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

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?

- Each sphere is colored on the inside.
- One of the colors occurs for a strict majority of the spheres (4 or more).
- When two spheres of the same color touch each other, they both glow.

Source:Stan Wagon (Macalester College) posed this problem for the recent Iowa problem fest.© Copyright 1997 Stan Wagon. Reproduced with permission.

2 October 1998