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/