math weight problem?

Question

You have six weights. One pair is red, one pair white, one pair blue. In each pair one weight is a trifle heavier than the other one but otherwise appears to be exactly like its mate. The tree heavier weights (one of each color) all weigh the same. This is also true of the three lighter weights. In two separate weighings on the balance scale, how can you identify which is the heavier weight of each pair?
Please consider that this is a balance taht does not tell you the weight, just which one is heavier adn which is lighter. Please complete the problem. While I did get some good help before, I am so exhausted from writing an essay and I really cannot understand it unless someone gives a full explanation.

Answer 1

I'll call the weights R1, R2, W1, W2, B1, B2.

First, weigh R1 and W1 against B1 and W2.

- If R1 + W1 is heavier than B1 + W2, we know that W1 must be heavy and W2 must be light. (If they were the other way around, the other pair of weights could at most cancel this difference, since the weights of the three heavy ones and of the three light ones are the same, so R1 + W1 would either be the same or lighter than B1 + W2.) Also, R1 is not lighter than B1, so either they are the same or R1 is heavy and B1 is light. For the second weighing, weigh R1 + B1 against R2 + B2. If R1 + B1 is heavier, R1 and B1 are heavy and R2 and B2 are light; if it is lighter, the other way around; if they match, R1 and B2 are heavy, R2 and B1 are light.

- If R1 + W1 is lighter than B1 + W2, the opposite applies: we know W1 is light and W2 is heavy, and R1 is lighter than or the same as B1. Again weigh R1 + B1 against R2 + B2. If they match, R1 and B2 are light, B1 and R2 are heavy; if R1 + B1 is lighter than R2 + B2, R1 and B1 are light and R2 and B2 are heavy; if R1 + B1 is heavier than R2 + B2 then R1 and B1 are heavy and R2 and B2 are light.

- If R1 + W1 matches B1 + W2, then either R1 and W2 are light and W1 and B1 are heavy (hence also B2 is light and R2 is heavy), or the exact opposite. So weigh R1 + W2 against W1 + B1; that will tell you which case is true.

Answer 2

The way i would figure which is the heaviest of each pair is simple. I would put one pair on the balance scale. Whichever lowers is obviously the heavier, and the one that raises is the lighter. I would then leave the heavier one on the scale, and try it against one weight from each of the other pairs. the orginal Pair we will say RED for example. So you know you have the heavy red weight on there, try it against one of the white weights, if it is equal you are weighing the heavy weight. So the other weight in the white pair has to be the lighter weight. Follow the same steps for the other pair, and you should be good to go.