Difference between revisions of "1976 IMO Problems"
(New page: Problems of the 18th IMO 1976 in Austria. ==Day 1== ===Problem 1=== In a convex quadrilateral (in the plane) with the area of <math>32 \text{ cm}^{2}</math> the sum of two opposite si...) |
(No difference)
|
Revision as of 23:19, 10 February 2009
Problems of the 18th IMO 1976 in Austria.
Contents
Day 1
Problem 1
In a convex quadrilateral (in the plane) with the area of 
the sum of two opposite sides and a diagonal is 
. Determine all the possible values that the other diagonal can have.
Problem 2
Let 
and 
for 
Prove that for any positive integer n the roots of the equation 
are all real and distinct.
Problem 3
A box whose shape is a parallelepiped can be completely filled with cubes of side 
If we put in it the maximum possible number of cubes, each of volume 
, with the sides parallel to those of the box, then exactly 
percent from the volume of the box is occupied. Determine the possible dimensions of the box.
Day 2
Problem 4
Determine the greatest number, who is the product of some positive integers, and the sum of these numbers is 
