For 6 months, I'll be organizing, as part as my volunteer work in an NGO, math classes with small groups (~10 students, aged 16 or 17). These classes are not compulsory, but students willing to stay past the third class must accept to attend all subsequent classes, for a full year. In fact, it's not even true classes: the focus is mostly on discussing and solving interesting exercises, and motivated kids from low-income backgrounds to pursue advanced studies in the future.
I'll be giving my first "class" next Tuesday, and since the first class doesn't require any future commitment, I'm expecting around 30-40 people. I'm therefore thinking on focusing on fun math questions, little problems and mind twisters, but I'm not sure where to start.
Do you have ideas of fun problems that could motivate kids to stay? The first class will last two hours.