There are numerous solutions to this little agricultural problem. The
version I give in the next column is rather curious on account of the
long parallel straight lines formed by some of the moves.
[Illustration: Farmer Lawrence's Cornfields.]
336.--THE GREYHOUND PUZZLE.
There are several interesting points involved in this question. In the
first place, if we had made no stipulation as to the positions of the
two ends of the string, it is quite impossible to form any such string
unless we begin and end in the top and bottom row of kennels. We may
begin in the top row and end in the bottom (or, of course, the reverse),
or we may begin in one of these rows and end in the same. But we can
never begin or end in one of the two central rows. Our places of
starting and ending, however, were fixed for us. Yet the first half of
our route must be confined entirely to those squares that are
distinguished in the following diagram by circles, and the second half
will therefore be confined to the squares that are not circled. The
squares reserved for the two half-strings will be seen to be symmetrical
and similar.
The next point is that the first half-string must end in one of the
central rows, and the second half-string must begin in one of these
rows. This is now obvious, because they have to link together to form
the complete string, and every square on an outside row is connected by
a knight's move with similar squares only--that is, circled or
non-circled as the case may be. The half-strings can, therefore, only be
linked in the two central rows.
[Illustration]
Now, there are just eight different first half-strings, and consequently
also eight second half-strings. We shall see that these combine to form
twelve complete strings, which is the total number that exist and the
correct solution of our puzzle. I do not propose to give all the routes
at length, but I will so far indicate them that if the reader has
dropped any he will be able to discover which they are and work them out
for himself without any difficulty. The following numbers apply to those
in the above diagram.
Public-domain text, read in full here on John Shaqi.
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