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Amusements in Mathematics

Puzzle Games
"He that is beaten may be said
To lie in honour's truckle bed."
It may be said generally that a game is a contest of skill for two or more persons, into
which we enter either for amusement or to win a prize. A puzzle is something to be done
or solved by the individual. For example, if it were possible for us so to master the
complexities of the game of chess that we could be assured of always winning with the
first or second move, as the case might be, or of always drawing, then it would cease to
be a game and would become a puzzle. Of course among the young and uninformed,
when the correct winning play is not understood, a puzzle may well make a very good
game. Thus there is no doubt children will continue to play "Noughts and Crosses,"
though I have shown (No. 109, "Canterbury Puzzles") that between two players who both
thoroughly understand the play, every game should be drawn. Neither player could ever
win except through the blundering of his opponent. But I am writing from the point of
view of the student of these things.
The examples that I give in this class are apparently games, but, since I show in every
case how one player may win if he only play correctly, they are in reality puzzles. Their
interest, therefore, lies in attempting to discover the leading method of play.
Here is an interesting little puzzle game that I used to play with an acquaintance on the
beach at Slocomb-on-Sea. Two players place an odd number of pebbles, we will say
fifteen, between them. Then each takes in turn one, two, or three pebbles (as he chooses),
and the winner is the one who gets the odd number. Thus, if you get seven and your
opponent eight, you win. If you get six and he gets nine, he wins. Ought the first or
second player to win, and how? When you have settled the question with fifteen pebbles
try again with, say, thirteen.
This is a puzzle game for two players. Each player has a single rook. The first player
places his rook on any square of the board that he may choose to select, and then the
second player does the same. They now play in turn, the point of each play being to
capture the opponent's rook. But in this game you cannot play through a line of attack
without being captured. That is to say, if in the diagram it is Black's turn to play, he
cannot move his rook to his king's knight's square, or to his king's rook's square, because
he would enter the "line of fire" when passing his king's bishop's square. For the same
reason he cannot move to his queen's rook's seventh or eighth squares. Now, the game
can never end in a draw. Sooner or later one of the rooks must fall, unless, of course, both
players commit the absurdity of not trying to win. The trick of winning is ridiculously
simple when you know it. Can you solve the puzzle?