The Scales Problem I found two tricky part of this puzzle. First, when I thought about this puzzle, I didn't think that to balance the scale with the only four weights I have, I could actually put weights on both sides. The second tricky part is that it should start from the biggest number and going backwards to find the 4 weights. I started from number 1 and I knew 1 must be one of the 4 weights. When I realized that there is no way by putting all the weights on one side and the herbs on the other, I started to try to herbs and weights on both sides. Soon I discovered that it is not possible to weigh bigger grams of herbs. I still need 1 as one of the weighs because it will be needed to weigh 1 gram. Then go back and started my trial and error from the biggest number 40. Here is a picture of the combinations, the 4 weighs are 1,3,9, and 27. To extend this puzzle, I could probably choose other numerbs such as 121. However the combinations will be too large that may be too difficult using trial and error method since there so many number to try. Maybe give a smaller number set say 1,3,9 first and let students work on it first. Once they have figure out the pattern, then I can extend the large set say 1, 3, 9, 81 and let them find the generality of this puzzle.