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Special Similar Set (Posted on 2005-06-27) Difficulty: 3 of 5
A man offered me a set of eleven weights, not all them equal, each an integer number of pounds, which he said had the following property: if you removed any of the eleven weights, the other ten could form two five weights sets that balanced each other. Is this possible?

And if the weights didn't weigh an integer number of pounds each?

No Solution Yet Submitted by Old Original Oskar!    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Keep Hope Alive | Comment 8 of 11 |
One part 1, both McWorter's proof and e.g.'s infinite descent proof work for me.  I have a preference for McWorter's proof, since it does not involve 0 weights, which are more theoretical than I care for.  Well done!

On part 2, I am sorry this thread died.  I still don't know whether this is possible or not, but I agree with Tristan that it is unlikely, since it would need to involve irrational weights.  (Otherwise, we could multiply to get an integer solution).  I haven't figured out a solution, but I haven't figured out an impossibility proof, either.

So, Great problem, Oskar!

Do we get a hint?

  Posted by Steve Herman on 2005-07-01 17:12:35
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