1960 IMO Problems
Problems of the 2nd IMO 1960 Romania.
Contents
[hide]Day I
Problem 1
Determine all three-digit numbers having the property that is divisible by 11, and is equal to the sum of the squares of the digits of .
Problem 2
For what values of the variable does the following inequality hold:
Problem 3
In a given right triangle , the hypotenuse , of length , is divided into equal parts ( and odd integer). Let be the acute angle subtending, from , that segment which contains the midpoint of the hypotenuse. Let be the length of the altitude to the hypotenuse of the triangle. Prove that: