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2024 AMC 12B Problem 1

Problem 1 of 25EasierCombinatorics

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?

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Solution

The target person has 1013−1=10121013 - 1 = 1012 people to the left and 1010−1=10091010 - 1 = 1009 people to the right. Including the person themself, the line has 1012+1009+1=20221012 + 1009 + 1 = 2022 people. Thus, the correct answer is B.
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Tagged: counting integers in a range · basic counting

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