PLACING HALFPENNIES.
(
Unclassified Problems.)
Here is an interesting little puzzle suggested to me by Mr. W. T. Whyte.
Mark off on a sheet of paper a rectangular space 5 inches by 3 inches,
and then find the greatest number of halfpennies that can be placed
within the enclosure under the following conditions. A halfpenny is
exactly an inch in diameter. Place your first halfpenny where you like,
then place your second coin at exactly the distance of an inch from the
first, the third an inch distance from the second, and so on. No
halfpenny may touch another halfpenny or cross the boundary. Our
illustration will make the matter perfectly clear. No. 2 coin is an inch
from No. 1; No. 3 an inch from No. 2; No. 4 an inch from No. 3; but
after No. 10 is placed we can go no further in this attempt. Yet several
more halfpennies might have been got in. How many can the reader place?
Answer:
Thirteen coins may be placed as shown on page 252.
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