MathDB

Seven classmates are comparing their end-of-year grades in

12

subjects. They observe that for any two of them, there is some subject out of the

12

where the two students got different grades. It is possible to choose n subjects out of the

12

such that if the seven students only compare their grades in these

n

subjects, it will still be true that for any two, there is some subject out of the n where they got different grades. What is the smallest value of

n

for which such a selection is surely possible?
Note: In Hungarian high schools, students receive an integer grade from

1

5

in each subject at the end of the year.

Problem Statement