Daily Brain Teaser #1

This is the first of what will become a vast collection of brain teasers for kids in the upper elementary grades. I plan to post a new puzzle each weekday.

Lucy collects troll dolls. She has more than 12 trolls, but less than 35.
If she puts all of of her trolls in two groups, she will have one left over.
If she put them in groups of three, there will be two left over.
If she puts them in groups of four, there will be three left over.
How many troll dolls does Lucy have?

Please feel free to share how you or your students solved the puzzles!