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): 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.
For your sake my answer is in another post.
re(3): solution WRONG
