Math Is Fun Forum

puzzloholic

Member

Registered: 2008-06-28

Posts: 3

Weird King

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?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Weird King

Are shopkeepers allowed to give change, as long as whatever change they give is also restricted by the limit of 3 coins?

For example, with your first case of 1Cn and 4Cn, Mr. Customer could pay 7Cn by giving two 4Cn coins and then receiving 1Cn from the shopkeeper, which keeps to the coin limit.
If that kind of thing is allowed, then you can pay for anything up to 9Cn with those two coins.

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Why did the vector cross the road?
It wanted to be normal.

puzzloholic

Member

Registered: 2008-06-28

Posts: 3

Re: Weird King

No, the shopkeeper doesn't allowed to give a change. U must buy everything with exact amount of money.