[Illustration]
In the county of Devon, where the cider comes from, fifteen of the
inhabitants of a village are imbued with an excellent spirit of friendly
rivalry, and a few years ago they decided to settle by actual experiment
a little difference of opinion as to the cultivation of apple trees. Some
said they want plenty of light and air, while others stoutly maintained
that they ought to be planted pretty closely, in order that they might
get shade and protection from cold winds. So they agreed to plant a lot
of young trees, a different number in each orchard, in order to compare
results.
One man had a single tree in his field, another had two trees, another
had three trees, another had four trees, another five, and so on, the
last man having as many as fifteen trees in his little orchard. Last year
a very curious result was found to have come about. Each of the fifteen
individuals discovered that every tree in his own orchard bore exactly
the same number of apples. But, what was stranger still, on comparing
notes they found that the total gathered in every allotment was almost
the same. In fact, if the man with eleven trees had given one apple to
the man who had seven trees, and the man with fourteen trees had given
three each to the men with nine and thirteen trees, they would all have
had exactly the same.
Now, the puzzle is to discover how many apples each would have had (the
same in every case) if that little distribution had been carried out. It
is quite easy if you set to work in the right way.