MathDB

5

Part of 2010 Malaysia National Olympiad

Problems(3)

ratio of areas, square, circle - Malaysia 2010 OMK Bongsu / Juniors p5

Source:

10/26/2021
A circle and a square overlap such that the overlapping area is 50%50\% of the area of the circle, and is 25%25\% of the area of the square, as shown in the figure. Find the ratio of the area of the square outside the circle to the area of the whole figure. https://cdn.artofproblemsolving.com/attachments/e/2/c209a95f457dbf3c46f66f82c0a45cc4b5c1c8.png
ratioareasgeometry
OMK 2010

Source: Malaysia National Olympiad 2010 Muda Category Problem 5

6/4/2011
Find the number of triples of nonnegative integers (x,y,z)(x,y,z) such that x2+2xy+y2āˆ’z2=9.x^2+2xy+y^2-z^2=9.
algebra unsolvedalgebra
All Odd Numbers

Source: Malaysia National Olympiad 2010 Sulung Category Problem 5

6/4/2011
Let nn be an integer greater than 1. If all digits of 97n97n are odd, find the smallest possible value of nn.
number theory unsolvednumber theory