If there were no
puzzles to solve, there would be no questions to ask; and if there were
no questions to be asked, what a world it would be! We should all be
equally omniscient, and conversation would be useless and idle.

It is possible that some few exceedingly sober-minded mathematicians,
who are impatient of any terminology in their favourite science but the
academic, and who object to the elusive x and y appearing under any
other names, will have wished that various problems had been presented
in a less popular dress and introduced with a less flippant phraseology.
I can only refer them to the first word of my title and remind them that
we are primarily out to be amused--not, it is true, without some hope of
picking up morsels of knowledge by the way. If the manner is light, I
can only say, in the words of Touchstone, that it is "an ill-favoured
thing, sir, but my own; a poor humour of mine, sir."

As for the question of difficulty, some of the puzzles, especially in
the Arithmetical and Algebraical category, are quite easy. Yet some of
those examples that look the simplest should not be passed over without
a little consideration, for now and again it will be found that there is
some more or less subtle pitfall or trap into which the reader may be
apt to fall. It is good exercise to cultivate the habit of being very
wary over the exact wording of a puzzle. It teaches exactitude and
caution. But some of the problems are very hard nuts indeed, and not
unworthy of the attention of the advanced mathematician. Readers will
doubtless select according to their individual tastes.

In many cases only the mere answers are given. This leaves the beginner
something to do on his own behalf in working out the method of solution,
and saves space that would be wasted from the point of view of the
advanced student. On the other hand, in particular cases where it seemed
likely to interest, I have given rather extensive solutions and treated
problems in a general manner. It will often be found that the notes on
one problem will serve to elucidate a good many others in the book; so
that the reader's difficulties will sometimes be found cleared up as he
advances. Where it is possible to say a thing in a manner that may be
"understanded of the people" generally, I prefer to use this simple
phraseology, and so engage the attention and interest of a larger
public. The mathematician will in such cases have no difficulty in
expressing th