"All cannon-balls are to be piled in square
pyramids," was the order issued to the regiment.
This was done.
came the further order, "All pyramids are to contain a square number of
Whereupon the trouble arose.
"It can't be done," said the
"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
"All you have to do is to put the right number of balls in
"I've got it!" said a lieutenant, the mathematical
genius of the regiment.
"Lay the balls out singly."
the general. "You can't pile one ball into a
Is it really possible to obey both orders?