2010 AMC 10A Problem 20
Problem 20 of 25HarderAlgebraGeometryCounting & Probability
A fly trapped inside a cubical box with side length meter decides to relieve its boredom by visiting each corner of the box. It will begin and end in the same corner and visit each of the other corners exactly once. To get from a corner to any other corner, it will either fly or crawl in a straight line. What is the maximum possible length, in meters, of its path?
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Solution
Note that all the paths the fly can take have lengths of or
There are only space diagonals in the cube, so at most moves can have length The other moves have length at most
This upper bound is attainable, for example by alternating space diagonals and face diagonals around the vertices.
The path has length
Thus, D is the correct answer.