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Hanging Boots Puzzle

Have you ever seen a math puzzle or game and wondered how it worked?

Many of these math puzzles and game rely on the mathematical study of shapes and spaces called topology.

Topology is the mathematical study of shapes and spaces.

Topology involves looking at the shapes that result through stretching, transforming, deforming, folding and twisting. Tearing, on the other hand, is not allowed!

In this activity, students can make their own 3D math puzzle. The solution to this puzzle relies on manipulating the pieces in three dimensions.


  • Develop mathematical reasoning.

  • Make connections and solve problems.

  • Explain the importance of observation when doing math.


Key Questions

  • Can you predict how large of a loop you will make, knowing only the size of your paper and the number/size of cuts you will make?

What To Do

  1. Cut out the pieces of the Hanging Boots puzzle.
  2. Assemble the pieces as shown in the three steps. The puzzle is harder to solve if the large rectangular piece is not creased.
  3. Challenge a friend to remove the boots without tearing the paper or forcing the boots through the hole in the black piece.