Math Club Resource Hub

The 3 Utilities Problem is a classic mathematics puzzle that introduces students to graph theory.

Students begin with three houses and three utilities (e.g., electricity, water, and gas). The challenge is to connect each house to all three utilities without any of the utility lines crossing each other.

First, give your students a piece of paper and have them draw three houses in a row and then draw images for the three utilities below. Ask them to try and connect each house to all three utilities without crossing any utility lines; this task is impossible to solve on a flat, 2-D surface.

Next, give students a coffee mug (or any torus-shaped object) and a white board maker, asking them to recreate the three houses and three utilities. When they try the challenge again on the coffee mug, they’ll find out that it can be done!

See the attachment below for instructions and an activity handout.

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