# Find number of elements in a set given the number of subsets it has

How do I find the number of elements in a set that has exactly $16$ subsets and an odd number of elements?

I don't really understand.

I mean I know that the number of subsets in a set is equal to $2^n$, where $n$ is the number of elements in the set. So here if the number of subsets is $16$, I would say that the set has $4$ elements ($2^4 = 16$). But it says that the set has an odd number of elements.. and $4$ is not odd. In the book, the answer is $5$, and I don't understand how that would be.

• but with the 2^n formula you count that too.. right. for example the set {1, 2} it has 0, 1, 2, 12. – Alexandra Jul 13 '17 at 8:07
• Can you quote the exact formulation of the question from the book? – Mikhail Katz Jul 13 '17 at 8:11
• Find the number of elements of a set that has exactly 16 subsets with an odd number of elements – Alexandra Jul 13 '17 at 8:12
• It's the subsets that have an odd number of elements, not the original set. – Mikhail Katz Jul 13 '17 at 8:12
• ooh. I get it. thanks. so we only take the subsets with and odd number of elements. so that would be 2^{n-1} = 16 so n = 5 – Alexandra Jul 13 '17 at 8:16