This is a question from a math contest I did a little while back. 3 parts: a. There are 3 different colours of balls: red, green, and yellow. Suppose you have 4 green balls, 5 red balls and 6 yellow balls. You are to constantly remove 1 ball from any 2 colours and than add 1 to the third colour. If you keep doing this until only 1 colour remains, what colour will it be? ex. If you take away one red ball and one yellow ball, than you would have to add one green ball. Thus leaving you with 5 green balls, 4 red balls, 5 yellow balls. b. If you are to start with 3 green balls, 5 red balls and 6 yellow balls. What colour will you always be left with? c. Suppose this time you change the process so that instead of adding 1 ball to the colour you dont remove from, you instead add 2 colours. If you start with 4 green, 5 red and 6 yellow balls, show that there will never be one colour left. ex. If you take away 1 green and 1 red you would than have to add 2 yellow. Leaving you with 3 green, 4 red and 8 yellow balls. I wanted to see what people did with this. Because after the contest was over I was fairly confident about my solution. However, when i got my result i got 4/10 for this question.