After reading How to build a class based on Project Euler? I was inspired to suggest some work on Project Euler over the summer as part of an ad-hoc math/programming club. It looks like I will be able to put together a small audience for the project and need to start organizing soon.
I'm looking for any speculation on how well this might go, from people who have some experience with Project Euler problems (I have no such experience).
Imagine five to six students meeting with pizza and a goal to complete a few Euler problems in a collaborative setting. What are some pitfalls or possible issues I should avoid? Is there really any room for collaboration at all? The students are very good and are unafraid of programming.