AoPS Wiki talk:Problem of the Day/July 28, 2011

Problem

AoPSWiki:Problem of the Day/July 28, 2011

Solution

The distances the ball bounces form a geometric sequence. The sequence goes $24, 18, 18, \frac{27}{2}, \frac{27}{2}...$ infinitely (each, except for the 24, is duplicated because the ball goes up $n$ inches, and comes back down $n$ inches). If we add together the terms that are the same (and add a 24 to the beginning for the sake of a nice pattern), we get $48, 36, 27...$. Thus, our solution is $\frac{48}{1-\frac{3}{4}}=192-24=\boxed{168 inches}$.

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