You have 4 weights weighing 2,3,5 and 7 pounds. The problem is none of them are marked. What is the fewest number of weighings you need using a balance scale figure out which weights are which?
Like Penny I found that trying to weigh more than 2 weights at a time resulted in too many possibilities. It seems to me that the best way to determine which weights are which is to find the seven pound weight. It takes 3 weighings to determine which is the seven.
Weigh 2 then weigh the next two. When we weigh the two heaviest against each other, we know two things. The heaviest of the third weighing must be the seven and the lighter of the two heaviest cannot be the 2. It must be the 5 or 3.
For the fourth weighing take the lighter of the two heaviest weights and one of the two lighter weights and weigh them against the 7.
If the two weights are lighter than the 7, we know that the lighter of the two heavier weights must be a 3 and the lighter weight we added must be the 2, leaving the weight not on the scale to be the 5.
If the two weights balance with the seven, we know that the lighter of the two heavy weights must be the 5 and the lighter weight we added must be the 2, leaving the weight not on the scale to be the 3.
If the two weights are heavier than the 7, we know that the two weights must be the 3 and the 5, leaving the weight not on the scale to be the 2. The problem here is that we do not know which weight is the 3 and which is the 5. In this case only we would need to make a fifth weighing to determine which is the 3 and which is the 5.
four or five
