You have 10 identical cartons each holding 10 water bottles. All bottles weigh 10 oz. each, except

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You have 10 identical cartons each holding 10 water bottles. All bottles weigh 10 oz.

each, except for one defective carton in which each of the 10 bottles weighs on 9 oz. only.

A scale is available for weighing.

(a) Suggest a method for locating the defective carton.

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(b) What is the smallest number of times the scale is used that guarantees finding the defective carton? (Hint: You will need to be creative in deciding what to weigh.)

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