138 Geometrical Problems
- THE FOUR PENNIES
Take four pennies and arrange them
on the table without the assistance of
another coin or any other means of
measurement, so that when a fifth
penny is produced it may be placed in
exact contact with each of the four
(without moving them) in the man-
ner shown in the illustration. The
shaded circle represents the fifth
penny.
If you trust to the eye alone you will
probably fail to get the four in correct
position, but it can be done with
absolute exactitude. How should you
proceed?- THE SIX PENNIES
Lay six pennies on the table, and
then arrange them as shown by the
six white circles in the illustration, so
that if a seventh penny (the black
circle) were produced it could be
dropped in the center and exactly
touch each of the six. It is required
to get it exact, without any depend-
ence on the eye. In this case you are
not allowed to lift any penny off the
table-otherwise there would be no
puzzle at all-nor can any measuring
or marking be employed. You require
only the six pennies.