Let us assume that we have a box of coins which contains
10 normal coins and
11 counterfeit coins. We know that each counterfeit coin is 1 gram less than each of the normal. One coin was taken from the box.
If we have a regular scale and we can only use it once (for one single measurement), how can we find out what was the coin which was taken out of the box (figure out whether it was a counterfeit or normal one)?
We can assume that the coins' weight can be any real number.
What I have considered so far:
- I know that if we measure the coin alone, which was taken out of the box, we have no way of figuring out whether it is a counterfeit or a normal one without measuring the whole box - and we cannot measure it since we will be breaking our rule of having to use the scale just once.
- I do not know how will measuring just the box would help either. Correct me if I am wrong but since we do not know how much is the weight of an individual coin, the total weight wouldn't be of any use to us, right? So I am stuck.