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Australian Intermediate Mathematics Olympiad 2024 Question 7

AIMO AUSTRALIA · Australian Intermediate Mathematics Olympiad 2024

Question 7

A survey of $N$ people was taken to determine which of the different types $A,B,C$ of screen entertainment they used, if any. The survey found:
- $50$ people used $B$;
- $61$ did not use $A$;
- $13$ did not use $C$;
- $74$ used at least two of $A,B,C$.
Find the minimum value of $N$.