Question

You have 9 marbles. 8 marbles weigh 1 ounce each, & one marble weighs 1.5 ounces. You are unable to determine which is the heavier marble by looking at them. You have a weighing scale that consists of 2 pans, but the scale is only good for 2 total weighings. How can you determine which marble is the heaviest one using the scale & in 2 weighings?

Solution

1. Divide 9 marbles into 3 groups of 3 marbles each.

2. Take any 2 groups and place them on each pan. If they balance, remove the marbles from the pans, & place any 2 of the marbles from the remaining un-weighed group on the pans, 1 on each pan.

2.1. If one is heavier, it is the heavier marble, but if they balance, the remaining un-weighed marble is the heavier one.

2.2. If your first weighing does not balance, the heavier pan has the heavy marble.

3. Remove the marbles from the lighter pan, & place 1 marble on each pan from the heavier pan.

3.1. The heavier 1 is the 1.5 ounce marble.

3.2. But if they balance, then the marble from the heavy pan from the first weighing that was not weighed in the second weighing is the heavy one.

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