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

No Subject by Ady TZIDON)

Ady's answer isn't the solution.

Ady's solution was:

111881

111818

111888

181888

181818

188888

But this set of numbers also adds to the same total as your solution:

181881

111818

111888

181888

181818

118888

Therefore given the final answer, you would not arrive at your unique solution. See my solution for correct answer.

*Edited on ***August 13, 2012, 2:05 am**

*Edited on ***August 13, 2012, 2:05 am**

*Edited on ***August 13, 2012, 2:09 am**