and welcome to the Republic of al'Alghaz!
This is the International School of al'Alghaz (ISA), the best (and most expensive) school in the country. It's built for all the children of expats, royals, diplomats, and any other snob-nosed foreign children those parents have too much money.
But you see, there's a problem. There are two kinds of teachers in ISA, foreign teachers ($F$) and Alghazi teachers ($A$). We suspect that foreign teachers are paid salaries that are much higher than us local teachers, but we cannot find out for sure - because discussing salaries is forbidden. However, we'd like to find some way to rank salaries - even if we cannot know the actual salaries themselves.
How can we find out the ranking of salaries for teachers, without knowing the actual salaries themselves?
- You may not ask a teacher about their salary,
- You may not ask a teacher about their salary in relation to others (they don't know anyone elses salary apart from themselves)
- You may ask any other question, and they will answer 100% honestly.
Naturally, we'd come up with a solution to this problem ourselves, but you see - the only Math teacher here is the second cousin to the Dean's sister, and ah... well, that's a problem in our country...
For the sake of simplicity, assume that there are 6 subjects, each taught by a single teacher: