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Problem of the Day #311: Making Powers January 24, 2012

Posted by Alex in : potd , trackback

Albert starts with a list, containing only $1$ and $2$. At any step, he is allowed to take any two elements from his list (not necessarily distinct) and either multiply or divide them, adding the new result to the list. After some set of operations, the number $2^{17}$ is in the list. What is the smallest possible size of the list?

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