Los Angeles Math Circle

10/11 -- Circle Jr: Weighing with powers of 2

You have a balance scale and a lot of weights. All the weights are powers of two (that is, they represent numbers 1, 2, 4, 8, 16, 32, 64, ..., expressed in grams). You have just one copy of each of these weights. Using just these weights, can you balance any object weighing the whole number of grams on the balance scale? We will find out!