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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): Numbers involved remarks | Comment 16 of 33 |
(In reply to re: Numbers involved by Chris, PhD)

It looks complicated, by it is NOT

a} you did not provide an answer

b) why not treat each colimn separetely (see my post and answer)?

the sum digit=(9x*8+6-x+carry)mod 10= one or eight

Working backwards you get a solution - if similar numbers appear - switch ones and eights  within a column between numbers that differ in more than one place.

All said , it took me an hour of manual "try and error" entertainment

 Posted by Ady TZIDON on 2012-08-13 01:53:54

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