What are the possible values of a six digit positive integer N, where all digits of N are different, and 4*N has the same six digits as N?

Prove that there are no others.

(In reply to

Let me count the ways by Steve Herman)

**Let Me REcount the ways:**

.....So at first glance we have 12*8*7*6*5 = 20,160 possibilities.

But the number must equal **0 OR 3 OR 6 mod 9**, because N and 4N have the same digits.

And approximately **1/3** of the 20,160 possibilities meet this criteria.

So I guess that there are only **6720 ** viable candidates for N...

see the **sod** of Charlie's numbers" :18,21,27 etc.