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Problem of the Day #202: Binary Strings October 7, 2011

Posted by Billy in : potd , trackback

Albert creates a random binary string of length $20$. He searches from left to right through the string and replaces any instance of $101$ with $0$. He does this same procedure for $010$ and $1$. Albert continues applying these steps until there are no valid moves left. What is the expected value of the number Albert’s final binary string represents?

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