Euler Squares - Solving Euler Squares of Order Five

Euler squares were introduced on the first day of a problem solving class for mathematics teachers. Nineteen teachers were placed in collaborative groups and given a pegboard holding five different geometric shapes in five different colors (see Figure 4). The author acknowledges ETA Cuisenaire for providing the six Geo-Shapes Pegboards for her research.

Figure 4: A Geo-Shapes Pegboard

Challenged to find a way to place the pegs so that no shape or color repeated in any row or column, groups were observed using three methods to find a solution: diagonalization (shown above in Figure 4), the knight’s move, and Sudoku skills.