# Breaking pencils in two

Probability Level 3

You have 2016 sticks of the same length in a box. You pick a stick at random, break it into two equal halves, and put them back in for a total of 2017 sticks. You repeat this process of random picking and breaking indefinitely.

What is the maximum value of $x$ such that, at any time during this process, you are guaranteed to have at least $x$ sticks of the same length?

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