2. (8 points) if you have n gold coins with one a fake that you know is slightly lighter, how many weighings on the pan balance will you need to ensure that you can find the fake? explain your answer.

Only 1 Time

Step-by-step explanation:

Since you know that one coin is fake and that the coin is lighter than the rest , then you would only need to weigh all the coins together 1 time to ensure that you will find the fake coin. We can determine this by doing the following.

Example:

Lets say we have 100 coins that weigh 1 gr each. Meaning that the total weight of the 100 coins would be (100coins*1gr = 100gr) IF there are no fake coins in the batch.

Knowing this we can weigh the entire batch 1 time and if the total weight is less than 100gr we know that the fake coin is in that batch.

I hope this answered your question. If you have any more questions feel free to ask away at