In my country there is a possibility for high school students to attend "Math Olympics". It's a nice competition starting from your school and advancing to the region and ending in a national final. The first set of problems are rather easy for anyone interested in Math or even just quick of mind; the second are more intriguing and the final ones are pretty hard and even University students struggle a lot on them. You need a special preparation for them.
All the material from past years competitions is online and free to download, but sadly it's not translated in English. I believe though that some similar competition exists in this language too, so try to google it and you might be happy with the results.
Bear in mind that these problems are usually "funny and lighthearted": they never mentions sets, groups, hardcore proofs or even Math question for that matter. They are basic Math problems disguised as funny quizzes (often with some theme background too) to make it more enjoyable. Whatever your level and preparation, if such a thing exists in English you'll be satisfied.