[VA] SRC #012a - Then and Now: Probability

[PeterP]

I am afraid I am missing something in Valentin’s description and I was hoping someone from the community can help me find my error.

I can only find 144 possible 4-step paths in the triangle with 5 rows. Rather than, as the answer/hint in the OP points out 288 (probability of success = good outcomes / all possible outcomes)

Each dot can reach each neighboring dot in 1 step. Each dot has either 2 (the corners of the pyramid), 4 (the middle part of the edges), or 6 (the inner part of the pyramid) neighbors.

I have now gone through the manual process of writing out all possible paths by naming the dots in the Pyramide from 1 to 15 (ie the starting point is dot 1, the second row is dots 2 and 3, the third row is dots 4, 5, and 6, and so forth )

That manual process yields the same outcome as my code = 144 possible 4-step paths, of which 16 end up in the last row. (How often you hit each dot in the last row seems to be the binomial triangle row equivalent to the number of steps, so 1-4-6-4-1 or a total of 16 times)

Clearly I am missing something fundamentally here. Maybe some kind soul can give me a pointer on what I am missing?