Mathematical Problem Solving for Enthusiasts

• Project Euler. Over 800 mathematically-oriented problems that require writing computer programs to solve. The problems are mainly computational in nature, but “brute force” solutions usually don’t work, which forces you to think more creatively. New problems are periodically added to the list.
• IBM Ponder this. A collection of puzzle problems from the IBM Research team. A new problem is posted each month, with its solution published a month later. The problems are non-trivial, and often very challenging. Although the problem statements are usually competition-style, many problems have serious mathematical foundations, and finding a general solution represents a research problem.

Computer Science and Programming Problems

• Regex Tuesday. A collection of tricky regular expression (regex) problems. Useful practice for those planning to work in web development or process unstructured text data. You can practice and debug your regular expressions here.
• Code Golf. Solving programming problems with minimal code size. Each programming language naturally has its own independent hall of fame.

Tournaments and Competitions

Research Problem Catalogs

• Open Problem Garden. This is a collection of unsolved mathematical problems. You can periodically think about them - maybe you’ll figure something out… Each problem comes with a comment indicating what is known to date and a short bibliography.