2024 AMC 10B Problem 1

Start with a tiny line to see how positions work. In a line of $5$ people, the $4$th from the left is also the $2$nd from the right. Adding $4 + 2 = 6$ is one too many, because that person got counted from both sides.

So count the people on each side instead, and then add the person themself once.

1. This person is $1013$th from the left, so there are $1012$ people to their left.
2. This person is $1010$th from the right, so there are $1009$ people to their right.
3. The line is the left group, the person, and the right group:
$$1012 + 1 + 1009 = 2022.$$

The answer is $\boxed{\textbf{(B)}\ 2022}$.

Being "$k$th from one end" means there are $k - 1$ people on that side. When you add the two positions, the person in the middle is counted twice, so the rule is: left position plus right position, minus one. Checking a rule on a line of $5$ people is a quick way to avoid off-by-one mistakes.

Being $1013$th from the left means there are $1012$ people to this person's left. Being $1010$th from the right means there are $1009$ people to the right.

The line consists of those two groups plus the person in question:
$$1012 + 1 + 1009 = 2022.$$

The answer is $\boxed{\textbf{(B)}\ 2022}$.