Hard 5*5 Latin Squares

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Hard 5*5 Latin Squares

Postby qiuyanzhe » Wed Sep 19, 2018 4:22 pm

5*5 is the smallest size for Latin Squares to contain chains, and I think it is small enough for us to find out all puzzles requiring chains.
I used JSudoku to generate such puzzles(setting 1+ guess) and got several non-equivalent puzzles. I wonder if there are more.
qiuyanzhe
 
Posts: 21
Joined: 21 August 2017
Location: China

Re: Hard 5*5 Latin Squares

Postby qiuyanzhe » Wed Sep 19, 2018 5:54 pm

As rows, columns, digits can be switched each other to make isomorphic puzzles that "look quite different", only one of each equivalence class is shown.
If no extra marks, the puzzles can be solved by Pairs, X-wings and 5-step chains.
When a grid has multiple automorphisms, number of automorphisms is marked(titled "Symmetry"), including identity transformation.

The puzzle grids are after singles and normalization(shape first, then digits)
Code: Select all
pattern 1: 7 givens
12...
2.3..
.4...
...1.
....5
//Uniqueness Allowed: Gurth's_Symmetrical_Placement
//Symmetry:6
//Uniqueness Disabled: (unknown)

Code: Select all
pattern 2: 8 givens
123..
34...
..5..
...1.
....2

Code: Select all
pattern 3: 8 givens
12...
34...
..12.
..4..
....5
//Symmetry: 2

Code: Select all
pattern 4: 10 givens
123..
45.3.
..42.
..5..
....3

Code: Select all
pattern 5: 12 givens
12345
31...
4.2..
2..3.
5....
//Symmetry: 2
qiuyanzhe
 
Posts: 21
Joined: 21 August 2017
Location: China


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