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BMT 2022 Algebra Tiebreaker p3

Source:

September 27, 2023
algebra

Problem Statement

Tej writes 2,3,...,1012, 3, ..., 101 on a chalkboard. Every minute he erases two numbers from the board, xx and yy, and writes xy/(x+yāˆ’1)xy/(x+y-1). If Tej does this for 9999 minutes until only one number remains, what is its maximum possible value?
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