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(2): Idea, no proof by Jer)
I don't understand your variables. What do m and n have to do with k?
Answer: Fair question, and as usual I wasn't clear enough!
256=m, approximately 258=3k, then (2k-1) = 171, larger than 169 (=2k-3), and larger still than 166 = the sum of available candidates.
32768=m, approximately 32769=3k, then (2k-1) = 21845, larger than 21844(=2k-2), and larger still than 21837 = the sum of available candidates.
2097152, approximately 2097153=3k, then (2k-1) = 1398101, larger than 1398100(=2k-2), and larger still than 1398090 = the sum of available candidates.
But see post (9) for a correction which modifies this.
Edited on May 3, 2022, 3:30 am
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Posted by broll
on 2022-05-02 23:23:29 |
re(3): Idea, no proof
