100 Followers Problem Combinatorics
Discrete Mathematics
Level
4
Find the smallest integer \(k\) with the following property:
Given any real numbers \(a_{1}, a_{2} ,\ldots, a_{d}\) such that \(a_{1}+a_{2}+\cdots +a_{d}=100\) and \( 0 \le a_{i} \le 1\) for \(i=1,2,\ldots,d\) it is possible to partition these numbers into \(k\) groups (some of which may be empty) such that the sum of the numbers in each group is at most 1.
by
Lakshya Sinha