Try this beautiful problem from the PRMO, 2018 based on Smallest value. Smallest Value – PRMO 2018 Let a and b natural numbers such that 2a-b, a-2b and a+b are all distinct squares. What is the smallest possible value of b? is 107is 21is 840cannot be determined...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Algebra and Positive Integer. Algebra and Positive Integer – AIME I, 1987 What is the largest positive integer n for which there is a unique integer k such...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2015 based on Arithmetic Mean. Arithmetic Mean of Number Theory – AIME 2015 Consider all 1000-element subsets of the set {1, 2, 3, … , 2015}. From each such subset choose...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2012 based on Distance Time. Distance Time – AIME 2012 When they meet at the milepost, Sparky has been ridden for n miles total. Assume Butch rides Sparky for a miles, and...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and fraction. Sequence and fraction – AIME I, 2000 A sequence of numbers \(x_1,x_2,….,x_{100}\) has the property that, for every integer k...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2000 based on Arithmetic and geometric mean with Algebra. Arithmetic and geometric mean with Algebra – AIME 2000 Find the number of ordered pairs (x,y) of integers is it...