Question 8
A natural number $n$ has the following property. For any real numbers $a_1,a_2,\ldots,a_d$ satisfying both $a_1+\cdots+a_d=2013$ and $0\le a_i\le1$ for $i=1,\ldots,d$, there is a partition of the collection of these real numbers into $n$ pairwise disjoint subsets (some may be empty), such that the sum of the numbers in each subset is at most $1$. Determine the smallest such $n$.