Difference between revisions of "2000 Pan African MO Problems"
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Latest revision as of 13:39, 4 December 2019
Contents
Day 1
Problem 1
Solve for :
Problem 2
Define the polynomials by: Find the coefficient of in .
Problem 3
Let and be coprime positive integers such that: Prove is divisible by 2003.
Day 2
Problem 4
Let , and be real numbers such that , solve the system: in real numbers and .
Problem 5
Let be circle and let be a point outside . Let and be the tangents from to (where ). A line passing through intersects at points and . Let be a point on such that . Prove that bisects .
Problem 6
A company has five directors. The regulations of the company require that any majority (three or more) of the directors should be able to open its strongroom, but any minority (two or less) should not be able to do so. The strongroom is equipped with ten locks, so that it can only be opened when keys to all ten locks are available. Find all positive integers such that it is possible to give each of the directors a set of keys to different locks, according to the requirements and regulations of the company.
See Also
2000 Pan African MO (Problems)  
Preceded by First Pan African MO 
1 • 2 • 3 • 4 • 5 • 6  Followed by 2001 Pan African MO 
All Pan African MO Problems and Solutions 