4×4 Face Card Puzzle

Here’s a puzzle that seems simple but is harder than it looks. Arrange all 16 face cards into a 4×4 grid such that each row, each column, and the two major diagonals has only one card of each suit and only one card of each value. You can play the game by dragging and dropping the cards within the HTML5 frame below.

This puzzle dates from 1725 and its solution is an example of a Graeco-Latin square of order 4. In the 18th century, these squares were studied by Leonhard Euler, who was able to construct squares where the order n is odd or a multiple of 4, but he could not find a solution for a 6×6 square, known as the Thirty-six Officers Problem. In 1959, nearly two centuries later, mathematicians were able to demonstrate that Graeco-Latin squares exist for all orders greater than 2, except for 6. Graeco-Latin squares are used to design experiments and organize tournaments.

Need a Hint?
Try working from the corners. Once you place a certain card in a corner, you eliminate several other positions where cards of that value or suit can go.


See Answer
4x4 Puzzle SolvedThere are many possible solutions, one of which is pictured to the right.

According to Martin Gardner, there are 144 possible solutions, each of which can be rotated and reflected, giving eight variations, or 1,152 solution variations.


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