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MathNet 2012 Question 54

Math Olympiad Vault · MathNet 2012

Question 54

When two red amoebas join, the result in one blue amoeba; when a red amoeba and a blue amoeba join, they turn into three red amoeba; and when two blue amoeba join, they become four red amoeba. Fernando observes a test tube with initially $201$ blue amoebas and $112$ red amoebas.

a. Is it possible that after some amoebas transform the test tube contains $100$ blue amoebas and $314$ red amoebas?

b. Is it possible that after some amoebas transform the test tube contains $99$ blue amoebas and $314$ red amoebas?