Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Number of points and planes. Number of points and planes – AIME I, 1999 Ten points in the plane are given with no three collinear. Four distinct segments...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME 2012 based on Arithmetic Sequence. Arithmetic Sequence Problem – AIME 2012 The terms of an arithmetic sequence add to \(715\). The first term of the sequence is increased by...

Try this beautiful problem from the PRMO, 2018 based on Digits of number. Digits of number – PRMO 2018 Consider all 6-digit numbers of the form abccba where b is odd. Determine the number of all such 6-digit numbers that are divisible by 7. is 107is 70is...

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 Positive Integer Problem from Algebra from PRMO 2017, Question 1. Positive Integer – PRMO 2017, Question 1 How many positive integers less than 1000 have the property that the sum of the digits of each such number is divisible by 7 and the...