The 36 Officers Puzzle

The 36 Officers Puzzle is an impossible problem studied by Leonhard Euler.

You can attempt the puzzle above by clicking and dragging the chess pieces into the squares. The goal is to arrange the pieces in a 6×6 grid in such a way that each row and each column has 6 different colors and 6 different chess pieces. (Euler’s formulation was officers of 6 different ranks and 6 different regiments.) Euler conjectured correctly that this problem is impossible. The task is equivalent to creating a Graeco-Latin square, and a Graeco-Latin square of order 6 does not exist.

However, the puzzle is solvable as a 5×5 grid, without using the pawns or the grey pieces. Try it! You may find the 5×5 puzzle relatively easy, because there is a fairly simple pattern you can follow. The puzzle is also solvable as a 4×4 grid, without using the knights and pawns and the grey and purple pieces. This puzzle, which is equivalent to the 4×4 Face Card Puzzle, is a little trickier. Solutions are below.