Whats the minimum number of numbers we should take from $[1,2n-1]$ so as to ensure there is atleast two numbers whose sum results in an number which is one of the taken one . And whats the minimum in case of $[1,2n]$.
- Any ideas /hints fine for this . I am not even able to know where to start from .
Note: from @paw88789 hint i did check for small cases : for $[1,3]$ its all three elements , for $[1,5]$ i guess 4 elements since for $3$ elements we have a counter example ${1,3,5}$ , for $[1,7]$ it cannot be 4 element since $1,3,5,7$ is a counter example . So minimum $5$ i think so . From this i get a idea of looking at odd and even parity but nothing more . Does this idea proves it for all ?