equaalize the balloons
Source: Italy TST 2001
September 27, 2008
inductioncalculusintegrationcombinatorics unsolvedcombinatorics
Problem Statement
We are given balloons and a positive integer . Each balloon has been blown up to a certain size (not necessarily the same for each balloon). In each step it is allowed to choose at most balloons and equalize their sizes to their arithmetic mean. Determine the smallest value of such that, whatever the initial sizes are, it is possible to make all the balloons have equal size after a finite number of steps.