Don't Think Outside The Box!

Geometry Level 2

Brilli the ant is trapped on a cube-shaped planet. She wants to go from one corner [pointAA] to the opposite corner [point BB]. However she wants do this in a way such that she has to cross the shortest distance possible. If the length of the sides of the cube is 11, the shortest distance between AA and BB can be expressed as p+qp+\sqrt{q} where pp and qq are non-negative integers and qq is square-free. What is qpq-p?


Details and assumptions:

Brilli the ant is completely confined to the surface of the cube. She can't move inside or outside the cube.

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