The problem is to find the smallest number n such that n, 2n, 3n, 4n, 5n, and 6n all contain the same digits. For those who know the 1/7 rule, that's wise of you. For the rest of us, brute force comes to rescue. Python can do it in a few lines:

n = 1
while not all( set(str(i*n))==set(str(n)) for i in [2,3,4,5,6] ):
      n+= 1	
print n

 The funny thing is if I change the all function slightly to:

     all( [ set(str(i*n))==set(str(n)) for i in [2,3,4,5,6] ] )

 the runtime increases by 4 times to 5 seconds. I am guessing all() is smart enough to employ short-circuit, but don't take my words for it.

Live and learn.