MathDB

Let

n

be a positive integer. In

n

-dimensional space, consider the

2^n

points whose coordinates are all

\pm 1

. Imagine placing an

n

-dimensional ball of radius 1 centered at each of these

2^n

points. Let

B_n

be the largest

n

-dimensional ball centered at the origin that does not intersect the interior of any of the original

2^n

balls. What is the smallest value of

n

such that

B_n

contains a point with a coordinate greater than 2?

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