[Illustration]
This is the form in which I first introduced the question of magic
squares with prime numbers. I will here warn the reader that there is a
little trap.
A fruit merchant had nine baskets. Every basket contained plums (all
sound and ripe), and the number in every basket was different. When
placed as shown in the illustration they formed a magic square, so that
if he took any three baskets in a line in the eight possible directions
there would always be the same number of plums. This part of the puzzle
is easy enough to understand. But what follows seems at first sight a
little queer.
The merchant told one of his men to distribute the contents of any
basket he chose among some children, giving plums to every child so that
each should receive an equal number. But the man found it quite
impossible, no matter which basket he selected and no matter how many
children he included in the treat. Show, by giving contents of the nine
baskets, how this could come about.