by Michelle and Dave Youngs.
Topsy-Turvy Triangles is a classic puzzle in recreational mathematics which has been around for many years. Students are challenged to take a triangular arrangement of ten pennies and change the direction that the triangle points by moving only three pennies. At first this task seems impossible, but with a little persistence students will discover the solution. (There are actually several solutions to this puzzle, depending on which direction the final triangle is pointing.) For those students who solve it quicker than most, there is an extra challenge to determine the minimum number of moves needed to flip an array of 15 pennies.
If you do not have enough pennies for students to have their own puzzles, other small manipulatives such as plastic disks or checkers can be substituted, but they work best if they are round and can be arranged as shown in the diagram.
I hope you and your students enjoy this puzzle.