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Math question on binary vectors

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BMWE

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question in math

Let u, v, w be three binary vectors such that every two of them are at Hamming
distance exactly d from each other.

1. Prove that d is even.
2. Prove that there is exactly one vector at distance d/2 from u, v, w.

the first one i succeeded to solve somehow, but how to solve the second one?
 

question in math

Can the rule of contraries help?
 

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