# Questions tagged [latin-square]

A combinatorial puzzle related to Latin squares.

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### sums and differences in consecutive grid [closed]

Fill in each square of the grid with a number from $1$ to $16$, using each number exactly once. Numbers at the left or top give the largest sum of two numbers in that row or column. Numbers at the ...
987 views

### magic square operations

Fill in the grid with the numbers $1$ to $6$ so that each number appears exactly once in each row and column. A horizontal gray line marks any cell when it is the middle cell of the three consecutive ...
1 vote
263 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 ...
1 vote
133 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 ...
• 2,915
499 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,...
• 7,624
415 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 ...
651 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 ...
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660 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 ...
• 34.6k
113 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 ...
• 34.6k
195 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 ...
• 2,915
498 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. ...
• 7,534
402 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?...
• 4,199
183 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,...
• 2,915
1 vote
121 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
553 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 ...
• 193
435 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 ...
• 265
665 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 ...
• 265
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, ...
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402 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 ...