ILL 1992 Problem 72
In a school six different courses are taught: mathematics, physics, biology, music, history, geography. The students were required to rank these courses according to their preferences, where equal preferences were allowed. It turned out that:
- (i) mathematics was ranked among the most preferred courses by all students;
- (ii) no student ranked music among the least preferred ones;
- **(iii)**all students preferred history to geography and physics to biology; and
- (iv) no two rankings were the same.
Find the greatest possible value for the number of students in this school.
Dataset text AI-MO AoPS. Quoted with source.
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