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(4): IMHO - STILL REDUNDANT by Ady TZIDON)

"no comments on the new text (post #28)?"

I didn't want to beat a dead horse, but of course once one adds new text, the original text, which was not redundant, becomes redundant. Or rather the new text " is an unique set of " is the actual redundancy to the paragraph to which you object.

I think the original paragraph says it more explicitly than calling the set of numbers unique, as one could ask "unique in what way?". Actually any set of numbers is unique, in that it's not some other set. That's why, in cards, 10H, 5D, 2S, 8C, AceD is unique, for example, though the much maligned expression "more unique" would apply to say 10H, JH, QH, KH, AceH.

Truly everything is unique in some way, even two peas in a pod. There may be different wrinkles, a slightly different size or shade of green, say. Certainly they differ in their number of atoms as it would be astronomically unlikely that two numbers that are in the order of 10^26 would be exactly the same.  It makes one think that the word "unique" is useless, as it applies to everything. I'd like to think that, say, the Hope Diamond is more unique than, say, an unremarkable penny in my pocket.

Posted by Charlie on 2012-08-15 12:49:22