Problem:
A lemming sits at a corner of a square with side length meters. The lemming runs meters along a diagonal toward the opposite corner. It stops, makes a right turn and runs more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters?
Answer Choices:
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Solution:
Wherever the lemming is inside the square, the sum of the distances to the two horizontal sides is meters and the sum of the distances to the two vertical sides is meters. Therefore the sum of all four distances is meters, and the average of the four distances is meters.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions