Project Euler has an ever-growing collection of 500+ such problems, and all of them can be accessed freely. You can start with simple problems (that over 500,000 users have solved) and eventually work your way to harder and harder questions. As of the time of publishing the post, the last question (question 579) has only been solved by 53 people. It starts fairly easy, but gets difficult quickly - so make yourself a community and challenge your friends as you work through the questions.
In fact, Project Euler has a community built around it. When you solve a question, you get access to a discussion thread about that question. That way you can look at other solutions and improve your own, and share your own solution too. The idea is to share and learn, and ensure that you solve the question with an algorithm that gives the answer in under 1 minute.
So here’s the first question: