Ascending Numbers Problems

We say a number is ascending if it's digits are strictly increasing. For example, 189 and 3468 are ascending while 142 and 466 are not. For which ascending number *n* is 6*n *also ascending?

I have got the answer to this problem after a while with some guess and check, but I would like to know a quicker way to work it out with a proper method. Can you please provide a relatively detailed explanation.

Thanks in advance

Atrey

Re: Ascending Numbers Problems

578 * 6 = 3468 (only tried 3digit numbers; that's the only one)

Easy enough with a looper program, like:

loop a from 1 to 7

loop b from a+1 to 8

loop c from b+1 to 9

u = 100a + 10b + c

v = u*6

are v's digits in ascending order?

As far as a "method" goes, you'd need to start by setting up "u" something like (if 3digit number):

u = 100a + 10(a+w) + a+w+x

So u = 111a + 11w + x where 8>a>0 and a+w+x<10

Does 666a + 66w + 6x = an ascending 3digit or 4digit number?

Perhaps someone here with "number theory expertise" can help you further...I can't

Re: Ascending Numbers Problems

Thank you for explaining a logical way to do this problem quicker