The Swiss mathematician Leonhard Euler first investigated square arrays in which symbols appeared once in each row and column, and named them “Latin squares” since he used letters of the Latin alphabet.  They have proven useful in the design of scientific experiments, and they are interesting as mathematical objects.  On this website I also publish my own small discoveries about Latin Squares.

To solve these puzzles, fill in the empty spaces with the letters A to F so that every letter appears once in each row, each column, and each outlined and colored region.

Click on any puzzle to find its solution.  Thanks to David Schilling for his extensive help with proofreading, suggestions, and clarifying many of the solutions!

Some hints for solving:

• Find a cell which can only contain one particular symbol (because the others are already present elsewhere either in its row, its column, or its region).
• Find a cell which is the only possible position for some symbol in its region, or in its row or column.
• Find two (or more!) cells which must contain the same symbol, and apply the first principle above to deduce what that symbol must be.
• If you notice that a particular symbol’s position in some region has to be in a certain column (or row), then even if you can’t pin down the cell yet you know that the symbol cannot appear elsewhere in that column (or row) -- this may help you locate the symbol in another region.
• Each symbol has to occur 6 times somewhere in the square, once in each row and column.  Very often after you have located one or two instances of a symbol, you will find there is only one possible combination of cells where the remaining instances can be.

I originated this puzzle-type, and have great hopes for it.  My first set of them was published in GAMES World of Puzzles (July 1996).  The first four shown here were published in Chime, the Chicago Mensa newsletter, in August 1998.  Website-visitor David Schilling writes me that he has also seen puzzles of this type in a German puzzle magazine, he thinks it was in one called Jumbo Raetsel which is published by Bastei, so apparently they have crossed the Atlantic!  If anyone would know where I could get one, I’d love to see a copy of this.

Everett Kaser, who writes shareware implementations of puzzles (see his website), saw Latin Squares in World of Puzzles and liked the idea enough to write a program that generates such puzzles.  He tells me he is considering preparing a shareware version, which would create an unending supply of Latin Square puzzles for the user’s enjoyment.

Stephen Bennett has written a freeware Java applet for solving Latin Squares, which you can find on his website.

Questions, corrections, comments:  Send me e-mail at  markthom@flash.net