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A mouse enters a maze, represented below, at its entrance at the top, and travels consistently downward toward the exit point shown at the bottom, taking no paths upwards or sideways.

How many paths are possible for the mouse to take?

 

 I know the mouse can move down 8 times and has to move left or right 4 times but I don't know what to do next.

 Jul 22, 2021
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Okay, I actually haven't solved the problem but I quickly noticed some things.

 

First, we can ignore all horizontal lines (we can't move sideways so thinking about moving left or right isn't exactly correct).

Second, due to ignoring the horizontal lines, we can limit our problem to a rhombus shape (forgive me I don't know how to create diagrams).

Now instead of thinking it as a rhombus shape imagine it as a square (or a 4x4 grid as shown)

Take one corner as the entrance and the opposite corner as the exit and now it's become an easier path problem.

 

Hope this makes sense.

 Jul 22, 2021

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