Question

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.

Answer 1

Answer:

Step-by-step explanation:

Given that  you have n gold coins with one a fake that you know is slightly lighter.

Case I: n is odd.  Separate the gold coins into two groups containing (n-1) on one side and one separate.  Since n-1 is even split it into two equal sets and weigh on each side of the balance. If both balance then the one coin separate is the answer.  Otherwise take the one which show higher weight and continue the process for n/2 also, if odd.

Case II: If n is even do the process as you did for n-1 in the previous explanation.

So minimum weighings required would be r where

$2^r<n<2^{r+1}$

For example, if 33 coins are there minimm weighings would be = 5 since

2^5<33<2^6