Mathematical_Recreations-Kraitchik-2e

~84 Mathematical Recreations
To begin the game each player locates his own fleet on one
of his charts in any manner he chooses, subject to the following
restrictions: (1) Each ship must cover a rectangle of cells
of the same shape and size as itself. (2) No two ships may
touch, even at a vertex. (3) A ship may have at most one
side of one cell in common with the border of the field. (Thus
a submarine may not be placed in a corner.)
When the fleets have been drawn up in battle array one of
the players fires a salvo of 3 shots, by announcing to his opponent
the locations of the 3 cells in which they are supposed
to land. The opponent must then announce the effect of the
shots on his fleet, by indicating how many fell in "open
water" and how many hit which types of ships, but without
specifying the effect of each individual shot. (For example,
he may say, "Two in the water and one on a cruiser," regardless
of the order in which these results were obtained.)
The second player now fires a salvo and receives the report
of its effect. The play alternates in this manner until one of
the players disposes of his opponent's entire fleet and announces
the fact.
The game raises a number of interesting questions. For
example, what disposition of the fleet will require the maximum
number of salvos for the determination of its location?
Or again, what is the minimum number of salvos that suffice
to end a particular game?
10. CHECKERS (DRAUGHTS). As this game is undoubtedly
familiar to our readers we shall confine our remarks to
comments on variations commonly played in other countries.
In France the game is played on an 8 X 8 board. A piece
is called a pawn until it reaches the eighth row, when it becomes
a queen. (The game is known as jeu des dames, game
of the queens.) Unlike our king, the queen may move as far
along any diagonal as she wishes, over any number of pieces,
taking all over which she passes.