Questions tagged [latin-square]
A combinatorial puzzle related to Latin squares.
19
questions
1
vote
1
answer
230
views
How many 4x4 Latin Squares are there?
I thought of this problem when playing Sudoku. Let A = {1,2,3,4}. I have to make a 4x4 box (i.e. the size of A in both dimensions) and fill it with data such that ...
- 11
1
vote
1
answer
129
views
Maximum and minimum numbers of combinations in a double Latin Square
Let's have a double 6x6 Latin Square (see Figure 1). You can see that this Latin Square has thirteen combinations (see Figure 2). Can you make a double Latin Square that contains the maximum number of ...
- 2,917
8
votes
1
answer
491
views
Tiling a 5x5 square with five pentominoes AND a Latin square
Suppose that a 5x5 square has been tiled with five (not necessarily distinct) pentominoes. Is it true that there will necessarily exist at least one Latin square of size 5x5 (using the numbers 1,2,3,...
- 5,877
6
votes
2
answers
382
views
Taking turns adding a number 1,2,3 to a 3x3 matrix without repeating numbers in the rows or columns: does the first player always win?
Alice and Bob are playing a game on an initially empty 3x3 matrix. They take turns, and each turn:
They add a number in {1,2,3} to an empty cell.
They are not allowed to repeat a number in a row or ...
9
votes
1
answer
632
views
Sudoku with no grid and no numbers!!? - SS#12
An entry in Fortnightly Topic Challenge #47: "Wacky Sudokus"
Other puzzles in this series
Welcome to the twelfth puzzle in this series! For more information about the series, see the first ...
- 56.4k
7
votes
4
answers
651
views
8x8 square with no adjacent numbers summing to a prime
Can you fill a 8x8 grid with numbers from 1 to 8 such that:
Every number occurs exactly once in each row and in each column (Latin square).
No two adjacent (horizontally or vertically) numbers sum to ...
- 33.2k
3
votes
1
answer
112
views
4x4 square with no increasing triples
Can you fill a 4x4 grid with numbers from 1 to 4 such that:
Every number occurs exactly once in each row and in each column (Latin square).
No row or column contains 3 adjacent numbers that are all ...
- 33.2k
5
votes
2
answers
177
views
Combinations on superimposed latin squares
Let's have two latin squares. When we superimpose them we obtain a 6x6 superimposed square as shown in the diagram.
By visual inspection we see this contains 15 combinations and their repetitions ...
- 2,917
11
votes
3
answers
488
views
Perfect Latin Squares
The following Latin Square has an interesting property: there are 6*5=30 possible “ordered dominos” containing distinct digits, each occurring exactly once horizontally and exactly once vertically. ...
- 7,444
8
votes
2
answers
399
views
Q: Henry Goldman's Square of Digits
Jaap Scherphuis introduced The Arithmachinist by Henry Goldman in his post Goldman's Transformation Puzzle.
In the book I found a curious figure on p.52. I wonder what it means. Could you let me know?...
- 4,179
-2
votes
1
answer
169
views
Latin Squares puzzle
Let’s have two Latin Squares 6X6 superimposed on each other, represented here by marking one with 1s and one with 0s. The two Latin Squares contain twelve 5,2 pairs, a total of twelve pairs 6,4 and 4,...
- 2,917
1
vote
0
answers
120
views
Filling a sudoku/latin square like array
Let us build a square array in the following manner, which I would like to call a modified sudoku:
1) Every row and column contains only one copy of a positive entry and there are exactly $t$ such ...
- 111
5
votes
4
answers
537
views
Do there exist Graeco-Latin Square style puzzles?
Sudoku, KenKen, and Skyscrapers are three examples of Latin square puzzles. In all three, players are challenged to complete a Latin Square, a NxN grid (typically 9x9) in which the numbers 1-N appear ...
- 183
7
votes
1
answer
415
views
Latin Square Puzzle - Difficult
Follow on puzzle from the introductory Latin square puzzle post.
The rules
It’s a Latin square like sudoku, so there must be the numbers 1-9 exactly once in every row and column.
Notice that each ...
- 245
7
votes
1
answer
643
views
Latin square puzzle
This is a sudoku-esque puzzle I came up with when trying to solve some harder sudoku.
The rules
It’s a Latin square like sudoku, so there must be the numbers 1-9 exactly once in every row and ...
- 245
5
votes
4
answers
7k
views
Special 5x5 Sudoku-like table
This is a special 5x5 Sudoku-like table.
Each row, column, and diagonal contains digits from 1 to 5 (including diagonals obtained by wrapping around the edges).
To filter duplicates (by rotation, ...
- 17.8k
3
votes
3
answers
401
views
Team Picnic Round Robin
What seemed like a simple setup for a team picnic has turned into a nightmare logic puzzle.
There are 8 teams and 8 events/locations. Each event requires two teams who play against each other.
There ...
- 31
3
votes
1
answer
99
views
Coprime latin squares
The numbers {1 to 11}, excluding 8 and 10, are arranged in a 3 x 3 matrix.
The bottom row sums to 22.
The rightmost column sums to 24.
The back diagonal (/) values sum to 14.
Each triplet of values ...
- 475
4
votes
2
answers
2k
views
How to generate and count the 7x7 Latin squares
How many 7 by 7 Latin squares are there, and how can one generate examples of them? I am working on classes for a game, and typing in numbers manually from 1-7 in rows and columns from scratch is ...
- 41