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More cool problems
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You are trapped in a room with 10 gumball machines, lots of change, and one not very good scale. Nine of the machines contain gumballs that all weigh exactly one ounce, but one machine is defective and its gumballs weigh only half an ounce. The scale is highly accurate, but can only be used once. You have to figure out which gumball machine is defective. The defective gumballs look, feel, and taste just like normal gumballs.
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Start with 5 short pieces of string. Pick two ends at random and join them. Pick two more ends at random and join them. Keep doing this until there are no more free ends. What is the expected number of closed loops? (Think of the "expected number" of closed loops as the average number of loops, if a large number of people each have 5 pieces of string and each carry out this process. Since it is an average, it may not be a whole number.)
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