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2010 Math Kangaroo

Problem 8

Problem 8 · 2010 Math Kangaroo Medium
Number Theory divisibility

Which of the following numbers could be the number of edges of a prism?

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Answer: E — 2010
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Hint 1 of 2
A prism with an n-sided base has the same number of edges each time.
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Hint 2 of 2
Count: n on top, n on the bottom, n verticals.
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Approach: edge count of a prism is always a multiple of 3
  1. An n-gon prism has n top edges, n bottom edges, and n vertical edges: 3n total.
  2. So the number of edges must be a multiple of 3.
  3. Among the options only 2010 = 3×670 is a multiple of 3, so 2010.
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