Minimults and Maximults

Answer 1

In Vortzegia, the unit of money is the finbar. The Vortzegians like to keep things simple, so they passed a law long ago stating that when you want to buy an item, the transaction must involve at most two coins including the change.

In Western Vortzegia before 2011 there were only 1-finbar and 8-finbar coins. With these coins only goods with the following values could be purchased: 1 finbar, 2 finbars (1+1), 7 finbars (8-1, pay 8 and get 1 finbar change), 8 finbars, 9 finbars (8+1) or 16 finbars (8+8).

In Eastern Vortzegia before 2011 there were also only two coin denominations in use, but they could transact all amounts from 1 to 6 finbars.

a) Which two coin denominations could the Eastern Vortzegians have had? Show how these coins were used to transact all amounts from 1 to 6 finbars.

In 2011, Eastern and Western Vortzegia merged to form one powerful country under Prime Minister Otto von Ochsenkopf. It was announced that all old coins would be withdrawn from circulation and a new set of coins would be released for the entire country with the face of the Prime Minister on them.

b) If 1-finbar, 3-finbar, 6-finbar and 10-finbar coins were issued and the two-coin-only-per-transaction law still applied, what amounts could be transacted?

The Vortzegian Mint seeks to implement a system that would make it possible to transact all amounts from 1 to 20 finbars and still obey the two-coin-only-per-transaction law.

c) Give a set of five coin denominations, none larger than 10 finbars, that will allow the mint's system to work.

d) Show that the mint's system cannot be implemented with only four denominations. (But you can make it.. just like how you can make question b)