Maths Olympiad Exam

In a book with page numbers from 1 to 100, some pages are torn off. The sum of
the numbers on the remaining pages is 4949. How many pages are torn off?

Read Solution (Total 2)

How can the sum be 4949 if the total summation of 1st 100 numbers is 4914?
10 years agoHelpfull: Yes(0) No(0)

51 pages are torn off
4 years agoHelpfull: Yes(0) No(0)

Maths Olympiad Other Question

A convex polygon is such that the distance between any two vertices of does not exceed 1.
(i) Prove that the distance between any two points on the boundary of does not exceed 1.
(ii) If X and Y are two distinct points inside, prove that there exists a point Z on the boundary of such that XZ + Y Z 1. Show that there is no integer a such that a^2 - 3a - 19 is divisible by 289.