The Collatz conjecture is an Erdos problem. They're all deceptively easy to state.

Ramsey numbers are a perfect example. How many people do you have to invite to a party so that there's always a subset of n people who either all have met before or all haven't met before? For n = 3, the answer is 6. For n = 4, the answer is 18 (hard). For n = 5, no one knows. Finding Ramsey(5) is also an Erdos problem.