THE LEVEL PUZZLE.
(
Unicursal and Route Problems)
This is a simple counting puzzle. In how many different ways can you
spell out the word LEVEL by placing the point of your pencil on an L and
then passing along the lines from letter to letter. You may go in any
direction, backwards or forwards. Of course you are not allowed to miss
letters--that is to say, if you come to a letter you must use it.
Answer:
Let us confine our attention to the L in the top left-hand corner.
Suppose we go by way of the E on the right: we must then go straight on
to the V, from which letter the word may be completed in four ways, for
there are four E's available through which we may reach an L. There are
therefore four ways of reading through the right-hand E. It is also
clear that there must be the same number of ways through the E that is
immediately below our starting point. That makes eight. If, however, we
take the third route through the E on the diagonal, we then have the
option of any one of the three V's, by means of each of which we may
complete the word in four ways. We can therefore spell LEVEL in twelve
ways through the diagonal E. Twelve added to eight gives twenty
readings, all emanating from the L in the top left-hand corner; and as
the four corners are equal, the answer must be four times twenty, or
eighty different ways.
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