8,9
What is the minimum number of weights needed to be able to weigh any number of grams from
1 to 100 on a balance scale, if the weights can only be placed on one side of the scale?

#
Any number can be written in binary notation. Therefore, to weigh any number of grams from 1 to 100, it is sufficient to have seven weights with the following weights: $1,2,4,8,16,32,64$. Six weights are not enough, as with them, one can weigh no more than $2^{6}$ - 1 different weights (each weight either participates or does not participate in the weighing).