NL-NWO 1980 Problem 4

In Venetiania, the smallest currency is the ducat. The finance minister instructs his officials as follows: "I wish six kinds of banknotes, each worth a whole number of ducats. Those six values must be such that there exists a number N with the following property: Any amount of money of $n$ ducats ( $n$ positive and integer) where $n \le N$ may be paid in such a way that no more than two copies of each kind are required either to pay or to return. I also wish those six values to be as large as possible for $N$ . Determine those six values and provide proof that all conditions have been met." Solve the problem of those officials