Problem:
What is the largest number of solid -in -in -in blocks that can fit in a -in -in -in box?
Answer Choices:
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B.
C.
D.
E.
Solution:
A possible arrangement of blocks is shown by the figure.
Four blocks do not completely fill the box because the combined volume of the blocks is only cubic inches, whereas the volume of the box is cubic inches. Because the unused space, cubic inches, is less than the volume of a block, cubic inches, no more than blocks can fit in the box.
The problems on this page are the property of the MAA's American Mathematics Competitions