Thought Process

I have done a bit too many counting problems recently, so although I'm not happy with my solution since it's just brute force I don't care too much.

My idea is simple, given an n-digit number and d our repeating digit, I simply tested all possible numbers. The way I do this is to calculate S(n, d) as follows:

1. for i in range 0 to n - 1:

   1. There are doing to be n - i, d's in my number, this leaves me with i position left. To generate all possibilities for these i positions I use itertools.product([0,1,2,3,4,5,6,7,8,9], i) to generate all i-tuples of numbers (This essentially is the same as doing a bunch of nested loops (in this case we will do i nested loops))

      1. Now I generate all permutations of [d]*(n - i) + y, where y is an i-tuple from above using itertools.permutations([d]*(n - i) + list(y), n)

         1. Now if our permutation starts with a 0, we exclude it since this is not allowed.

         2. Otherwise, we simply test if it is prime, and if it is I add it to a set to avoid duplicates (yes this is how unbothered I was to optimize)