# Math Help - Problem: The counterfeit coin

1. ## Problem: The counterfeit coin

There are 9 coins. 1 coin is counterfeit.

You have a set of brass weighing scales (the ones that look like this: http://chantelt.files.wordpress.com/...over_white.jpg)

You know that the counterfeit coin weighs considerably less than the others.
If you placed the counterfeit coin one one end of the scale and a real coin on the other, you would notice the difference.

The coins all look exactly the same. You cannot tell which coin is the lightest by simply holding them in your hands. The only way to tell is to use the scales.

Explain how, in exactly TWO uses of the scales, the counterfeit coin can be found.

2. Split them in triples. Easy from there

3. Originally Posted by blueirony
There are 9 coins. 1 coin is counterfeit.

You have a set of brass weighing scales (the ones that look like this: http://chantelt.files.wordpress.com/...over_white.jpg)

You know that the counterfeit coin weighs considerably less than the others.
If you placed the counterfeit coin one one end of the scale and a real coin on the other, you would notice the difference.

The coins all look exactly the same. You cannot tell which coin is the lightest by simply holding them in your hands. The only way to tell is to use the scales.

Explain how, in exactly TWO uses of the scales, the counterfeit coin can be found.
Originally Posted by Rebesques
Split them in triples. Easy from there
Right, Rebesques.

Put two groups of three on the scale. If it's balanced, then the counterfeit coin is in the third group. If not balanced, then the counterfeit is on the side of the scale that tipped up.

In either case, this leads you to one set of three coins, one of which is the bogus one.

Pick any two and place them on each side of the scale. If it is balanced, then you are holding the bad coin. If it is not balanced, then it's pretty easy to tell where that bad boy is.

4. Both of you are correct