Difference between revisions of "1976 IMO Problems"
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Revision as of 17:35, 23 April 2012
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
Find the largest number obtainable as the product of positive integers whose sum is 
.
