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# Flipping Fish

This puzzle has been around in various forms for a number of years. All forms begin with eight toothpicks or matches arranged in the shape of a fish. One version challenges you to move exactly three toothpicks to make the fish face the opposite direction. Another version challenges you to move just two toothpicks to make the fish face a different direction. Other versions add a small object for an eye that is moved along with the toothpicks.

I have slightly modified this classic puzzle by making it more open-ended and by asking students to think about their solutions. Flipping Fish begins by simply asking students to make a toothpick fish face another direction by moving any number of toothpicks. With this approach there are many possible solutions, instead of the one or two possible in the classic versions. When students discover an initial solution, they are asked to examine that solution and determine if they can come up with a better one (one that moves fewer toothpicks). They are then challenged to find the minimum number of moves in order to get the fish to face a different direction, and to defend this number. This strategy forces students to think more deeply about the problem and helps develop higher-order thinking skills.

We hope that you will enjoy using Flipping Fish with your students!

Arrange eight toothpicks in the shape of a fish. Move toothpicks until the fish is facing another direction. How many did you move?

Try to get the fish to change directions by moving fewer toothpicks than you did the first time.

What is the minimum number of toothpicks that must be moved to make the fish face another direction?