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 Sixes and Sevens--Not! (Posted on 2012-08-12)
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.

 See The Solution Submitted by Charlie Rating: 5.0000 (2 votes)

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 Solution | Comment 17 of 33 |
Continuing working from my previous comments I have the solution:
118888
111888
181818
181888
111818
111881

I will explain how I got from my previous post to the answer when I have more time.

The last statement: "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." was needed to solve.

 Posted by Chris, PhD on 2012-08-13 02:00:05

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