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)

Excellent work, Hugo. I knew the answer, because this number (142857) is too known. Itīs the period that you obtain dividing 1 by 7, and after multiplying it by 7 (which gives 999999), following the multiplication by 8, 9, 10, etc... itīs interesting to see the digits spliting into two digits to give the result. 

You can obtain interesting numbers dividing 1 by some primes. Dividing by 13, the period is 076923 :

076923 x 2 =  153846

076923 x 3 =.............230769

076923 x 4 = ............307692

076923 x 5 = 384615

076923 x 6 = 461538

076923 x 7 = 538461

076923 x 8 = 615834

076923 x 9 =.............692307

076923 x 10 =...........769230

076923 x 11 = 846153

076923 x 12 = ..........923076.

 

Posted by pcbouhid on 2005-07-04 21:10:53