Questions tagged [latin-square]

A combinatorial puzzle related to Latin squares.

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9
votes
1answer
535 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 ...
5
votes
4answers
591 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 ...
2
votes
1answer
84 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 ...
4
votes
1answer
90 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 ...
11
votes
3answers
374 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. ...
8
votes
2answers
340 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?...
-2
votes
1answer
138 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,...
1
vote
0answers
115 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 ...
4
votes
4answers
447 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 ...
7
votes
1answer
315 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 ...
7
votes
1answer
551 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 ...
5
votes
4answers
6k 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, ...
3
votes
3answers
399 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 ...
3
votes
1answer
94 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 ...
3
votes
2answers
1k 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 ...