## Problem of the Day #306: The Clock
*January 19, 2012*

*Posted by Saketh in : potd , trackback*

Alex is stuck in a room with a very strange clock. Every time the minute hand of the clock reaches the $12$, the clock picks a real number $n$ between $1$ and $N$. The minute hand will then complete its next full rotation in $1/n$ real minutes.

Although Alex cannot keep track of the time exactly using this clock, he *can* estimate the current real time based on what the clock shows. Devise a formula he can use to do this.

**Bonus:** Devise a function $f(k)$ that gives the probability that Alex’s estimate of the real time is correct at $k$ clock hours.

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