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2013 AMC 10B Problem 4

Problem 4 of 25EasierCounting & Probability

When counting from 33 to 201,201, the number 5353 is in position 51.51. When counting backward from 201201 to 3,3, the number 5353 is in position n.n. What is n?n?

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Solution

When counting backward, 201201 is the first number, 200200 is the second, and in general xx is the 202x202-xth number. Thus 5353 is the 20253=149202-53=149th number counted. Thus, the correct answer is D .

More practice

Concepts: counting integers in a range

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