2002 Pan African MO Problems
Find all functions , (where is the set of all non-negative integers) such that for all and the minimum of the set is .
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.
Prove for every integer , there exists an integer such that can be written in decimal notation using only digits 1 and 2.
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.
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.
If and , then prove:
|2002 Pan African MO (Problems)|
2001 Pan African MO
|1 • 2 • 3 • 4 • 5 • 6||Followed by|
2003 Pan African MO
|All Pan African MO Problems and Solutions|