Weighing problem
Source: IV Caucasus Mathematic Olympiad
April 7, 2019
combinatoricsKvant
Problem Statement
Dima has 100 rocks with pairwise distinct weights. He also has a strange pan scales: one should put exactly 10 rocks on each side. Call a pair of rocks {\it clear} if Dima can find out which of these two rocks is heavier. Find the least possible number of clear pairs.