# Test Your Intuition (1)

Question:  Suppose that we sequentially place $n$ balls into $n$ boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability $(1+o(1))\ln n/\ln \ln n$ balls in it. Suppose instead that for each ball we choose two boxes at random and place the ball into the one which is less full at the time of placement. What will be the maximum occupancy?

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