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Advanced Math/Hard maths question


Please see attached

Here, the important observation to make is about the faces -- every step must make progress from P to Q, which means that the path can only traverse two faces. If so, you can "unfold" the two faces and get something like this:
P_ _ _ _

Here, the number of paths is easy to count -- six steps are required, two of them must be down (and the other four are to the right), so the total number of possibilities is 6 choose 2 = 15.

However, you can start with any face that includes P (3 choices) and from that face, go to any of the two faces it touches that include Q (2 choices).

The total number, then, is 2 3 15 = 90.

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Clyde Oliver


I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.


I am a PhD educated mathematician working in research at a major university.


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BA mathematics & physics, PhD mathematics from a top 20 US school.

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