IMO 1992 LL TUR72

Origin: TUR

Problem

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 stu- dents; (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.