2014 dimensions?

Geometry Level 4

Consider a hypercube of side length 2 in a 2014-dimensional space. Inscribe a unit hypersphere in the hypercube. Inscribe a smaller hypersphere tangent to the unit hypersphere and the sides of the hypercube.

The radius of the smaller sphere can be written as \(\frac{a-\sqrt{b}}{c}\) where \(a\), \(b\) and \(c\) are coprime positive integers. Find \(a+b+c\).

Based on this problem.

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