2. (3 points) In a puddle, there live three types of amoebas: red, blue, and yellow. From time to time, any two amoebas of different types can merge into one amoeba of the third type. It is known that in the morning, there were 47 red, 40 blue, and 53 yellow amoebas in the puddle, and by evening, only one amoeba remained. What color is it?

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# Solution:

It is not hard to notice that as a result of the changes that the original population of amoebas can undergo, the parities of the absolute differences of the numbers of different types of amoebas do not change.

Let $n_{1}, n_{2}$, and $n_{3}$ be the numbers of red, blue, and yellow amoebas in the initial population, respectively, and let $\varepsilon_{1,2}$, $\varepsilon_{1,3}$, and $\varepsilon_{2,3}$ be the indicators of the oddness of $\left|n_{1}-n_{2}\right|$, $\left|n_{1}-n_{3}\right|$, and $\left|n_{2}-n_{3}\right|$, respectively.

In the considered case, $\varepsilon_{1,2}=1, \varepsilon_{1,3}=0$, and $\varepsilon_{2,3}=1$. Therefore, if the population degenerates into a single individual, the individual will be blue.

Answer: blue.