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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): IMHO - STILL REDUNDANT | Comment 23 of 33 |
(In reply to re: IMHO - STILL REDUNDANT by Chris, PhD)

"You claim:
..."There are multiple such examples.  My solution is the only solution where given a sum, there is a unique set of answers."

That is true .  NOW READ THIS CAREFULLY.

If  818181 is the  ONLY sum that qualifies (i.e. has only one unique set of addends) therefore  it is redundant to be revealed in the text and should be discovered  (D4) by the SOLVER,

Q.E.D.

 Posted by Ady TZIDON on 2012-08-13 14:36:41

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