Not your typical Mickey Mouse!

Geometry Level 3

A cubic cheese consists of 125 smaller cubes of cheeses (\(5\times5\times5\)), made of Provolone and Cheddar cheese cubes alternately. A mouse sitting at the corner cube, which is a Provolone cheese, will start eating that cube before heading to eat the adjacent one. Being picky minded, the mouse won't eat diagonal cubes, only adjacent ones. The mouse will eat every cube and won't move into an empty space. Is it possible that the mouse will finish at the middle cheese, and if yes, what type of cheese would it be?


This problem was inspired by my homework from Graph Theory.
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