Hi Chas, Roald, These are all complicated formula that i believe are not expected at this level. If you look at the source (see my first submission) you will see that this exercise is only the second in a series called "Introduction to Programming". Therefore i am convinced that there is a much simpler solution.
Now, i believe that the number of consecutive passes required to make this work is equal to the smallest number of pack sizes. So if we have packs of (9,12,21) the number of passes needed would be 9 and the theorem would read "If it is possible to buy n,n+1,n+2,...n+8 nuggets it is possible to buy any number of nuggets >= 9 given that they come in packs of 9,12,21" However i turn in circles because i don't seem to get any results for some random pack combinations like (9,12,21) or (10,20,30). The must always be a solution i'm thinking, be it the smallest pack - 1 Thoughts? tnx Raoul -- http://mail.python.org/mailman/listinfo/python-list