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Math Prize 2015 Problem 7

Source:

September 22, 2015

Problem Statement

Let nn be a positive integer. In nn-dimensional space, consider the 2n2^n points whose coordinates are all ±1\pm 1. Imagine placing an nn-dimensional ball of radius 1 centered at each of these 2n2^n points. Let BnB_n be the largest nn-dimensional ball centered at the origin that does not intersect the interior of any of the original 2n2^n balls. What is the smallest value of nn such that BnB_n contains a point with a coordinate greater than 2?
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