Quandaries
and Queries 

Got a question for you "You are considering buying 45 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found the counterfeit coin?" Now to me this is a hard one. How can you do this with out having the coins and scales in front of you??? Kim 

Hi Kim, I can get you started. Put 15 coins on one side of the balance and 15 coins on the other side of the balance. If the left side of the balance goes up then one of the 15 coins on the left side is the counterfeit coin. If the right side of the balance goes up then one of the 15 coins on the right side is the counterfeit coin.If the scale balances then one of the 15 coins not on the balance is the counterfeit coin. Thus, in one weighing you have reduced the problem from a problem with 45 coins to a problem with 15 coins. What do you do next? Penny 

