Accolades for j---I didn't solve this the easy way. With quite a few other j solutions already posted:
I arrived at a formula empirically. By enumerating solutions from 1 to 10 digits long in base 3, 4, and 6 I discovered I needed polynomials of order of the base to satisfy the problem for any number of digits in that base. My computer system rapidly enumerated the solutions for up to 7 digits in base 10. I then needed to find counts for 8 and 10 digit numbers base 10 since the 1e9 count was given. J works easily with arbitrary bases, used to find the pattern. J can solve matrix division with rational arithmetic, used to find the polynomial. There wasn't much code nor computer time but boy did I struggle. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
