13......97.1....6....29.....45..4..7..9..82.....38....5....1.76......32....1 initial

Autosolve

position: 6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 5,7 => CTR => A3: 1,3,4
* DIS # D6: 4,5 => CTR => D6: 9
* PRF # F5: 3 => SOL
* DIS # I4: 8 => CTR => I4: 6,7
* CNT   4 HDP CHAINS /  21 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 # A3: 5,7 => CTR => A3: 1,3,4
* DIS A3: 1,3,4 # A9: 4 => CTR => A9: 5,7
* DIS A3: 1,3,4 + A9: 5,7 # D6: 4,5 => CTR => D6: 9
* PRF A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 3 => SOL
* STA A3: 1,3,4 + A9: 5,7 + D6: 9 + F5: 3
* CNT   4 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

6....13......97.1....6....29.....45..4..7..9..82.....38....5....1.76......32....1 initial
6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1 autosolve
659421387428397615371658942937812456146573298582946173864135729215769834793284561 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A6: 5,7
E6: 4,5
I5: 6,8
H6: 6,7
E9: 4,8
H7: 2,3
H8: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,C3: 1.. / A3 = 1  =>  8 pairs (_) / C3 = 1  => 14 pairs (_)
D7,E7: 1.. / D7 = 1  => 12 pairs (_) / E7 = 1  =>  8 pairs (_)
A3,A5: 1.. / A3 = 1  =>  8 pairs (_) / A5 = 1  => 14 pairs (_)
E4,E7: 1.. / E4 = 1  => 12 pairs (_) / E7 = 1  =>  8 pairs (_)
A2,B2: 2.. / A2 = 2  => 16 pairs (_) / B2 = 2  =>  9 pairs (_)
B7,A8: 2.. / B7 = 2  => 16 pairs (_) / A8 = 2  =>  9 pairs (_)
H7,H8: 2.. / H7 = 2  =>  9 pairs (_) / H8 = 2  => 16 pairs (_)
B7,H7: 2.. / B7 = 2  => 16 pairs (_) / H7 = 2  =>  9 pairs (_)
A8,H8: 2.. / A8 = 2  =>  9 pairs (_) / H8 = 2  => 16 pairs (_)
A2,A8: 2.. / A2 = 2  => 16 pairs (_) / A8 = 2  =>  9 pairs (_)
B2,B7: 2.. / B2 = 2  =>  9 pairs (_) / B7 = 2  => 16 pairs (_)
B4,A5: 3.. / B4 = 3  => 14 pairs (_) / A5 = 3  => 12 pairs (_)
H7,H8: 3.. / H7 = 3  => 16 pairs (_) / H8 = 3  =>  9 pairs (_)
F8,H8: 3.. / F8 = 3  => 16 pairs (_) / H8 = 3  =>  9 pairs (_)
E3,E6: 5.. / E3 = 5  => 13 pairs (_) / E6 = 5  => 10 pairs (_)
G2,I2: 6.. / G2 = 6  =>  9 pairs (_) / I2 = 6  => 12 pairs (_)
F5,F6: 6.. / F5 = 6  => 10 pairs (_) / F6 = 6  => 24 pairs (_)
F6,H6: 6.. / F6 = 6  => 24 pairs (_) / H6 = 6  => 10 pairs (_)
H6,H9: 6.. / H6 = 6  => 10 pairs (_) / H9 = 6  => 24 pairs (_)
I4,H6: 7.. / I4 = 7  => 10 pairs (_) / H6 = 7  => 24 pairs (_)
A6,H6: 7.. / A6 = 7  => 10 pairs (_) / H6 = 7  => 24 pairs (_)
I4,I5: 8.. / I4 = 8  =>  0 pairs (X) / I5 = 8  =>  8 pairs (_)
F8,G8: 8.. / F8 = 8  =>  0 pairs (X) / G8 = 8  =>  8 pairs (_)
I1,G3: 9.. / I1 = 9  =>  9 pairs (_) / G3 = 9  =>  9 pairs (_)
D6,F6: 9.. / D6 = 9  =>  8 pairs (_) / F6 = 9  =>  0 pairs (X)
D6,D7: 9.. / D6 = 9  =>  8 pairs (_) / D7 = 9  =>  0 pairs (X)
* DURATION: 0:00:34.047780  START: 04:55:24.661635  END: 04:55:58.709415 2017-05-01
* CP COUNT: (26)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,E6,E9,H6,H7,H8,I5)
* 6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1
* PAIR A6: 5,7 COL A
A3: 5,7,1,3,4                            # reduction candidate for 5,7
A3: 5,7 => CTR
* 6...213..32..97.1...16.3.8293.81245.14.37629..829..1.38..135.2421.76483.4.3289..1
A3: 1,3,4                                #  7 pairs
A9: 5,7,4                                # reduction candidate for 5,7
A9: 5,7                                  # 10 pairs
* PAIR E6: 4,5 BLK 5
D6: 4,5,9                                # reduction candidate for 4,5
D6: 4,5 => CTR
* 67.5213.92...97516...6..7.29....2457.45.76298782..91638279156344197638255632..971
D6: 9                                    #  8 pairs
* PAIR E6: 4,5 COL E
E3: 4,5,3,8                              # reduction candidate for 4,5
E3: 3,8                                  # 12 pairs
E3: 4,5                                  # 11 pairs
* PAIR I5: 6,8 BLK 6
I4: 6,8,7                                # reduction candidate for 6,8
I4: 6,8                                  # 24 pairs
I4: 7                                    # 10 pairs
* PAIR I5: 6,8 ROW 5
F5: 6,8,3                                # reduction candidate for 6,8
F5: 3 => SOLVED
* 659421387428397615371658942937812456146573298582946173864135729215769834793284561
F5: 6,8                                  # 10 pairs
* PAIR H6: 6,7 BLK 6
I4: 6,7,8                                # reduction candidate for 6,7
I4: 8 => CTR
* 6...213..4...9761.1..653..29....24583415782965829461738....5....15769834793284561
I4: 6,7                                  #  8 pairs
* PAIR H6: 6,7 COL H
H9: 6,7,4,8                              # reduction candidate for 6,7
H9: 6,7                                  # 16 pairs
H9: 4,8                                  # 15 pairs
* PAIR E9: 4,8 BLK 8
F8: 4,8,3,9                              # reduction candidate for 4,8
F8: 4,8                                  # 10 pairs
F9: 4,8,9                                # reduction candidate for 4,8
F9: 4,8                                  # 22 pairs
* PAIR E9: 4,8 ROW 9
H9: 4,8,6,7                              # reduction candidate for 4,8
H9: 6,7                                  # 16 pairs
H9: 4,8                                  # 15 pairs
* PAIR E9: 4,8 COL E
E3: 4,8,3,5                              # reduction candidate for 4,8
E3: 4,8                                  # 15 pairs
E3: 3,5                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0083-base-pr-000.dot
* REASONING
* DIS # A3: 5,7 => CTR => A3: 1,3,4
* DIS # D6: 4,5 => CTR => D6: 9
* PRF # F5: 3 => SOL
* DIS # I4: 8 => CTR => I4: 6,7
* CNT   4 HDP CHAINS /  21 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,E6,E9,H6,H7,H8,I5)
* 6...213......97.1....6....29....245..4..7.29..82...1.38....5....1.76......32....1
* PAIR A6: 5,7 COL A
A3: 5,7,1,3,4                            # reduction candidate for 5,7
A3: 5,7 => CTR
* 6...213..32..97.1...16.3.8293.81245.14.37629..829..1.38..135.2421.76483.4.3289..1
A9: 5,7,4                                # reduction candidate for 5,7
A9: 5,7                                  # 10 pairs
* RESTART
* PAIR A6: 5,7 COL A
A9: 5,7,4                                # reduction candidate for 5,7
A9: 4 => CTR
* 6...213.92...97615...6.87429..8.2457.4..76298782954163827.45936519763824463289571
* PAIR RESTART
* PAIR E6: 4,5 BLK 5
D6: 4,5,9                                # reduction candidate for 4,5
D6: 4,5 => CTR
* 67.5213.925..97.16.9.6..7.29....2457.45.76298782..91638279156344197638255632..971
* PAIR E6: 4,5 COL E
E3: 4,5,3,8                              # reduction candidate for 4,5
E3: 3,8                                  # 21 pairs
E3: 4,5                                  # 15 pairs
* PAIR I5: 6,8 BLK 6
I4: 6,8,7                                # reduction candidate for 6,8
I4: 6,8                                  # 22 pairs
I4: 7                                    # 12 pairs
* PAIR I5: 6,8 ROW 5
F5: 6,8,3                                # reduction candidate for 6,8
F5: 3 => SOLVED
* 659421387428397615371658942937812456146573298582946173864135729215769834793284561
* DURATION: 0:00:11.594416  START: 04:56:14.927606  END: 04:56:26.522022 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0083-base-pr-001.dot
* REASONING
* DIS # A3: 5,7 => CTR => A3: 1,3,4
* DIS A3: 1,3,4 # A9: 4 => CTR => A9: 5,7
* DIS A3: 1,3,4 + A9: 5,7 # D6: 4,5 => CTR => D6: 9
* PRF A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 3 => SOL
* STA A3: 1,3,4 + A9: 5,7 + D6: 9 + F5: 3
* CNT   4 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=83

Solution

position: 659421387428397615371658942937812456146573298582946173864135729215769834793284561 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 # A3: 5,7 => CTR => A3: 1,3,4
* INC # A3: 1,3,4 => UNS
* INC # A9: 5,7 => UNS
* DIS # D6: 4,5 => CTR => D6: 9
* INC # D6: 9 => UNS
* INC # E3: 4,5 => UNS
* INC # E3: 3,8 => UNS
* INC # I4: 6,8 => UNS
* INC # I4: 7 => UNS
* INC # F5: 6,8 => UNS
* PRF # F5: 3 => SOL
* INC # I4: 6,7 => UNS
* DIS # I4: 8 => CTR => I4: 6,7
* INC # H9: 6,7 => UNS
* INC # H9: 4,8 => UNS
* INC # F8: 4,8 => UNS
* INC # F9: 4,8 => UNS
* INC # H9: 4,8 => UNS
* INC # H9: 6,7 => UNS
* INC # E3: 4,8 => UNS
* INC # E3: 3,5 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 5,7 => CTR => A3: 1,3,4
* INC A3: 1,3,4 # A9: 5,7 => UNS
* INC A3: 1,3,4 # A9: 5,7 => UNS
* DIS A3: 1,3,4 # A9: 4 => CTR => A9: 5,7
* DIS A3: 1,3,4 + A9: 5,7 # D6: 4,5 => CTR => D6: 9
* INC A3: 1,3,4 + A9: 5,7 + D6: 9 # E3: 4,5 => UNS
* INC A3: 1,3,4 + A9: 5,7 + D6: 9 # E3: 3,8 => UNS
* INC A3: 1,3,4 + A9: 5,7 + D6: 9 # I4: 6,8 => UNS
* INC A3: 1,3,4 + A9: 5,7 + D6: 9 # I4: 7 => UNS
* INC A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 6,8 => UNS
* PRF A3: 1,3,4 + A9: 5,7 + D6: 9 # F5: 3 => SOL
* STA A3: 1,3,4 + A9: 5,7 + D6: 9 + F5: 3
* CNT  11 HDP CHAINS /  11 HYP OPENED