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Amusements in Mathematics

Arithmetical And Algebraical Problems
"And what was he?
Forsooth, a great arithmetician."
Othello, I. i.
The puzzles in this department are roughly thrown together in classes for the convenience
of the reader. Some are very easy, others quite difficult. But they are not arranged in any
order of difficulty—and this is intentional, for it is well that the solver should not be
warned that a puzzle is just what it seems to be. It may, therefore, prove to be quite as
simple as it looks, or it may contain some pitfall into which, through want of care or
over-confidence, we may stumble.
Also, the arithmetical and algebraical puzzles are not separated in the manner adopted by
some authors, who arbitrarily require certain problems to be solved by one method or the
other. The reader is left to make his own choice and determine which puzzles are capable
of being solved by him on purely arithmetical lines.
"Put not your trust in money, but put your money in trust."
In every business of life we are occasionally perplexed by some chance question that for
the moment staggers us. I quite pitied a young lady in a branch post-office when a
gentleman entered and deposited a crown on the counter with this request: "Please give
me some twopenny stamps, six times as many penny stamps, and make up the rest of the
money in twopence-halfpenny stamps." For a moment she seemed bewildered, then her
brain cleared, and with a smile she handed over stamps in exact fulfilment of the order.
How long would it have taken you to think it out?
The precocity of some youths is surprising. One is disposed to say on occasion, "That boy
of yours is a genius, and he is certain to do great things when he grows up;" but past
experience has taught us that he invariably becomes quite an ordinary citizen. It is so
often the case, on the contrary, that the dull boy becomes a great man. You never can tell.
Nature loves to present to us these queer paradoxes. It is well known that those wonderful