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MathNet 2020 — Math Olympiad Vault — Part 01 Question 134

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 01

Question 134

By replacing each * in the expression $1 * 2 * 3 * 4 * 5 * \cdots * 2019 * 2020$ by a $+$ or a $-$ sign, we get a long calculation. Put the $+$ and $-$ signs in such a way that the outcome is a positive number (greater than $0$) which is as small as possible.
What is this outcome?