after Martin Gardner
Four bugs, the Green, the Yellow, the Red, and
the Blue occupy the corners of a square as shown in the illustration. The
side of the square is 10 units long. Simultaneously the Green bug starts
to crawl directly toward the Yellow one, the Yellow toward the Red, the
Red toward the Blue and the Blue toward the Green.
Since all four bugs crawl at the same constant rate, they will describe
four congruent logarithmic spirals which meet at the center of the square.
Thus the question is: how far does each bug travel before they meet?