Latin Squares and KenKen Puzzles

An introduction to puzzles involving Latin Squares.

A Latin Square is an NxN square array of N unique symbols – each row has one of each symbol, each column has one of each symbol.

Examples with N=4:

Originally, a Latin Square was a square of Latin letters, but any symbol will do.  In fact, we can even use colors or numbers:

Latin Squares are different from Magic Squares


One of the most popular puzzles are based on Latin Squares: Sudoku

We are not going to analyze Sudoku solving techniques today


KenKen is a puzzle invented by Tetsuya Miyamoto in 2004

The 4-by-4 grid below is divided into special outlined boxes called cages

Note that we fill in some information based on our deductions... using small numbers near the edge to indicate that the numbers might switch

Finally, we can check the answers:

KenKen puzzles are a good mental exercise:

But... the puzzles are relatively small, and a 4-by-4 puzzle can be done in 2 to 5 minutes (compared with a hard 9-by-9 Sudoku, which might take an hour).

For more about larger KenKen puzzles (and examples of 6x6 and 7x7 KenKen puzzles), see More KenKen Puzzles.


The Swiss mathematician Leonhard Euler wrote about Latin Squares in the 18th century

Martin Gardner wrote about a more complicated version of Latin Squares – “Greco-Latin Squares” –

Orthogonal Latin Squares are used in software testing (to ensure good test coverage)

Online KenKen practice:

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Last modified: Jan. 3, 2020
Dennis Mancl -