2002 Pan African MO Problems
Contents
Day 1
Problem 1
Find all functions , (where is the set of all non-negative integers) such that for all and the minimum of the set is .
Problem 2
is a right triangle with . and are moving on and respectively such that . Show that there is a fixed point through which the perpendicular bisector of always passes.
Problem 3
Prove for every integer , there exists an integer such that can be written in decimal notation using only digits 1 and 2.
Day 2
Problem 4
Seven students in a class compare their marks in 12 subjects studied and observe that no two of the students have identical marks in all 12 subjects. Prove that we can choose 6 subjects such that any two of the students have different marks in at least one of these subjects.
Problem 5
Let be an acute angled triangle. The circle with diameter AB intersects the sides AC and BC at points E and F respectively. The tangents drawn to the circle through E and F intersect at P. Show that P lies on the altitude through the vertex C.
Problem 6
If and , then prove:
See Also
2002 Pan African MO (Problems) | ||
Preceded by 2001 Pan African MO |
1 • 2 • 3 • 4 • 5 • 6 | Followed by 2003 Pan African MO |
All Pan African MO Problems and Solutions |