Smallest value | PRMO 2018 | Question 15

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...

Arithmetic Mean | AIME I, 2015 | Question 12

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...

Distance Time | AIME I, 2012 | Question 4

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...

Sequence and fraction | AIME I, 2000 | Question 10

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...