2024 AMC 12B Problem 1

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?

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Solution

The target person has

1013 - 1 = 1012

people to the left and

1010 - 1 = 1009

people to the right. Including the person themself, the line has

1012 + 1009 + 1 = 2022

people. Thus, the correct answer is B.

Concepts: counting integers in a range · basic counting

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.