A positive integer N fulfills the following demands:.
N is a 7 digit number.
N's digits can be arranged as seven distinct members of an arithmetic progression(either ascending or descending) .
N is a multiple of 11.
How many positive integers like N exist?
Evaluate the lowest and the highest N.
BONUS : How about 8 digits? Nine? All ten?
Rem: It is D4 for fully explained and errorless P&P result,might be significantly lower for software solution.