Advent calendar 2022
15 December
There are 3 even numbers between 3 and 9.
What is the only odd number \(n\) such that there are \(n\) even numbers
between \(n\) and 729?
Show answer & extension
Hide answer & extension
There are \((729-n)/2\) even numbers between \(n\) and 729, and so we want to solve \((729-n)/2=n\). The solution of this is 243.
Extension
For which odd numbers \(N\) does there exist an odd number \(n\) such that there are \(n\) even numbers between \(n\) and \(N\)?
