Ten stacks of gold coins have ten coins each. Nine of the stacks have coins made of pure gold, and one stack has coins made of an alloy that looks exactly like gold. Each pure gold coin weighs 10 grams and each alloy coin weighs 9 grams. You have an electronic scale that can display the weight of any pile of coins with 99.99 percent accuracy. What is the fewest number of weighings needed to
determine which stack contains the alloy coins.
What will be an ideal response?
One weighing is sufficient. Weigh a pile of 55 coins made up of one coin
from the first stack, two coins from the second, three from the third and so on. If all coins weighed 10 grams, the total weight would be 550 grams. Because some of the coins are alloy, the pile will weigh less. (Between 549 and 540.) The number of grams under 550 corresponds to the stack number of the alloy coins.
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What will be an ideal response?
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