By signing up, you'll gain access to our full library of puzzles and riddles. Plus, being a part of our community means you'll never have to puzzle alone again! Sign up now and become a part of our community of puzzle-lovers today!
Welcome to our puzzle and riddle website! Our website is a great way to exercise your mental muscles, improve your problem-solving skills, and have fun in the process.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
You are given 9 coins which look identical, 
but one is lighter than the rest.
Using the balance scale under,
What is the minimum number of weighings you need
to guarantee that you can find the counterfeit coin ?
To guarantee finding the counterfeit coin, we need to ensure that we can identify which of the 9 coins is lighter than the others.
We can do this by dividing the coins into three groups of three coins each, and weighing two of the groups against each other.
1. There are three possible outcomes:
The two groups weigh the same: In this case, the counterfeit coin must be in the remaining group of three coins, which we can identify with a second weighing.
2. One of the groups is lighter: In this case, we know that the counterfeit coin is one of the three coins in the lighter group. We can identify the counterfeit coin with a second weighing by weighing two of the coins against each other. If they weigh the same, then the third coin is the counterfeit. Otherwise, the lighter of the two coins is the counterfeit.
3. One of the groups is heavier: This case is similar to case 2, but we know that the counterfeit coin is one of the three coins in the heavier group. We can identify the counterfeit coin with a second weighing using the same method as in case 2.
Therefore, the minimum number of weighings needed to guarantee finding the counterfeit coin is 2.