THE CROSS TARGET.
(
Combination and Group Problems)
+-+-+
|||
+-+-+
|||
+-+-+-+-+-+-+
| | | || | |
+-+-+-+-+-+-+
| | || || |
+-+-+-+-+-+-+
| ||
+-+-+
| | |
+-+-+
In the illustration we have a somewhat curious target designed by an
eccentric sharpshooter. His idea was that in order to score you must hit
four circles in as many shots so that those four shots shall form a
square. It will be seen by the results recorded on the target that two
attempts have been successful. The first man hit the four circles at the
top of the cross, and thus formed his square. The second man intended to
hit the four in the bottom arm, but his second shot, on the left, went
too high. This compelled him to complete his four in a different way
than he intended. It will thus be seen that though it is immaterial
which circle you hit at the first shot, the second shot may commit you
to a definite procedure if you are to get your square. Now, the puzzle
is to say in just how many different ways it is possible to form a
square on the target with four shots.
Answer:
[Illustration:
-- --
(CD)( )
-- --
(AE)(A )
-- -- -- -- -- --
(CE)(E )(A )(AB)(C )(D )
-- -- -- -- -- --
(D )( )(B )(E )(EB)( )
-- -- -- -- -- --
(C )(B )
-- --
( )(ED)
-- --
]
Twenty-one different squares may be selected. Of these nine will be of
the size shown by the four A's in the diagram, four of the size shown by
the B's, four of the size shown by the C's, two of the size shown by the
D's, and two of the size indicated by the upper single A, the upper
single E, the lower single C, and the EB. It is an interesting fact that
you cannot form any one of these twenty-one squares without using at
least one of the six circles marked E.
