What six digit number added to itself five times will give a sum each time having the same 6 digits as the original number?

(It's not 000000.)

(In reply to re(2): Wild guess by pcbouhid)

Reply,

Yes excellent deduction. 

I too knew this immediately because of x/7.  There have been a few problems that have 'exploited' this fact.  In fact I have one in the queue that uses this sequence as well.  Hopefully it will be deemed different enough to post.  They really are pretty different.   Only in knowing this sequence, could you even see that they are similar.  Dustin has a problem that uses this sequence as well, I do not want to link to it as it would serve as too much of a hint as to the solution of these problems.  Again excellent deduction, I used similar deduction on Dustin's problem, (and probably would have not been able to carry it through to completion like you did) until I started to recognize the sequence.

Posted by john on 2005-07-07 14:11:07