# Niven numbers and descriptive numbers

#### bodycare

Hi. I have a problem relating niven numbers and self-descriptive numbers. It's posted below. Basically what I've done to try and solve the problem is to look at the wiki-page of these numbers. I've tried bruteforce but this didn't work. I bruteforced by looking at if the numbers are niven numbers in the bases given in the question. I couldn't find a number which satisfied the conditions that were set in the question, and therefore I think it is an impossible task.

I'm quite sure that there is an answer though so if someone could tell me what I did wrong or maybe lead me towards the answer I'd be very greatful.

Here is the problem: