Suppose a building has a cuboid shape, with two-way elevators at all four corners of the building’s layout connecting th

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Suppose a building has a cuboid shape, with two-way elevators atall four corners of the building’s layout connecting the groundfloor to the roof. Suppose a corner route is defined as movementfrom one of the eight adjacent corners (see below) to another.
(a) Explain why it is impossible to start at the ground-floorsouthwest (GF SW) corner and traverse each of the twelve availablecorner routes only once, and returning to the original.
(b) Suppose the corner routes are expanded to include diagonalmovements on a single floor (i.e. GF NW – GF SE, GF NE – GF SW,Roof NW – Roof SE, Roof NE – Roof SW). Explain why this does ordoes not change your answer to part