irect solution, up to the profoundest
problems in the elegant domain of the theory of numbers.

Next we have the Geometrical Puzzle, a favourite and very ancient branch
of which is the puzzle in dissection, requiring some plane figure to be
cut into a certain number of pieces that will fit together and form
another figure. Most of the wire puzzles sold in the streets and
toy-shops are concerned with the geometry of position.

But these classes do not nearly embrace all kinds of puzzles even when we
allow for those that belong at once to several of the classes. There are
many ingenious mechanical puzzles that you cannot classify, as they stand
quite alone: there are puzzles in logic, in chess, in draughts, in cards,
and in dominoes, while every conjuring trick is nothing but a puzzle, the
solution to which the performer tries to keep to himself.

There are puzzles that look easy and are easy, puzzles that look easy and
are difficult, puzzles that look difficult and are difficult, and puzzles
that look difficult and are easy, and in each class we may of course have
degrees of easiness and difficulty. But it does not follow that a puzzle
that has conditions that are easily understood by the merest child is in
itself easy. Such a puzzle might, however, look simple to the uninformed,
and only prove to be a very hard nut to him after he had actually tackled
it.

For example, if we write down nineteen ones to form the number
1,111,111,111,111,111,111, and then ask for a number (other than 1 or
itself) that will divide it without remainder, the conditions are
perfectly simple, but the task is terribly difficult. Nobody in the world
knows yet whether that number has a divisor or not. If you can find one,
you will have succeeded in doing something that nobody else has ever
done.[A]

The number composed of seventeen ones, 11,111,111,111,111,111, has only
these two divisors, 2,071,723 and 5,363,222,357, and their discovery is
an exceedingly heavy task. The only number composed only of ones that we
know with certainty to have no divisor is 11. Such a number is, of
course, called a prime number.

The maxim that there are always a right way and a wrong way of doing
anything applies in a very marked degree to the solving of puzzles. Here
the wrong way consists in making aimless trials without method, hoping to
hit on the answer by accident--a process that generally results in our
getting hopelessly entangled in the trap that has