# Inspired by Maggie Miller

**Discrete Mathematics**Level 5

You have a large jar filled with colored marbles. It contains \(2013 \,\color{Blue}{\text{blue}}\) marbles, \(2014\,\color{Red}{\text{red}}\) marbles, \(2015\,\color{Orange}{\text{orange}}\) marbles, \(2013 \,\color{#CCCC00}{\text{yellow}}\) marbles, \(2014\,\color{Purple}{\text{purple}}\) marbles, and \(2015\,\color{Green}{\text{green}}\) marbles.

You draw four marbles out of the jar, then put three marbles in (decreasing the total number of marbles in the jar by one) using the following rule:

If the four marbles are \(1\,\color{Blue}{\text{blue}}\) marble, \(2\,\color{Red}{\text{red}}\) marbles and \(1\,\color{Orange}{\text{orange}}\) marble, put \(2\,\color{#CCCC00}{\text{yellow}}\) marbles and \(1\,\color{Green}{\text{green}}\) marble into the jar.

If the four marbles are \(2\,\color{Orange}{\text{orange}}\) marbles and \(2\,\color{Purple}{\text{purple}}\) marbles, put \(1\,\color{Red}{\text{red}}\) marble, \(1\,\color{#CCCC00}{\text{yellow}}\) marble and \(1\,\color{Green}{\text{green}}\) marble into the jar.

If the four marbles are \(3\,\color{Green}{\text{green}}\) marbles and \(1\,\color{Red}{\text{red}}\) marble, put \(1\,\color{Blue}{\text{blue}}\) marble, \(1\,\color{#CCCC00}{\text{yellow}}\) marble and \(1\,\color{Purple}{\text{purple}}\) marble into the jar.

If the four marbles are \(2\,\color{#CCCC00}{\text{yellow}}\) marbles and \(2\,\color{Green}{\text{green}}\) marbles, put \(1\,\color{Red}{\text{red}}\) marble, \(1\,\color{Orange}{\text{orange}}\) marble and \(1\,\color{Purple}{\text{purple}}\) marble into the jar.

If the four marbles are \(3\,\color{Purple}{\text{purple}}\) marbles and \(1\,\color{#CCCC00}{\text{yellow}}\) marble, put \(1\,\color{Blue}{\text{blue}}\) marble and \(2\,\color{Green}{\text{green}}\) marbles into the jar.

If the four marbles are \(4\,\color{Green}{\text{green}}\) marbles, put \(2\,\color{Orange}{\text{orange}}\) marbles and \(1\,\color{Blue}{\text{blue}}\) marble into the jar.

In all other scenarios, return all four marbles into the jar.

Repeat this process until one marble remains. What color is it?

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