Recreational Math

Math Puzzles

What is a Latin square?

A Latin square is considered to be an n by n (n × n) array filled with n different letters (called Latin letters). These letters occur exactly once in each row and column. The name “Latin square”—considered in the field of combinatorics—was first mentioned by Leonhard Euler who used the Latin characters as symbols. (For more about combinatorics, see “Foundations of Mathematics”; for more about Euler, see “History of Mathematics” and “Mathematical Analysis.”)


In the haberdasher problem, an equilateral triangle is divided and rearranged into a square.


The Pythagorean square puzzle tests your geometry skills by asking you to take two square shapes and reconfigure them into one larger square.


In the T-puzzle, several shapes must be assembled into the letter T.


A 15 Puzzle might not be a fair challenge of a person’s skills, if the numbers don’t begin in the correct order.

Other characters can be used in a Latin square, as can numbers in numerical order. Latin squares are used most often in such fields as science, engineering, statistics, and even computer science; in other words, fields in which the researcher desires to control the variation in an experiment related to rows and columns in the field. For example, in plant genetics or forestry, data can be put into a Latin square to determine the growth characteristics of a plant, or to see which plants are growing best where in a forestry situation.


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