Two piles of coins
Source: All-Russian Olympiad, Grade 9, Second Day, Problem 7
April 18, 2013
combinatorics proposedcombinatorics
Problem Statement
Two piles of coins lie on a table. It is known that the sum of the weights of the coins in the two piles are equal, and for any natural number , not exceeding the number of coins in either pile, the sum of the weights of the heaviest coins in the first pile is not more than that of the second pile. Show that for any natural number , if each coin (in either pile) of weight not less than is replaced by a coin of weight , the first pile will not be lighter than the second.D. Fon-der-Flaas