[Illustration: [Pyramid of cannon-balls]]
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"All cannon-balls are to be piled in square pyramids," was the order
issued to the regiment. This was done. Then came the further order, "All
pyramids are to contain a square number of balls." Whereupon the trouble
arose. "It can't be done," said the major. "Look at this pyramid, for
example; there are sixteen balls at the base, then nine, then four, then
one at the top, making thirty balls in all. But there must be six more
balls, or five fewer, to make a square number." "It _must_ be done,"
insisted the general. "All you have to do is to put the right number of
balls in your pyramids." "I've got it!" said a lieutenant, the
mathematical genius of the regiment. "Lay the balls out singly." "Bosh!"
exclaimed the general. "You can't _pile_ one ball into a pyramid!" Is it
really possible to obey both orders?