a)You want to be able to weight a number of objects of unknown weight by balancing them against fixed weights on a balan

a)You want to be able to weight a number of objects of unknown weight by balancing them against fixed weights on a balance scale.For simplicity the objects are assumed to be weight whole numbers of grams.Consider the case where you can put the fixed weights only on one side of the balancing scale.What fixed weights should be chosen in order to have as few such fixed weights as possible?
b) Consider the case where you can put the fixed weights on both sides of the balance scale.What fixed weights should be chosen in order to have as few such weights as possible?
参考翻译(不一定准）（第一个答案的翻译更准！）：
a)用固定的重量来找到未知重量（用天秤类似的磅秤）。假设未知重量的单位是克而且是整数，如果固定的重量只可以放在秤的一边，用什么固定的重量才可以让固定的重量用的最小？
b）固定的重量可以放在两边？