Consider a skyscraper problem on a 9x9 board. When a number is visible on the edge there will be some number of possible arrangements of buildings that could achieve this.

Find the number of possible arrangements of building if the edge number is each of {1,2,3,4,5,6,7,8,9}

For example on a 3x3 board there are three possibilities if a 2 is visible on the end (viewing from the left): (1,3,2), (2,3,1), (2,1,3)

(1,3,2), (2,3,1), (2,1,3)
What you would see: