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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(3): solution WRONG | Comment 7 of 33 |
(In reply to re(2): solution by Dej Mar)

DM,r

your choice of digits is right : 1 & 8

2. Your numbers sum up to 989681 - 4 distinct digits

Hint: Work your way backwards column by column (starting from the last) using the following formula for the sum:

s=8x+6-x+carry
x is the quantity of 8s vertically
c is the carry from the previous column

simplified to: (7x+6 ) mod 10= (either  1 or 8 )

Making the right choices for x you get a SINGLE solution.

 Posted by Ady TZIDON on 2012-08-12 23:48:30

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