A PACKING PUZZLE.
(
Measuring, Weight, and Packing Puzzles.)
As we all know by experience, considerable ingenuity is often required
in packing articles into a box if space is not to be unduly wasted. A
man once told me that he had a large number of iron balls, all exactly
two inches in diameter, and he wished to pack as many of these as
possible into a rectangular box 24+9/10 inches long, 22+4/5 inches
wide, and 14 inches deep. Now, what is the greatest number of the
balls that he could pack into that box?
Answer:
On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing
alternately 7 and 6 balls, or 85 in all. Above this we can place another
layer consisting of 12 rows of 7 and 6 alternately, or a total of 78. In
the length of 24+9/10 inches 15 such layers may be packed, the alternate
layers containing 85 and 78 balls. Thus 8 times 85 added to 7 times 78
gives us 1,226 for the full contents of the box.
