What is the purpose of the contest? That will greatly influence your decision.

When it comes to problems, there are two types, those with just one problem to solve, and those with multiple problems (each counting for a number of points).

There are open ones and controlled ones. Open/public, you announce the task to be done and deadline when to submit the result/entry, then examine them. Or controlled, having people come to a scheduled event, and try to solve the problems (not know ahead of time) that you give them, in a certain amount of time.