Question 37
Suppose that $3 \le n$ is a natural number. Find the maximum value of the natural number $k$ for which there are real numbers $a_1, a_2, \dots, a_n \in [0, 1)$ (not necessarily distinct) such that for every natural number $j$ satisfying $j \le k$, there exists a sum of a certain number of $a_i$'s equal to $j$.