Question 2
The sunshine cost of a sequence $ a_{1}, a_{2}, \ldots, a_{100} $ of integers is the largest possible value of
$$ \left|\left(a_{1}+a_{2}+\cdots+a_{i}\right)-a_{j}\right| $$
as i and j vary over all integers 1,2,...,100.
Determine the smallest possible sunshine cost over all sequences $ a_{1}, a_{2}, \ldots, a_{100} $ of pairwise distinct integers.
$$ \left|\left(a_{1}+a_{2}+\cdots+a_{i}\right)-a_{j}\right| $$
as i and j vary over all integers 1,2,...,100.
Determine the smallest possible sunshine cost over all sequences $ a_{1}, a_{2}, \ldots, a_{100} $ of pairwise distinct integers.