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Littlewood-Offord Problem

​
Drag the red points.
center of green circle
Form the
n
2
sums (black dots) of all possible subsets of
n
vectors (red dots). If all
n
vectors have norm at least 1, then at most
n
n
2
of the vectors lie in the green circle of diameter 1. (The function
⌊x⌋
is the floor of
x
.)
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