There once lived in
a small town in New Castile a
noted miser named Don Manuel Rodriguez.
His love of money was only
equalled by a strong passion for arithmetical problems.
usually dealt in some way or other with his accumulated treasure, and
were propounded by him solely in order that he might have the pleasure
of solving them himself.
Unfortunately very few of them have survived,
and when travelling through Spain, collecting material for a proposed
work on "The Spanish Onion as a Cause of National Decadence," I only
discovered a very few.
One of these concerns the three boxes that
appear in the accompanying authentic portrait.
Each box contained
a different number of golden
The difference between the number of doubloons in the upper
box and the number in the middle box was the same as the difference
between the number in the middle box and the number in the bottom
And if the contents of any two of the boxes were united they would form
a square number.
What is the
smallest number of doubloons that there
could have been in any one of the boxes?