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Problem of the Day #370: Rows of Counters March 23, 2012

Posted by Saketh in : potd , trackback

Alex is playing a game in which he manipulates a row of black and white counters. To change the row, he is allowed to remove any black counter and replace it with either a white counter and a black counter (in that order), or two black counters. He is not allowed to perform any other manipulations.

If he starts with a single black counter, how many distinct rows of $10$ counters can he arrange?

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