A pirate captain presents his prisoner with eight golden coins and a challenge: if the prisoner can identify the single genuine gold doubloon in the bunch, he can keep the coin, and his life. If he chooses one of the seven other counterfeit coins by mistake, he'll have to walk the plank.
The captain leaves the prisoner alone to contemplate this life or death decision. Luckily, there is a double tray balance scale in the room and the prisoner knows that a genuine gold doubloon weighs slightly more than a counterfeit coin. The captain may return any second, so the prisoner only has enough time to load each side of the scale and compare the balance twice. If all the coins look and feel totally identical, how can the prisoner most quickly and confidently identify the genuine article?
Solution: The prisoner places three coins on one side of the scale and three coins on the other for the first measurement. If the scale balances perfectly, he knows that one of the two remaining coins on the table is the genuine gold coin. He measures the two remaining coins and chooses the heavier one. If the first measurement shows that one set of three coins is heavier than the other, the prisoner removes the lighter coins from the scale. He takes the heavier set of three coins, places one on each side of the scale and holds the third in his hand. After the second measurement, he will see which coin on the scale is heavier than the other. If the coins on the scale balance perfectly, he holds the heavier (genuine) coin in his hand!
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