Identifying a Counterfeit Coin Using a Simple Balance: A Mathematical Challenge

[Chikawakajones]

You may have heard that money is the evil of this world, but as number devils it gives us the task to create math problems in the business world.
So here is the next problem.

You have twelve coins,
One of which is counterfeit and weighs less than the legal ones.

How can you use a simple balance, three times to determine which coin is counterfeit ?

 

[Chikawakajones]

Help Me Please

 

[geometer]

Help Me Please

Divide the 12 coins into two stacks of six and weigh them on the balance. The stack with the counterfeit coin will be lighter.

Now take the lighter stack of 6 and divide it into two stacks of three and weigh them on the balance. Again, the stack with the counterfeit coin will be lighter.

You figure it out from there.

 

[NateTG]

Why only 12?

You could find one ball in 27 in three weighings if you know it's light.

Could you find one light ball out of 3 in one weighing?
What about one light ball out of 9 in two?

 

[Integral]

The initial problem is more interesting if you do not know that the bad coin is lighter, only that it differs in weight.

 

[gravenewworld]

a better way would be to do what archimedes did and put each coin in the same amount of water to test how much water they displace

 

[Integral]

A basic assumption would be that each coin has the same volume, thus will displace that same amount of water. Also you must find the coin in 3 measurements.