## Problem of the Day #242: Lone Ducks
*November 16, 2011*

*Posted by Alex in : potd , trackback*

Saketh wants to organize his ducks into groups. He has somewhere between $1$ and $1000$ ducks. When he tries to organize his ducks into groups of size $2$ each, he ends up with $1$ duck left over. When he tries to organize his ducks into groups of size $5$ each, he ends up with $2$ ducks left over. When he tries to organize his ducks into groups of size $9$, he ends up with $5$ ducks left over. Let $x$ be the number of ducks Saketh has. Find the number of possible values of $x$.

## Comments»

We think the answer is -snipped- possible values of x. Are we correct?

Yes, your answer is correct!