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PrintSouth African Mathematics Olympiad
South Africa counting and probability
Problem
In a group of people, in of them has a pen and in has a pencil. What is the minimum possible number of people that have something to write with?
Solution
people must have a pen and must have a pencil. If all the people with pens also have pencils, this could be as few as people in all.
Final answer
36
Techniques
Inclusion-exclusion