Problem:
A grocer stacks oranges in a pyramid-like stack whose rectangular base is oranges by oranges. Each orange above the first level rests in a pocket formed by four oranges in the level below. The stack is completed by a single row of oranges. How many oranges are in the stack?
Answer Choices:
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Solution:
There are five layers in the stack, and each of the top four layers has one less orange in its length and width than the layer on which it rests. Hence the total number of oranges in the stack is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions