Let $z_{1}, \dots, z_{n} \in C$ with $1 \leq ∣ z_{i} ∣$ for $1 \leq i \leq n$ . Let $D$ be an arbitrary disc of radius $1$ . Is it true that the number of sums of the shape $i = 1 \sum n ϵ_{i} z_{i} for ϵ_{i} \in {- 1, 1}$ which lie in $D$ is at most $(⌊ n /2 ⌋ n)$ ?

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combinatorics · solved · 0 attempts

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