## Problem of the Day #174: The Operation GameSeptember 9, 2011

Posted by Saketh in : potd , trackback

Alex and Billy are playing a game. Starting with the value $1$, they take turns performing an operation on the current number. Alex takes his $n^{\mathrm{th}}$ turn by multiplying the current number by $n$. Billy performs each of his turns by simply replacing the current number with its square root.

If Alex and Billy play the game for an arbitrarily large number of turns, what value will the current number approach?

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