“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 bought feet, and each mother spent 8s. 51/4d. more than her daughter.  Mrs. Robinson spent 6s. more than Mrs. Evans, who spent about a quarter as much as Mrs. Jones.  Mrs. Smith spent most of all.  Mrs. Brown bought 21 yards more than Bessie—­one of the girls.  Annie bought 16 yards more than Mary and spent L3, 0s. 8d. more than Emily.  The Christian name of the other girl was Ada.  Now, what was her surname?

141.—­SATURDAY MARKETING.