I'm currently in grade 12, and I really enjoy solving tough math problems to challenge myself further. Can anyone suggest or link some hard problems with answers that I can work on? Thanks in advance!
Sure! I'd be happy to share a few challenging math problems for you to work on. One great resource for finding difficult math problems with solutions is the American Invitational Mathematics Examination (AIME). The AIME is a prestigious competition in the United States for high school students who excel in math. Many of the questions are designed for Grades 11 and 12, so they should provide a good challenge for you. Here are a couple of problems from recent AIME competitions:
1. In how many ways can the positive integers from 1 through 9 be arranged in a 3x3 grid so that the numbers in each row, column, and diagonal are non-decreasing from left to right, top to bottom?
2. Triangular numbers are numbers of the form Tn = n(n+1)/2 for some positive integer n, e.g., 1, 3, 6, 10, 15, and so on. Find the number of positive integers less than 1000 that are triangular and not perfect squares.
You can also find past AIME exams and solutions from the Art of Problem Solving (AoPS) website. Simply search for "AIME problems and solutions" on their site.
Additionally, you can check out the International Mathematical Olympiad (IMO) and its regional qualifying competitions like the USA Mathematical Olympiad (USAMO) and the European Girls' Mathematical Olympiad (EGMO), which often feature advanced problems. Just keep in mind that these competitions are for very high-level students and might be more challenging than AIME problems.
I hope you find these problems enjoyable and challenging! Good luck and have fun solving them!
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