2024 AMC 10B Problem 1

Problem 1 of 25EasierCombinatorics

In a long line of people arranged left to right, the

1013

th person from the left is also the

1010

th person from the right. How many people are in the line?

Show solution

Solution

There are

1012

people to the left of this spot and

1009

to the right. Add those two groups plus the person themselves:

1012 + 1009 + 1 = 2022.

Or, just as fast, the two positions overlap on one person, so

1013 + 1010 - 1 = 2022.

Thus, B is the correct answer.

Tagged: basic counting