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A WAR PUZZLE GAME.

(Puzzle Games.)
Here is another puzzle game. One player, representing the British
general, places a counter at B, and the other player, representing the
enemy, places his counter at E. The Britisher makes the first advance
along one of the roads to the next town, then the enemy moves to one of
his nearest towns, and so on in turns, until the British general gets
into the same town as the enemy and captures him. Although each must
always move along a road to the next town only, and the second player
may do his utmost to avoid capture, the British general (as we should
suppose, from the analogy of real life) must infallibly win. But how?
That is the question.


Answer:

The Britisher can always catch the enemy, no matter how clever and
elusive that astute individual may be; but curious though it may seem,
the British general can only do so after he has paid a somewhat
mysterious visit to the particular town marked "1" in the map, going in
by 3 and leaving by 2, or entering by 2 and leaving by 3. The three
towns that are shaded and have no numbers do not really come into the
question, as some may suppose, for the simple reason that the Britisher
never needs to enter any one of them, while the enemy cannot be forced
to go into them, and would be clearly ill-advised to do so voluntarily.
We may therefore leave these out of consideration altogether. No matter
what the enemy may do, the Britisher should make the following first
nine moves: He should visit towns 24, 20, 19, 15, 11, 7, 3, 1, 2. If the
enemy takes it into his head also to go to town 1, it will be found that
he will have to beat a precipitate retreat _the same way that he went
in_, or the Britisher will infallibly catch him in towns 2 or 3, as the
case may be. So the enemy will be wise to avoid that north-west corner
of the map altogether.
Now, when the British general has made the nine moves that I have given,
the enemy will be, after his own ninth move, in one of the towns marked
5, 8, 11, 13, 14, 16, 19, 21, 24, or 27. Of course, if he imprudently
goes to 3 or 6 at this point he will be caught at once. Wherever he may
happen to be, the Britisher "goes for him," and has no longer any
difficulty in catching him in eight more moves at most (seventeen in
all) in one of the following ways. The Britisher will get to 8 when the
enemy is at 5, and win next move; or he will get to 19 when the enemy is
at 22, and win next move; or he will get to 24 when the enemy is at 27,
and so win next move. It will be found that he can be forced into one or
other of these fatal positions.
In short, the strategy really amounts to this: the Britisher plays the
first nine moves that I have given, and although the enemy does his very
best to escape, our general goes after his antagonist and always driving
him away from that north-west corner ultimately closes in with him, and
wins. As I have said, the Britisher never need make more than seventeen
moves in all, and may win in fewer moves if the enemy plays badly. But
after playing those first nine moves it does not matter even if the
Britisher makes a few bad ones. He may lose time, but cannot lose his
advantage so long as he now keeps the enemy from town 1, and must
eventually catch him.
This is a complete explanation of the puzzle. It may seem a little
complex in print, but in practice the winning play will now be quite
easy to the reader. Make those nine moves, and there ought to be no
difficulty whatever in finding the concluding line of play. Indeed, it
might almost be said that then it is difficult for the British general
_not_ to catch the enemy. It is a question of what in chess we call the
"opposition," and the visit by the Britisher to town 1 "gives him the
jump" on the enemy, as the man in the street would say.
Here is an illustrative example in which the enemy avoids capture as
long as it is possible for him to do so. The Britisher's moves are above
the line and the enemy's below it. Play them alternately.
24 20 19 15 11 7 3 1 2 6 10 14 18 19 20 24
-----------------------------------------------
13 9 13 17 21 20 24 23 19 15 19 23 24 25 27
The enemy must now go to 25 or B, in either of which towns he is
immediately captured.










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