Analysis of zz-www.sudokuwiki.org-0044-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=44

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=44

position: ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....2....5...8.3.28..4.... initial

Autosolve

position: ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C5: 2,3 => SOL
* DIS # C5: 9 => CTR => C5: 2,3
* DIS # B6: 2,3 => CTR => B6: 4,7
* DIS # D5: 2,3 => CTR => D5: 1,5,9
* DIS # B3: 7 => CTR => B3: 2,3
* DIS # E4: 3,8 => CTR => E4: 6,9
* DIS # D6: 3,8 => CTR => D6: 2,5
* DIS # E2: 3,8 => CTR => E2: 1,2
* DIS # E3: 3,8 => CTR => E3: 1,2,9
* CNT   9 HDP CHAINS /  19 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C5: 2,3 => SOL
* STA C5: 2,3
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

....5..12.9.6...4....4....6.15......8...7...4..6...19.1....2....5...8.3.28..4.... initial
....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4.... autosolve
467853912398621745521497386915364827832179654746285193179532468654718239283946571 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
B5: 2,3
E6: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,C3: 1.. / C2 = 1  =>  4 pairs (_) / C3 = 1  =>  2 pairs (_)
D5,F5: 1.. / D5 = 1  =>  3 pairs (_) / F5 = 1  =>  0 pairs (X)
I8,I9: 1.. / I8 = 1  =>  0 pairs (X) / I9 = 1  =>  3 pairs (_)
E2,E3: 2.. / E2 = 2  =>  2 pairs (_) / E3 = 2  =>  0 pairs (X)
H4,H5: 2.. / H4 = 2  =>  3 pairs (_) / H5 = 2  =>  0 pairs (X)
C2,E2: 2.. / C2 = 2  =>  0 pairs (X) / E2 = 2  =>  2 pairs (_)
D4,H4: 2.. / D4 = 2  =>  0 pairs (X) / H4 = 2  =>  3 pairs (_)
B6,D6: 2.. / B6 = 2  =>  0 pairs (X) / D6 = 2  =>  3 pairs (_)
F4,F6: 4.. / F4 = 4  =>  3 pairs (_) / F6 = 4  =>  0 pairs (X)
A8,C8: 4.. / A8 = 4  =>  0 pairs (X) / C8 = 4  =>  4 pairs (_)
A4,F4: 4.. / A4 = 4  =>  0 pairs (X) / F4 = 4  =>  3 pairs (_)
B1,B6: 4.. / B1 = 4  =>  0 pairs (X) / B6 = 4  =>  0 pairs (_)
C1,C8: 4.. / C1 = 4  =>  0 pairs (X) / C8 = 4  =>  4 pairs (_)
A2,A3: 5.. / A2 = 5  =>  3 pairs (_) / A3 = 5  =>  4 pairs (_)
A1,B1: 6.. / A1 = 6  =>  0 pairs (X) / B1 = 6  =>  0 pairs (_)
B7,A8: 6.. / B7 = 6  =>  0 pairs (X) / A8 = 6  =>  0 pairs (_)
A8,E8: 6.. / A8 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
A1,A8: 6.. / A1 = 6  =>  0 pairs (X) / A8 = 6  =>  0 pairs (_)
B1,B7: 6.. / B1 = 6  =>  0 pairs (*) / B7 = 6  =>  0 pairs (X)
H7,I7: 8.. / H7 = 8  =>  3 pairs (_) / I7 = 8  =>  5 pairs (_)
G1,G3: 9.. / G1 = 9  =>  3 pairs (_) / G3 = 9  =>  2 pairs (_)
A4,C5: 9.. / A4 = 9  =>  0 pairs (*) / C5 = 9  =>  0 pairs (X)
A4,A8: 9.. / A4 = 9  =>  0 pairs (*) / A8 = 9  =>  0 pairs (X)
* DURATION: 0:00:29.785448  START: 04:17:57.266377  END: 04:18:27.051825 2017-05-01
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,E6)
* ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4....
* PAIR B5: 2,3 BLK 4
C5: 2,3,9                                # reduction candidate for 2,3
C5: 2,3 => SOLVED
* 467853912398621745521497386915364827832179654746285193179532468654718239283946571
C5: 9 => CTR
* 648.5..12.9.6...4....4....6.15......8.9.7...4..6.3.19.16..924..954.6823.28..4....
B6: 2,3,4,7                              # reduction candidate for 2,3
B6: 2,3 => CTR
* 648.5..12.9.6...4..7.4....6.15......8.9.7...4..6.3.19.16..924..954.6823.28..4....
B6: 4,7                                  #  4 pairs
* PAIR B5: 2,3 ROW 5
D5: 2,3,1,5,9                            # reduction candidate for 2,3
D5: 2,3 => CTR
* 64..5..12.9.6...4..7.4....6415..6.2.839271..47265.419.16...24..954.6823.28..45...
D5: 1,5,9                                #  2 pairs
* PAIR B5: 2,3 COL B
B3: 2,3,7                                # reduction candidate for 2,3
B3: 7 => CTR
* 468.5..12.9.6...4..7.4....6915.64...8.3179..474623519813...24..654.1823.28..4...1
B3: 2,3                                  #  7 pairs
* PAIR E6: 3,8 BLK 5
D4: 3,8,2,9                              # reduction candidate for 3,8
D4: 3,8                                  #  7 pairs
E4: 3,8,6,9                              # reduction candidate for 3,8
E4: 3,8 => CTR
* ...85..12.9.62..4..2.4....6915......832.7...4..62..19.1....24...5...823.28..4....
E4: 6,9                                  #  3 pairs
D6: 3,8,2,5                              # reduction candidate for 3,8
D6: 3,8 => CTR
* 648.5..12.9.6...4..7.4....6.15......839.7...4.26.3.19.16..924..954.6823.28..4....
D6: 2,5                                  #  3 pairs
* PAIR E6: 3,8 ROW 6
I6: 3,8,5,7                              # reduction candidate for 3,8
I6: 3,8                                  #  6 pairs
I6: 5,7                                  #  3 pairs
* PAIR E6: 3,8 COL E
E2: 3,8,1,2                              # reduction candidate for 3,8
E2: 3,8 => CTR
* .68.5..12.92681.4...142...6915.64...8.3179..4.4623519813...24..654.1823.28..4...1
E2: 1,2                                  #  3 pairs
E3: 3,8,1,2,9                            # reduction candidate for 3,8
E3: 3,8 => CTR
* 46.95..12.9.62..455..48.976915..4...8..179..4.462.519.1...92468654718239289.46..1
E3: 1,2,9                                #  2 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0044-base-pr-000.dot
* REASONING
* PRF # C5: 2,3 => SOL
* DIS # C5: 9 => CTR => C5: 2,3
* DIS # B6: 2,3 => CTR => B6: 4,7
* DIS # D5: 2,3 => CTR => D5: 1,5,9
* DIS # B3: 7 => CTR => B3: 2,3
* DIS # E4: 3,8 => CTR => E4: 6,9
* DIS # D6: 3,8 => CTR => D6: 2,5
* DIS # E2: 3,8 => CTR => E2: 1,2
* DIS # E3: 3,8 => CTR => E3: 1,2,9
* CNT   9 HDP CHAINS /  19 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,E6)
* ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4....
* PAIR B5: 2,3 BLK 4
C5: 2,3,9                                # reduction candidate for 2,3
C5: 2,3 => SOLVED
* 467853912398621745521497386915364827832179654746285193179532468654718239283946571
* DURATION: 0:00:02.620968  START: 04:18:40.033120  END: 04:18:42.654088 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0044-base-pr-001.dot
* REASONING
* PRF # C5: 2,3 => SOL
* STA C5: 2,3
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=44

Solution

position: 467853912398621745521497386915364827832179654746285193179532468654718239283946571 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:

* PRF # C5: 2,3 => SOL
* DIS # C5: 9 => CTR => C5: 2,3
* DIS # B6: 2,3 => CTR => B6: 4,7
* INC # B6: 4,7 => UNS
* DIS # D5: 2,3 => CTR => D5: 1,5,9
* INC # D5: 1,5,9 => UNS
* INC # B3: 2,3 => UNS
* DIS # B3: 7 => CTR => B3: 2,3
* INC # D4: 3,8 => UNS
* DIS # E4: 3,8 => CTR => E4: 6,9
* INC # E4: 6,9 => UNS
* DIS # D6: 3,8 => CTR => D6: 2,5
* INC # D6: 2,5 => UNS
* INC # I6: 3,8 => UNS
* INC # I6: 5,7 => UNS
* DIS # E2: 3,8 => CTR => E2: 1,2
* INC # E2: 1,2 => UNS
* DIS # E3: 3,8 => CTR => E3: 1,2,9
* INC # E3: 1,2,9 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C5: 2,3 => SOL
* STA C5: 2,3
* CNT   1 HDP CHAINS /   1 HYP OPENED