Mathematical_Recreations-Kraitchik-2e

~96 Mathematical Recreations
player's turn stops only when he draws a line which fails to
complete a square.
16. SQUARES-IN-LINE. The game is played on a square
array of n 2 cells, say on graph paper. The players alternate
in marking a cell at a time, each using his own distinguishing
mark. Whenever a player marks the last cell in a line of cells
parallel to a side or diagonal of the big square, he is credited
with all the cells in this line, and the player with the higher
final total wins. As in the Polytechnic School game, the
completion of a line usually is considered to give the player
another play.
17. l\L-\'RKED SQUARES. On a square array of 9 2 square
cells two players alternate in marking a cell at a time with a
crof'S (or they may place a counter in the cell). Whenever
a player marks the third, sixth, or ninth cell to be
marked in a row or column he wins 1, 2, or 3 points, respectively.
The player with the higher final total wins.
Variations may be introduced in the rules as follows: Diagonal
or broken diagonal alignments mayor may not be
counted. When a player scores one or more points he may
or may not be given another play. If two scores are obtained
simultaneously they mayor may not both be credited.
In another variation each player has his own mark, say
crosses for one and circles for the other. The marks are
placed on a board which is unbounded on two sides. The
object is then to obtain an orthogonal or diagonal line of
five successive marks of the same kind.
18. JOINING POINTS. An arbitrary set of points is marked
in an arbitrary manner on a plane. Alternately two players
join pairs of points by arbitrary (straight or curved) lines.
No point may be the end point of more than one line. No
line may pass through any point. No two points may be
joined by more than one line. No two lines may cross. The