INTRODUCTION
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.
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
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