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: Numbers involved by Chris, PhD)

It looks complicated, by it is **NOT**

a} you did not provide an **answe**r

b) why not treat each colimn separetely (see my post and answer)?

**the sum digit=(9x*8+6-x+carry)mod 10= one or eight**

Working backwards you get a solution - if similar numbers appear - switch **ones and eights** within a column between numbers that differ in more than one place.

All said , it took me an hour of manual "try and error" entertainment