Stuart has some 2-ounce, 3-ounce, and 4-ounce weights. How many different ways can Stuart combine the weights to make a total of 12 ounces?

Answer 1

start with as many big weights as you can.
4+4+4
4+4+2+2
since 4+2 = 3+3, you can now go to
4+3+3+2
now start working to eliminate the last 4. There aren't very many more ways to do it. Eventually you will get all the way down to
2+2+2+2+2+2