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Problem of the Week 836

Martian Artifacts

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You have just landed on Mars where you find 7 identical-looking spheres. From prior missions, you know the following:

  1. Each sphere is colored on the inside.
  2. One of the colors occurs for a strict majority of the spheres (4 or more).
  3. When two spheres of the same color touch each other, they both glow.
Your job is to carry out as few comparisons as possible, with the goal of holding in your hand a sphere that you are certain has the majority color. What is the smallest number of comparisons that is guaranteed to work?

Source: Stan Wagon (Macalester College) posed this problem for the recent Iowa problem fest.

© Copyright 1997 Stan Wagon. Reproduced with permission.

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The Math Forum

2 October 1998