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(2): IMHO - STILL REDUNDANT by Ady TZIDON)

Without the "if I were to tell you ..." statement, what would make

1 1 8 8 1 8
1 1 1 8 1 8
1 1 1 8 8 8
1 8 1 8 1 8
1 8 1 8 8 8
1 1 1 8 8 1
-----------
8 1 8 1 1 1

OR

1 1 8 8 8 8
1 1 1 8 1 8
1 1 1 8 8 8
1 8 1 8 1 8
1 8 1 8 8 8
1 1 1 8 1 1
-----------
8 1 8 1 1 1

wrong? How would either fail to fit the first paragraph if that paragraph stood alone?  How could the solver require uniqueness of the set of addends unless the "redundant" paragraph itself were present to require uniqueness?

Posted by Charlie on 2012-08-13 17:10:26