In a group of $n$ people $A_1,A_2… A_n$ each one has a different height. On each turn we can choose any three of them and figure out which one of them is the highest and which one is the shortest. What’s the least number of turns one has to make in order to arrange these people by height, if: a) $n=5$; b) $n=6$; c) $n=7$?
Problem
Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade
Tags: combinatorics, arrangement