# 100 Followers Problem Combinatorics

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.

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