30 Oct '11 07:00

It is fairly well known that if you have two sacks of beans, red and white, with the same number of beans in each, and take a cupful of red beans from the red to the white, mix perfectly, and then move as many beans from the mix of mainly white and some red into the red sack, the number of red beans in one sack equals the number of white beans in the other.

What if there are three sacks and three kinds of beans?

From red to white, and mix

From mainly white to black, and mix

From mainly black to red

Are the proportions of different kinds of beans the same in each sack, though of course with colors changed?

What if there are three sacks and three kinds of beans?

From red to white, and mix

From mainly white to black, and mix

From mainly black to red

Are the proportions of different kinds of beans the same in each sack, though of course with colors changed?