Problem:
A corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?
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Solution:
The square in the upper left-hand region is tessellated, so finding the proportion of darker tiles in this region will answer the question. The top left-hand corner of this region is a square that has darker tiles. So of the total area will be made of darker tiles.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions