There are six different 6-digit positive integers that add up to a seventh 6-digit integer. Interestingly, all seven of these numbers consist of combinations of only two different digits. That is, only two different digits are used to write the complete set of seven numbers--the same two digits in each number.

So far you can't deduce what the numbers are, but if I were to tell you that seventh number, that is, the total, you'd know what the other six numbers were that made up that total.

What are the seven numbers?

From Enigma No. 1702, "All the sixes",by Ian Kay, New Scientist, 16 June 2012, page 32.

(In reply to re: solution by Kenny M)

Tou are correct, I misread the text. They add up to a 7-digit number.
The two digits 1 and 8 work for a 6-digit number:

111811
111818
111888
181818
181888
188888
=====
888111

Edited on August 12, 2012, 10:44 pm

Posted by Dej Mar on 2012-08-12 21:57:26