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Problem of the Day #165: Redecorating the Barn August 31, 2011

Posted by Saketh in : potd , trackback

Alex is firing paintballs at the barn’s side wall. While each shot he fires is of a different color, he also wishes to produce “hybrid” colors by overlapping some of these splotches of paint. Unfortunately, he doesn’t have very good aim and cannot make any guarantees when it comes to producing overlaps.

Since Alex is in possession of a very large paint shooter, he knows that each shot will cover at least half of the barn wall. If he wishes to guarantee that at least one of the hybrid colors he produces will take up at least one fifth of the barn wall, how many paintballs must he fire?

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