Urns with marbles and gems

Solution 1:

You are not transcribing the facts correctly. You have taken the first statement to say that red is smaller than green and red is heavier than green. What it says is that whichever is smaller is the heavier of the two marbles that contain a gem. You therefore cannot use the transitivity to derive the contradiction you did.

I think I would just list the six possibilities for size ranking and see where each leads.

Say they are RGB from large to small. Then green is the heavier of the two that have gems (fact 1), red is the lighter of the two that have gems (fact 3), and blue is empty. Fact 2 now says that as green is the smaller that has a gem it is lighter than blue. Then they are BGR in order of weight. On the assumption that the puzzle is correctly posed, we could stop here and report the answer. Red and green have gems, red is larger and lighter.

To show how a problem can arise, say they are GBR from large to small. Now red is the heavier one with a gem and blue is the lighter one with a gem. Fact 2 says that the smaller one with a gem is blue or green, so we have a contradiction and this order of sizes is not possible.