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Each clown is required to use at least five different colour

Source: APMO 2006, Problem 5

March 24, 2006
combinatorics unsolvedcombinatoricsezeasy

Problem Statement

In a circus, there are nn clowns who dress and paint themselves up using a selection of 12 distinct colours. Each clown is required to use at least five different colours. One day, the ringmaster of the circus orders that no two clowns have exactly the same set of colours and no more than 20 clowns may use any one particular colour. Find the largest number nn of clowns so as to make the ringmaster's order possible.