ber of men there could have
been?

In order to make clear to the reader the simplicity of the question, I
will give the lowest solutions in the case of 60 and 62, the numbers
immediately preceding and following 61. They are 60 x 4 squared + 1 = 31 squared,
and 62 x 8 squared + 1 = 63 squared. That is, 60 squares of 16 men each would be 960
men, and when Harold joined them they would be 961 in number, and so
form a square with 31 men on every side. Similarly in the case of the
figures I have given for 62. Now, find the lowest answer for 61.

130.--THE SCULPTOR'S PROBLEM.

An ancient sculptor was commissioned to supply two statues, each on a
cubical pedestal. It is with these pedestals that we are concerned. They
were of unequal sizes, as will be seen in the illustration, and when the
time arrived for payment a dispute arose as to whether the agreement was
based on lineal or cubical measurement. But as soon as they came to
measure the two pedestals the matter was at once settled, because,
curiously enough, the number of lineal feet was exactly the same as the
number of cubical feet. The puzzle is to find the dimensions for two
pedestals having this peculiarity, in the smallest possible figures. You
see, if the two pedestals, for example, measure respectively 3 ft. and 1
ft. on every side, then the lineal measurement would be 4 ft. and the
cubical contents 28 ft., which are not the same, so these measurements
will not do.

[Illustration]

131.--THE SPANISH MISER.

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. These puzzles 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.

[Illustration]

Each box contained a different number of golden doubloons. 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 box. And if the
contents of any two of th