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

139.--THE DUTCHMEN'S WIVES.

I wonder how many of my readers are acquainted with the puzzle of the
"Dutchmen's Wives"--in which you have to determine the names of three
men's wives, or, rather, which wife belongs to each husband. Some thirty
years ago it was "going the rounds," as something quite new, but I
recently discovered it in the _Ladies' Diary_ for 1739-40, so it was
clearly familiar to the fair sex over one hundred and seventy years ago.
How many of our mothers, wives, sisters, daughters, and aunts could
solve the puzzle to-day? A far greater proportion than then, let us
hope.

Three Dutchmen, named Hendrick, Elas, and Cornelius, and their wives,
Gurtruen, Katruen, and Anna, purchase hogs. Each buys as many as he (or
she) gives shillings for one. Each husband pays altogether three guineas
more than his wife. Hendrick buys twenty-three more hogs than Katruen,
and Elas eleven more than Gurtruen. Now, what was the name of each man's
wife?

[Illustration]

140.--FIND ADA'S SURNAME.

This puzzle closely resembles the last one, my remarks on the solution
of which the reader may like to apply in another case. It was recently
submitted to a Sydney evening newspaper that indulges in "intellect
sharpeners," but was rejected with the remark that it is childish and
that they only published problems capable of solution! Five ladies,
accompanied by their daughters, bought cloth at the same shop. Each of
the ten paid as many farthings per foot as she