Difference between revisions of "1962 IMO Problems"
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| − | Determine all real numbers x which satisfy the inequality: | + | Determine all real numbers <math>x</math> which satisfy the inequality: |
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Revision as of 13:02, 29 November 2007
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 
.
