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2004 AMC 10A Problem 7

Problem 7 of 25EasierAlgebraCombinatorics

A grocer stacks oranges in a pyramid-like stack whose rectangular base is 55 oranges by 88 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?

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Solution

There are five layers, each one shorter and narrower than the one below. The total number of oranges is 5⋅8+4⋅7+3⋅6+2⋅5+1⋅4=40+28+18+10+4=100. \begin{aligned} &5\cdot 8 + 4\cdot 7 + 3\cdot 6 \\ &\quad {}+ 2\cdot 5 + 1\cdot 4 \\ &= 40 + 28 + 18 + 10 + 4 = 100. \end{aligned} Thus, the correct answer is C.
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