Question 46
John has a string of paper where $n$ real numbers $a_i \in [0, 1]$, for all $i \in \{1, \dots, n\}$, are written in a row. Show that for any given $k \lt n$, he can cut the string of paper into $k$ pieces, between adjacent numbers, in such a way that sum of the numbers on each piece does not differ from another by more than 1.