Problem 5
In a circus, clowns dress and paint themselves using a selection of 12 distinct colours. Each clown must use at least five different colours. The ringmaster requires that no two clowns have exactly the same set of colours and that no more than 20 clowns use any one particular colour. Find the largest possible .
Step 6 of 6: Conclude maximality
Detailed analysis
The upper bound and the construction coincide, so the largest possible number is .