You have 50 rolls of 50 pennies. You know that 49 of the rolls has normal pennies that each weigh 2.5 g. Unfortunately, one roll holds counterfeit pennies that weigh 3 g. Fortunately you have a scale. Describe a procedure that you could use to determine which of the rolls holds the counterfeit coins. You are only allowed a single weighing.

Solution

Take 1 penny from the first roll, 2 from the second, 3 from the third, etc. Do this for 49 rolls. You will have a total of 1225 pennies. Weigh them. If they are all real pennies, they will weigh 3062.5 g. If this is true, you’ll know that roll #50 was the counterfeit roll. If they weigh less that this amount, divide the difference by 0.5 to determine the number of counterfeit pennies on the scale. From this number, you can determine which roll holds the counterfeit pennies. There are of course variations of this solution.

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