The four coloured pieces can be put together in two different ways to make these shapes with base 13 units and height 5 units. Why is there one square missing in the second arrangement?
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Sam Loyd presented this Chessboard Paradox at the American Chess congress in 1858. Notice the Fibonacci numbers which can be found in both of these diagrams.
As you probably guessed, even though the red lines don't look parallel they actually are.
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Teacher, do your students have
access to computers?
Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to a related student activity.
Students can create their own presentation of the Missing Square Puzzle to show to other classes or in an assembly. Here are some guidelines for using PowerPoint
On the Home tab, in the Drawing group, click Arrange,
point to Align, and then click Grid Settings.
Tick the Snap objects to grid and the display grid on screen boxes. Select from the dropdown box a spacing of 1cm.
The red and blue
right-angled triangles can be made using the "Right Triangle" tool which can
be found in the Home tab, in the Drawing group.
The green and yellow shapes can be created by putting together a number of 1cm by 1cm squares. Upon completion of the shape drag over the shape to select all of the squares then select "Group" from the Format tab, Arrange group.
Turn the Snap To Grid option off an add custom animations to each of the shapes to make the first arrangement of shapes transform into the second.