Use One Weighing
Date: 02/06/2002 at 00:44:49 From: Hevedar Khidir Subject: Help me with this puzzle Dear Dr. Math, There are 100 coins divided into 10 stacks, with 10 coins in each stack. There are 90 genuine coins and 10 fake coins. A genuine coin weighs 2 ounces and a fake coin weighs 1 ounce. The 10 fake coins are contained in one of the stacks. You have a scale with which you can weigh any number of coins. Using only one weighing, describe how you would determine which stack contains the fake coins. Thank you for your time.
Date: 02/06/2002 at 01:28:50 From: Doctor Schwa Subject: Re: Help me with this puzzle Hi Hevedar, Here's a hint: If you weighed five coins, they should be 10 ounces. But if one of them is counterfeit, the weight would be one ounce less. If three of them were counterfeit, the weight would be three ounces less. In other words, your one weighing will determine how many counterfeit coins you have on the scale. Try that before you read the next hint: Okay, you're still stuck. Try to figure out a way to make a collection so that, if you knew how many counterfeit coins were in the collection, you'd know which stack was counterfeit. Think about that for a while... but in case you're still stuck, here's one last hint: If you take one coin from the first stack, two coins from the second stack, and so on, then if the net result is one ounce too light you'll know the first stack is counterfeit, if it's two ounces too light you'll know it's the second stack, and so on. - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/
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