There was a millionaire who loved collecting gold. He bought ten solid gold shapes from a man, but the man proposed a bet. He said:
“One of these shapes is fake. It is made from a metal that looks exactly like gold. The only difference is that it is 1 gram lighter per 10 sq cm. If you can find the fake, you can have all of the bars for free.”
So the man weighed all of the bars, and to his surprise, they all weighed the same. Because of their strange shapes, he could not simply measure them. How can the man discover the fake without any measuring tools?
Answer
He could fill a bucket with water and place each shape in separately. Then whichever makes the water level rise most is the fake, as it would have to be slightly bigger to make it weigh the same.
