Problem

Source: Iran TST 2006

Tags: combinatorics proposed, combinatorics



Suppose $n$ coins are available that their mass is unknown. We have a pair of balances and every time we can choose an even number of coins and put half of them on one side of the balance and put another half on the other side, therefore a comparison will be done. Our aim is determining that the mass of all coins is equal or not. Show that at least $n-1$ comparisons are required.