I have 9 coins; 3 coins each of 3 denominations.
Coins of the same denomination all weigh the same.
Each coin weighs an exact whole number of grams, and at most 9 grams.
I can weigh any subset of my coins together, to get their total weight accurate to the gram.
I want to determine how much a coin of each denomination weighs. Obviously I could do it in 3 weighings, just weighing one coin of each denomination separately.
How can I get the weights of the 3 denominations using only 2 weighings?