On Tue, Oct 14, 2008 at 10:10 AM, Michael Reid <reid@gauss.math.ucf.edu>wrote:
I have a book (at home, alas) that talks about this problem. Basically, for n a power of 2, the numbers are not necessarily determined by the sums taken two at a time. If n is not a power of 2, then the numbers are uniquely determined. I can dig up the reference later, if anyone is interested.
count me interested!
mike
I have the book in front of me. It is called Mathematical Mind Benders and is by Peter Winkler. On page 22 there's a problem called "Getting the numbers back" that states: For which positive integers n is it the case that, given the C(n, 2) pairwise sums of n distinct positive integers, you can recover the integers uniquely? I must say that this is a really good "puzzle" book. The puzzles are refreshingly original and the difficulty level is significantly higher than most books of this type. There are many problems that I would place at the USAMO/IMO level of difficulty. Consider this an unqualified recommendation! Cheers, Dave
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