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?
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Divide the 9 marbles into 3 groups: G1, G2, and G3. Weigh G1 with G2. If they balance, then the 1.5 ounce marble is in G3. Otherwise, the 1.5 ounce marble is in the heavier of G1 and G2.
Call the group that definitely contains the 1.5 ounce marble GS. Put one marble from GS in each pan. If they balance, the 1.5 is the member of GS not on a pan. Otherwise, it is the one in the pan on the heavier side.
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