# Long logic question from UMD math competition

There are 11 ants on a ruler. Each ant is on an inch marker (1 - 12). The ants on the left side of the ruler, on numbers 1-6, are crawling toward the right end of the ruler (towards 12). Ants on the other end of the ruler (7-12) are crawling toward the left end of the ruler (towards 1). All ants are crawling at the same speed. Every time two ants collide, they turn around and each ant reverses the direction it was travelling in. An ant is done crawling when it falls off the end of the ruler. How many inches, in total, did all of the ants travel before all falling off the ruler? And how do you solve this with nothing but pencil and paper? Thanks!

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