[seqfan] The weight puzzle sequence
mathoflove-seqfan at yahoo.com
Tue Aug 24 18:57:52 CEST 2010
I just wrote a piece for my blog with a problem from the 1966 Moscow Olympiad.
There is a sequence there. I didn't compute enough terms to check if it is in the database. I would like if someone can compute more terms of the sequence.
Here is the relevant part from the blog:
From the 1966 Moscow Math Olympiad:
Prove that you can choose six weights from a set of weights weighing 1, 2, ..., 26 grams such that any two subsets of the six have different total weights. Prove that you can’t choose seven weights with this property.
Let us define the sequence a(n) to be the largest size of a subset of the set of weights weighing 1, 2, ..., n grams such that any subset of it is uniquely determined by its total weight. I hope that you agree with me that a(1) = 1, a(2) = 2, a(3) = 2, a(4) = 3, and a(5) = 3. The next few terms are more difficult to calculate, but if I am not mistaken, a(6) = 3 and a(7) = 4.
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