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, It's your total that adds to 918981:

118111
118118
118188
188188
188188
188188
--------
918981

And also my apologies to you: they are intended to be all different addends.

 

Posted by Charlie on 2012-08-13 00:05:57