Try this beautiful problem from the PRMO, 2018 based on Nearest value. Nearest Value – PRMO 2018 If x=cos1cos2cos3…..cos89 and y=cos2cos6cos10….cos86, then what is the integer nearest to \(\frac{2}{7}log_2{\frac{y}{x}}\)? is 107is 19is 840cannot be...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME II, 2015 based on Sequence and permutations. Sequence and permutations – AIME II, 2015 Call a permutation \(a_1,a_2,….,a_n\) of the integers 1,2,…,n quasi...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME 2012 based on Numbers of positive integers. Numbers of positive integers – AIME 2012 Find the number of positive integers with three not necessarily distinct digits, \(abc\),...

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 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...