Math problem?
You are given ten stacks of silver dollars. Each stack contains ten coins. Nine of the stacks are completely genuine and one is completely counterfeit. You are told that a genuine silver dollar weighs 26.7 grams. You are given a scale and are allowed to weigh any number of coins, but you are allowed only one weighing! How many coins should you wwigh to eb sure of identifying the counterfeit stack?
Can someone help me solve this?
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Number your stacks from 1 to 10, and label the coins as well so as to not lose track of which are which. What you will do now is take 1 coin from stack one, 2 coins from stack 2, 3 coins from stack 3, and so one to 10. You will weigh all of that, and you should be able to identify the counterfeit stack by how far the scale is off from the weight you would expect if they were all real.
if you take one coin from the first stack, two coins from the second
stack, and so on, then if the net result is 26.7g too light you’ll
know the first stack is counterfeit, if it’s too light
you’ll know it’s the second stack, and so on.