Math Is Fun Forum

In some country, the king want to change on its monetery system.
The king want to make every transaction in his country be done with at most three coins.
Suppose, the country's currency is Cn

But, king's advisor found that with 1 Cn and 4 Cn, it can cover transaction up to 6 Cn consecutively, like this:

1 Cn : 1 Cn
2 Cn : 1 Cn + 1 Cn
3 Cn : 1 Cn + 1 Cn + 1 Cn
4 Cn : 4 Cn
5 Cn : 4 Cn + 1 Cn
6 Cn : 4 Cn + 1 Cn + 1 Cn

It can't get 7 Cn at any cost.
But, with 1 Cn and 3 Cn, it can reach up to 7 Cn consecutively.

1 Cn : 1 Cn
2 Cn : 1 Cn + 1 Cn
3 Cn : 1 Cn + 1 Cn + 1 Cn
4 Cn : 3 Cn + 1 Cn
5 Cn : 3 Cn + 1 Cn + 1 Cn
6 Cn : 3 Cn + 3 Cn
7 Cn : 3 Cn + 3 Cn + 1 Cn

To cover up to 8 Cn consecutively, seems that it needs more than two different types of coins.

Now,  question time

1. Can u find the maximum transaction they can cover consecutively with just using three different types of coins?

2. How bout using four different types of coins?

3. and five different types of coins?