It is that time of year that mathematics teachers search for new and interesting problems to share with their students (to help keep their attention) or to do themselves (to help renew your own attention). If you aren't searching for new problems for either of these reasons, then get with it!
One interesting problem resource site is MathsChallenge.net, a website "dedicated to the puzzling world of mathematics." I cannot determine who coordinates this web site, except that it originates in England.
First, MathsChallenge.net offers its "latest" problems on a sporadic basis (determining a pattern in the release of new problems is a problem in itself). These problems are rated by possible difficulty level:
- 1-star problems: require a logical mind and a willingness to explore ideas on paper
- 2-star problems: require insights and general mathematical tools/knowledge
- 3-star problems: require a solid knowledge of mathematics (skills and concepts) plus some ability to prove conjectures
- 4-star problems: require both a broad understanding of mathematics (high school level) and the use of advanced mathematical tools
You can also search the site's extensive problem bank, using both key words and difficulty level. For example, on my search for "triangle" prolems at the 3-star level, twenty-four interesting problems were returned for my exploration and use.
MathsChallenge.net also has an interesting FAQ section, which provides responses to a wide variety of questions sorted in the categories of Number, Geometry, Constructions, and Code-Breaking. Examples of questions range from "Is 0.999... equal to 1?" to "How do you prove the Pythagorean Theorem?" to "Is it possible to solve quadratics geometrically?" to "What is a shuffle/transposition cipher?"
Finally, MathsChallenge.net provides useful links grouped as resources for Problem Solving & Puzzles, References Resoutrces, History of Mathematics, Tools and Resources, Programming Problems, and selected Mathematics Links. If the website's collections of problems do not meet your needs, I guarantee that some of these sites will!