Task Write on the topic: (50 points) (60 – 80 words) My distric tand my flat

What is an investigation?

The problem given in 3c and 5c Stamps investigates the amounts of postage we can make with an unlimited number of 3c and 5c stamps. This is a one-off problem. The solution that we give there is that we can make up 3c, 5c, 6c, and everything else from 8c onwards.

In the Extension to the problem above, we look at 3c and 7c stamps and come to the conclusion that here we can get 3c, 6c, 7c, 9c, 10c and everything from 12c onwards. Once we’ve done 3c and 5c, the 3c and 7c problem is not too difficult.  Precisely the same techniques can be used.

But about now our curiosity might well have been aroused and we might start to wonder what amounts of postage we can get with 3c and nc stamps where n is any whole number. The number that seems to be of special interest here is the ‘onwards’ number. That is, the first number such that every other number from that one onwards, can be made up with sufficient of the 3c and nc stamps. To get some idea of what patterns we can find, we might set up a table. With a bit of effort we could find the ‘onwards’ numbers for various values of n using the  3c  and  5c  approach. At first these might give a confusing pattern

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