A positive integer is called shiny if it can be written as the sum of two not necessarily distinct integers a and b which have the same sum of their digits. For instance, 2012 is shiny, because 2012 = 2005 + 7, and both 2005 and 7 have the same sum of their digits. Find all positive integers which are not shiny (the dark integers).

that for any 2+ digit number you can always find a way to get a sum of two integers whose digits sum to the same value,
eg 11 = 10 +1 with digital sums equal to 1
100 = 50 + 50 with digital sums equal to 5
133 = 62 + 71 with digital sums equal to 8

I cannot do that with 1, 3, 5, 7 and 9;
1 = 1 + 0
3 = 3 + 0; 2 + 1
5 = 5 + 0; 4 + 1; 3 + 2
7 = 7 + 0; 6 + 1; 5 + 2; 4 + 3
9 = 9 + 0; 8 + 1; 7 + 2; 6 + 3; 5 + 4

Posted by brianjn on 2013-06-20 23:33:45