Minimum set of weight puzzle
This puzzle is a mix of weight and math puzzle.
Puzzle
What is the minimum number of weights needed for a scale that will be able to weigh objects from the weight of one pound to 100 pounds?
Solution

If only one side pan of the balancescale is used,
Weights are : 2^n <100 i.e. {1,2,4,8,16,32,64} = 7 
If both side pan of balancescale is used,
Weights are : 3^ n <100 i.e. {1,3,9,27,81} = 5
Mathematical Explanation
For each weight, there are three things you can do:
put it on the left pan, the right pan, or not on the balance at all.
So, if you have n weights, there are 3^{n} things you can do with them.
One of those things is not putting any weights on the scale, which is good if you want to weigh a 0pound object, so really there are only (3^{n} – 1) arrangements.
Then, for each arrangement there’s also its mirror image (where all the weights are switched to the opposite pan of the scale), so there are at most (3^{n} – 1)/2 arrangements of n weights.
That’s enough to prove that 4 weights can weigh at most 40 different things … 40 is really the upper limit for 4 weights.
With a fifth weight, you should be able to get up to (3^{5} – 1)/2 =121 pounds.