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.

Regarding all previous posts my conclusuon is that it is proven beyond any doubt that if I am told that the sum is 818181, then only one specific set of 6-digit different numbers  built by ones and eights fits the puzzle.

However since so far there is not (or not yet found) another sum corresponding to one unique specific set of 6-digit different numbers  built by ones and eights than the statement " if I WERE TO TELL    etc." is redundant.

If such sum ()anything like 888111, 811888 etc) exists

with another  set  of qualifying addends  then  I say:

OK  you reveaL A SUM and I provide the matching set

Unless such sum is found I maintain that the 818181 is a part
of solving process and as such need not to be disclosed .

PLEASE TELL ME WHERE I  ERR

thanks....

Posted by Ady TZIDON on 2012-08-13 08:31:34