Equal sums of powers of 2
Source: IV Caucasus Mathematic Olympiad}
April 7, 2019
power of 2combinatorics
Problem Statement
15 boxes are given. They all are initially empty. By one move it is allowed to choose some boxes and to put in them numbers of apricots which are pairwise distinct powers of 2. Find the least positive integer such that it is possible
to have equal numbers of apricots in all the boxes after moves.