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2024 AMC 10B Problem 1

Problem 1 of 25EasierCounting & Probability

In a long line of people arranged left to right, the 10131013th person from the left is also the 10101010th person from the right. How many people are in the line?

Answer choices

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Solution

There are 10121012 people to the left of this spot and 10091009 to the right. Add those two groups plus the person themselves: 1012+1009+1=2022.1012 + 1009 + 1 = 2022. Or, just as fast, the two positions overlap on one person, so 1013+1010−1=2022.1013 + 1010 - 1 = 2022. Thus, B is the correct answer.

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Concepts: basic counting

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