One possible solution is to take a string of 9's placed after 499998 (sod is 48). This string of 9's, when 1 is added, will become 499999 (sod is 49), followed by a bunch of zeros. So now we need to find, how many 9's would be necessary for the original number to have a S.O.D. divisible by 49.
Since 499998 has a S.O.D. value of 48, we need our S.O.D. for 999.... to equal 1 mod 49. So, set 9x = 1 + 49k, and check for a few values of k:
k = 1, 1 + 49 = 50: 50/9 = 5.55555555
k = 2, 1 + 49 * 2 = 99: 99/9 = 11
So, a string of eleven 9's, following 499998, or:
49,999,899,999,999,999
... seems like a good place to start.
Edited on February 1, 2011, 3:20 pm

Posted by Justin
on 20110201 15:18:34 