John has a string of paper where n real numbers ai∈[0,1], for all i∈{1,…,n}, are written in a row.
Show that for any given k<n, he can cut the string of paper into non-empty k pieces, between adjacent numbers, in such a way that the sum of the numbers on each piece does not differ from any other sum by more than 1. combinatoricscombinatorics proposed