Hot in the Pot
There's a new kid in class. She's smart. She has leaped to the head of the class and our protagonist wants her gone. She goes to the library and finds a book called How to Get Rid of your Enemy. There's a catch. You need one of your enemy's hairs. It has to be just one hair. While our protagonist is brewing her magic, she invites her enemy to visit -- to obtain that hair.
One of her own hairs falls in, too. Now, they must work together to stop the magic.