Where Is the 5?

This trick is based on a well-known 4-piece paradox which idea is that its pieces can be arranged into a square in two different ways as shown in Illustration 1. One way provides us with a complete square, while the second gives us a square with a little hole in it.

The first way was employed to complete the front view of our trick and then the pattern of the red magic square was depicted on it. Then the second way to form a square was employed. After that all the pieces were simultaneously flipped over and the blue magic square was drawn around the hole in the square. Surely, the number 5, which should go over the hole, is missing in the new magic square. Both front and back views of the square with the hole in it and the mutual positions of the red and blue patterns on both of its sides are shown in Illustrations 2 and 3.

Now you can see that, in fact, in the course of this trick the 5 doesn't disappear; simply, there is no 5 on the back side of the square at all!

What really happens is that completing the second magic square (the blue one) on the back side of the trick we, in fact, are making another square of the same set of the four pieces, but now with a hole in it.

Since the pieces have the same area in both cases - face and back - it's obvious the square with the inner hole must have a little bigger size. The difference between the squares assembled in both ways is shown in Illustration 4.

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Last Update
August 28, 2003

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Trick's visual concept: Copyright 2003 Serhiy Grabarchuk. All Rights Reserved.
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