Solution
Posted by Southern Man on Jul 12, 2002 at 08:34
(209.102.131.243)Re: Puzzle for the weekend (Southern Man)
13, 2, 12, infinite? I’m rather disappointed in the response. Bobbapink is the only one who had the cahones to take an honest guess? I’m sure there are others here who could have tried but didn’t. Is everyone else that afraid of being caught not able to find the answer? Is never having to admit you don’t know everything that important to all of you?
My initial reaction to the problem was that you could determine which of 3 bags was counterfeit in a single weighing. So set 3 bags aside and try 2 weighings to determine which if any bag is counterfeit. On the first weighing place 20 full bags on each side. If it balances it is one of the 3 bags we put on the side. Otherwise the side that goes down has the counterfeit and the amount that it goes down is 10 times the weight difference of a single coin. On the second weighing take the 20 bags that went down and on each side place one coin from one bag, two from the second, etc. Since we know the weight difference of a single counterfeit coin we can find which of the 20 bags contains the counterfeits. Now place 43 bags on the side and figure out how many we could isolate with 3 weighings. That’s where I got stuck. Just putting 43 on each side with 43 more left in case they balance is too few. We get too much information if they don’t balance (both which set of 43 AND the weight of a counterfeit) so we could have had more. Therfore the answer is more than 129.
But I was WAY low. The answer is 7491 (or more?).
http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/solutions/June2002.html