Can you create a subset of (1, 2, 3, ..., 3k) such that none of its 2k-1 members is twice the value of another?
Either provide such a set or show none exists.
Inspired by: Austrian-Polish Math. Competition.
(In reply to
re: Idea, no proof by broll)
I don't understand your variables. What do m and n have to do with k?
My method is sometimes one number short though:
n=128 is not possible as it is not a multiple of 3.
Suppose k=43 so 3k=129 and 2k-1=85
The included intervals are [1],[4,7],[16-30],[65,129]
1+4+15+65 = 85
This is fine.
Suppose k=42 so 3k=126 and 2k-1=83
The included intervals are [1],[4,7],[16-31],[64,126]
1+4+16+63 = 84
So this method doesn't quite do it.
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Posted by Jer
on 2022-05-02 13:35:07 |
re(2): Idea, no proof
