Puzzle Nekst 2: Opportunity to Strike Gold
Over the past few months, we received a large number of contributions for the coconometrics puzzle. In this new edition, we provide you with another puzzle which is about money this time. If you are in for a challenge, then grab some paper and a pencil and rack your brain! Who knows whether you will strike gold and win a delicious pie or a crate of beer. The smallest unit of currency in country X is the ducat. The minister of finance gave his officers the following command: “I want six types of bank notes, each worth an integer number of ducats. These six values should be such that there exists a number N with the following property:
Each sum of ducats n (with n positive and integer) where n ≤ N, can be determined in such a way that from any kind of banknote at most two units are used either to pay or to return money. I wish those six values also in a way that N is as large as possible. Determine which six values should be given to the banknotes and provide a proof that all conditions are fulfilled.” Solve the problem of the officials.
Each sum of ducats n (with n positive and integer) where n ≤ N, can be determined in such a way that from any kind of banknote at most two units are used either to pay or to return money. I wish those six values also in a way that N is as large as possible. Determine which six values should be given to the banknotes and provide a proof that all conditions are fulfilled.” Solve the problem of the officials.
Please send your solution to Nekst@Asset-Econometrics.nl before March 1, 2013. A crate of beer or a delicious pie, whichever the winner prefers, will be waiting for whoever has the best (partial) solution! Good luck!
