## Problem of the Day #242: Lone DucksNovember 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 $x$.