Missing Square Puzzle

Missing Square Puzzle

They say seeing is believing, but sometimes your eyes can trick you! Download this printable puzzle here and discover how a bit of math can help you figure out the solution.

Ages:
5 - 16
Est. Time:
<30 mins

How we did it:

Materials List

  1. printable
  2. scissors
  1. Step 1

    Gather your materials.

  2. Step 2

    Cut the colored shapes along the dotted lines. 

  3. Step 3

    Rearrange the shapes until they fit the shaded green area.

  4. Step 4

    Cut the colored shapes along the dotted lines. 

  5. Step 5

    Rearrange the shapes until they fit the shaded green area, BUT leave one green square BLANK. 

  6. Learn More!

    How is it that the same shapes can be rearranged to make the same big triangle, but there’s a whole square missing?


    Well, they don’t actually make the same big triangle. And maybe even more surprising, neither of those big triangles are really triangles! It looks like the longest side of the big triangle is a straight line, but it’s actually bent in the middle. (That’s because the two smaller triangles that make it up are secretly at different angles, so one of them is a little steeper than the other.) That means the big shape isn’t a triangle at all — it’s a quadrilateral.


    Check out the diagram above. The blue area shows the difference between the two “triangles,” which turns out to be exactly the same size as one of the squares. That’s why the rearranged “triangle” that fills up the blue area seems to have a missing square. Puzzle solved!