Magician and the Moon

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This exhibit is a variation on a familiar carnival activity. There is one large stationary white disk and five small magnetic black disks. The participant tries to place the five small disks to cover the large disk completely.

The natural tendency in trying to solve this problem is to look for a symmetric answer, like a star. However, the answer does not have 5-fold symmetry. (It does have left-right symmetry.) Let people work on it for a little while, and if they need a hint, you can first tell them that the answer is not completely symmetric. As a second hint, note that the outer points where adjacent circles touch each other all sit on the circumference of the big circle.

At a carnival, they generally don't let you move any disk once you've placed it. But our goal is different -- we want the visitors to be able to find the answer themselves, and trial and error is an important part of the process.


Magician and the Moon Solution

You can see that only three of the circles here overlap in the center. The other two, one on the left and one on the right, are further out. A symmetric placement of all 5 circles will always leave part of the large circle showing.

For more information, you can check out the explanation here.

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Magician and the Moon
Magician and the Moon