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Same Six Digits (Posted on 2014-03-26) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re: Let Me REcount the ways | Comment 5 of 6 |
(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.

  Posted by Ady TZIDON on 2014-03-26 13:42:26
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