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Making sure a shape-sorter works

Making sure a shape-sorter works

Making sure a shape-sorter works

I hardly dare put this one in, because it's so simple, but it's sort of cute, too:

Everyone knows a small child's shape-sorter. It's a box with holes in the side of different shapes, circles, squares, crosses, pentagons, banana-shapes, whatever. It comes with a set of shapes that the baby can post through each hole.

Obviously it's no fun if the shapes can be squeezed through the wrong holes. The square mustn't be so small that it can go through the circle's hole, nor should it be so big that the circle can go through its hole.

How can we choose sizes of arbitrary shapes so that they can never pass through the hole of any other shape?

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