Hi, I need help solving this please

Pavanello

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Jun 2, 2022
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Show that in a subset of n + 1 distinct numbers from the set A =
{1, . . . , 2n}, there are always two distinct elements such that one divides the other.
 
Hello. What have you tried or thought about so far? Please share your initial effort.

 
This being a help forum I was hoping that you would have posted what kind of help you need.
 
Show that in a subset of n + 1 distinct numbers from the set A =
{1, . . . , 2n}, there are always two distinct elements such that one divides the other.
When I don't have any idea what to do, I tend to "play" with the problem to get a feel for what it means.

Suppose n=2; they are claiming that any subset of 3 numbers from {1, 2, 3, 4} includes at least one pair, one of which is a multiple of the other. The possible subsets of 3 are {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, and {2, 3, 4}. The first three obviously work, and {2, 3, 4} has the subset {2, 4}.

You might try n=3, and see if there's a pattern in what is divisible by what. (For example, I wondered at first if there would always be a pair with the ratio 2:1, but {1, 3, 4} shows I was wrong.)

You might also think about methods you've learned. This sounds as if it could be a pigeonhole problem; is that something you're studying?

Now please show some work, so we can start actually helping!
 
This too sounds like a pigeonhole problem to me.
If you tell us what you recently learned we can offer more help.
For the record, if you had read the posting guidelines you would have known that it helps if you state what you just learned and show us exactly what you have tried.
 
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