The hole in the piece of paper is the size of a nickel. How can a quarter be passed through the hole without cutting, tearing, or ripping the hole?

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The quarter will slip through the hole if you (1) hold the paper so that the fold divides the nickel-size hole in half; (2) place the quarter in the fold; and (3) bend the paper upward as you hold it at the outer edges of the crease.

This puzzle, taken from the award-winning book Bet You Can! Science Possibilities to Fool You, by Vicki Cobb and Kathy Darling, is a topology problem. Topology is a branch of mathematics dealing with certain properties of geometric figures that remain constant even when the figures are bent, stretched, or molded. Topology makes no distinction between a sphere and a cube because those figures can be molded into each other. Topology does make a distinction between a sphere and a torus (a doughnut-shaped figure) because a sphere cannot be deformed into a torus.

By folding the paper, you change the circle into an ellipse, enabling the quarter to slip through the hole. Distorting the circle doesn’t change its topology. Topologically, the circle and the ellipse are the same.