Here is a really hard puzzle, and yet its conditions are so absurdly
simple. Every reader knows how to place four pennies so that they are
equidistant from each other. All you have to do is to arrange three of
them flat on the table so that they touch one another in the form of a
triangle, and lay the fourth penny on top in the centre. Then, as every
penny touches every other penny, they are all at equal distances from
one another. Now try to do the same thing with five pennies--place them
so that every penny shall touch every other penny--and you will find it
a different matter altogether.