How can you tell which of three balls is the lightest or heaviest using a simple balance that consists of two pans?


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Tough question to get into one sentence! You can do it in two weighings. Select any two of the balls and place one on each pan. If the scale balances, the third ball is the oddball. A second comparison will determine whether the oddball is lighter or heavier than the other two balls. Simply replace one of the first two balls with the oddball. If the oddball is heavier, its pan will drop; if it's lighter, its pan will rise. But what if the scale fails to balance the first time? (It is twice as likely that the scale will fail to balance when selecting two of the three balls at random for the first comparison!) If the scale fails to balance on the first comparison of two randomly selected balls, then you know that the oddball is on the scale, but you do NOT know which one it is, and you don't know whether it's heavier or lighter than the other two. A second comparison will resolve those issues. Remove the lighter ball from its pan and replace it with the third ball. If the scale remains out of balance, then you know that the heavier ball is the oddball, which is, of course, heavier than the other two. If, however, the scale balances, then the ball you removed is the oddball and is lighter than the other two.