The student of arithmetic who has mastered the first four rules of his art, and successfully striven with money sums and fractions, finds himself confronted by an unbroken expanse of questions known as problems. These are short stories of adventure and industry with the end omitted, and though betraying a strong family resemblance, are not without a certain element of romance.

The characters in the plot of a problem are three people called A, B and C. The form of the question is generally of this sort:- ‘A, B and C do a certain piece of work. A can do as much work in one hour as B in two, or C in four. Find how long they work at it.’

Or thus:- ‘A, B and C are employed to dig a ditch. A can dig as much in one hour as B can dig in two, and B can dig twice as fast as C. Find how long, etc., etc.’

Or after this wise:- ‘A lays a wager that he can walk faster than B or C. A can walk half as fast again as B, and C is only an indifferent walker. Find how far, and so forth.’ […]