School and students - IMO LongList 1992 TUR1
Source:
September 2, 2010
combinatoricscountingInclusion-exclusionIMO ShortlistIMO Longlist
Problem Statement
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:
* mathematics was ranked among the most preferred courses by all students;
* no student ranked music among the least preferred ones;
* all students preferred history to geography and physics to biology; and
* no two rankings were the same. Find the greatest possible value for the number of students in this school.