How can we determine, in two weighings on a balance scale, which ball is which?

Question

You are given six balls: two red, two blue, and two green. From each pair of the same color, one is light and one is heavy (it is, however, impossible to tell that without weighing them). All the light balls are the same weight and so are all the heavy ones.

Puzzling · Answer

Weigh one red and one green ball against one blue and the other green ball. If the weights are equal, then the red and the blue differ in weight. A weighing between these two balls allows us to deduce the weights of all other balls.

If the red-green combination was heavier than the blue-green combination in the first weighing, then the green ball in the red-green combination is certainly heavy and the other green is light. Now take the red from the red-green combination and the blue from the blue-green combination. Weigh these together against the remaining red and the remaining blue. The only interesting case is when this weighing is "equal". Then, the red from the red-green combination must be heavy and the blue from the blue-green combination must be light.

Grid · Answer

http://www.cut-the-knot.org/blue/6Balls2Weighings.shtml#solution

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How can we determine, in two weighings on a balance scale, which ball is which?

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