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2023 Polish Junior Math Olympiad Round 1 P2

Source:

May 21, 2023
combinatorics

Problem Statement

Kamil wrote on a board an expression consisting of alternating addition and subtraction of natural numbers from 11 to 100100: 1−2+3−4+5−6+…−98+99−100.1-2+3-4+5-6+\ldots-98+99-100. Then, Kamil erased one of the plus or minus signs and replaced it with an equals sign, obtaining a true equality. Which number preceded the erased sign? Find all possibilities and justify your answer.
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