For this you will need four pennies. Arrange the pennies so that the centers of all four are equidistant from each other.

Example:

(1) (2) (3) (4)

This will not work because penny 1 and penny 4 are farther apart than penny 1 and penny 2.

The problem doesn't state that the four pennies need to remain on the same surface or in the same plane, so I think I'll form an equilateral triangle with three them on the table and hold the fourth up above to form an equilateral pyramid.

Posted by Jyqm on 2006-05-01 09:23:48