Question 2
Consider the $2n-1$ consecutive natural numbers $1,2,3,\ldots,2n-1$. Cross out at least $n-1$ numbers according to these rules:
- If $a$ is crossed out, then $2a$ must be crossed out.
- If $a$ and $b$ are crossed out, then $a+b$ must be crossed out.
Which numbers should be crossed out to maximize the sum of those remaining? Explain your answer.
- If $a$ is crossed out, then $2a$ must be crossed out.
- If $a$ and $b$ are crossed out, then $a+b$ must be crossed out.
Which numbers should be crossed out to maximize the sum of those remaining? Explain your answer.