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If you have 8 bags of gold and one weighs less than the others what is the quickest way to find the lightest bag using a pan balance scale?
Wiki User
∙ 14y ago
Assuming the heavier bags are all of identical weight, this can be done in three weighings, eliminating half of the bags each time.
Thus the first weighing compares the bags in two sets of four, and reduces the field to four possible bags.
The second weighing compares these in two sets of two, to identify two possible bags.
The third and final weighing compares these two remaining bags, determining which is in fact underweight.
It can be done in 2 weighings
The first weighing compares 3 and 3.
If the 3 and 3 are equal, you weigh the two originally left out and will get your answer.
If the 3 and 3 are not equal you take the set of 3 that are lighter and weigh 1 and 1, leaving one out. If this weighing is unequal you'll know which bag is lighter. If the weighing is equal then the one you left out is the lightest.
Wiki User
∙ 14y ago
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