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You could fold all of these up and get a cube! And you're right, we can pick any side we want to be the top of the cube. In the problem however, because we can pick any side to be the top, why don't we pick the middle square? It makes all of our calculations a lot easier.

Imagine if we were to actually pick the side you have designated to be the top of the cube. When you connect the two corners, you get a straight line! This is actually the exact line that Prof. Loh has in the video. It's the blue one. Do you see how that would actually be longer?

To be honest, you could pick any of the 6 sides to be the top one. But the middle square gives you the shortest distance between the two corners. It also makes sense that it would be the shortest, since it's a diagonal. Cutting corners is always faster than a straight path!

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