Ten bags of gold

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Here is a weighing puzzle I remember from Mind-quest.


You have ten bags filled with ten gold coins each -- or so you thought. A mysterious note arrives informing you that one of the bags contains fake coins, which weigh slightly less than the real coins. In fact, each real coin weighs one ounce, while the fake coins each weigh 0.9 ounces. You happen to have a scale which can display the weight accurate to a tenth of an ounce. However, the batteries in the scale are almost out, so you can only use it once. How can you find the bag of fake gold?


There is no combination of whole bags you could weigh to find the answer. You will need to try something else.