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MathNet 2000 — Math Olympiad Vault Question 79

Math Olympiad Vault · MathNet 2000 — Math Olympiad Vault

Question 79

On a table there are $1999$ tea cups with their mouths facing upward initially. In each move, $100$ of them are turned upside down. After a number of moves, can they be turned so that all their mouths face downward? Why?

Answer the above two questions for the case where the number of cups is $1998$.