 ## Nearest value | PRMO 2018 | Question 14

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...

## Sequence and permutations | AIME II, 2015 | Question 10

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...

## Numbers of positive integers | AIME I, 2012 | Question 1

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, $abc$,...

## Number of points and planes | AIME I, 1999 | Question 10

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...

## Arithmetic Sequence Problem | AIME I, 2012 | Question 2

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...

## 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...