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.

No, he won't reach the middle cube because he would be tired from overeating cheese.. None of the above. Yes, Cheddar Yes, Provolone

2 solutions

Hana Wehbi
May 19, 2016

Since the mouse started on a corner (provolone), it must end on a provolone. The center is provolone, such route from corner to center is possible.

James Wilson
Oct 31, 2017

She starts on the bottom corner, and starts eating the bottom, going around the outside. She eats the outside 16, then the next outside 12, then the next outside 8, and, finally, the center. Then she eats the entire next layer in backwards order. The next (middle) layer: she eats everything except the center. Then she eats everything except the center on the next layer in backwards order of course. And then she eats the entire top layer, the remaining center piece of the layer below it, and, finally, the middle, which is, of course, provolone cheese.

Thank you.

Hana Wehbi - 3 years, 7 months ago

You're welcome. What a fun problem. Thanks for posting. I'm waiting for a mathematician to come along and blow us out of the water.

James Wilson - 3 years, 7 months ago

Not your typical Mickey Mouse!

This problem was inspired by my homework from Graph Theory.

2 solutions

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