The problem is as follows:
The figure below shows a triangular arrangement with a set of numbers. Each time you read a number, you cannot repeat the same digit and the distance between the digits must be the same, and the minimum distance possible. How many different ways can the number $5556789$ be read?
Supposedly the answer is $256$.
I attempted to assign a small number by counting the ways going right and left a-la Pascal triangle of combinatorics.
Which would mean that the number of possibilities will result from summing the numbers at the base of the triangle:
Therefore I end up with $64$.
But this doesn't seem to be the answer. Can somebody tell me exactly what I am misunderstanding? How can I arrive to the right answer and more importantly how to do this? Please provide some graphic or visual aid with your answer to help me understand your solution.