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: Wild guess by Hugo)

Hugo, reading better your work, you said :

"If there is a 1 in the six digit number, there also needs to be at least one (odd) digit to get the number when 1 is at the end of the six digit number".

What makes you think that in the 6 numbers, in at least one of them, the 1 will be at the end ?

In fact, there is one of six-digit ending in 1. But you started your reasoning based on this, without proving it !

(In few lines itīs not difficult to show that the number is odd, divisible by 9, and there is a 8 in it, also.)

I think that something is missing yet, though we all know that the number is 142857.

 

  

 

Posted by pcbouhid on 2005-07-05 22:57:41