1962 IMO Problems
Contents
Day I
Problem 1
Find the smallest natural number which has the following properties:
(a) Its decimal representation has 6 as the last digit.
(b) If the last digit 6 is erased and placed in front of the remaining
digits, the
resulting number is four times as large as the original number .
Problem 2
Determine all real numbers which satisfy the inequality:
Problem 3
Consider the cube (
and
are the upper and
lower bases, respectively, and edges ,
,
,
are
parallel). The point moves at constant speed along the perimeter of the
square in the direction
, and the point
moves at the same
rate along the perimeter of the square in the direction
. Points
and
begin their motion at the same instant from
the starting positions and
, respectively. Determine and draw the
locus of the midpoints of the segments .