 ## 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...

## Digits of number | PRMO 2018 | Question 3

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...

## 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...

## Algebra and Positive Integer | AIME I, 1987 | Question 8

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...

## Positive Integer | PRMO-2017 | Question 1

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...