Hard Math Question: Where Can I Find One?

I want to challenge myself with a tough math question (and its answer) to practice my problem-solving skills. Where can I find such questions, ideally with a step-by-step solution for better understanding?

One excellent source for challenging math problems is the Art of Problem Solving (AoPS) website. They have an extensive collection of math problems from various math competitions, as well as forums where you can discuss the problems with other math enthusiasts. You can find problems from subjects such as algebra, geometry, number theory, and combinatorics. The site also has resources and online courses if you're looking to delve deeper into a specific area of math.

Another option is Brilliant.org, which offers a wide range of challenging math and science problems. They also provide step-by-step solutions and explanations to help you understand the problem-solving process. Additionally, you can check out Project Euler, a collection of challenging math and computational problems that require creative problem-solving skills.

Finally, consider exploring past problems from prestigious math competitions, such as the International Mathematical Olympiad (IMO), the American Invitational Mathematics Examination (AIME), and the American Mathematics Competitions (AMC). These contests often have archives of past problems available on their respective websites, along with solutions to help you learn from your mistakes.

Remember, the more you practice, the better you'll become at problem-solving. Don't be discouraged if you need to seek help or struggle with a problem—it's all part of the learning process. Good luck, and happy problem-solving!