Problem:
A box contains a collection of triangular and square tiles. There are tiles in the box, containing edges total. How many square tiles are there in the box?
Answer Choices:
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Solution:
Counting edges per tile gives a total of edges, and exactly edge per square tile is missing. So there are exactly square tiles.
Let be the number of square tiles in the box. Then there are triangular tiles and edges. Solving for gives square tiles.
The problems on this page are the property of the MAA's American Mathematics Competitions