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)
The Vortzegian Mint seeks to implement a system that would make it possible to transact all amounts from 1 to 22 finbars and still obey the two-coin-only-per-transaction law. The mint says this must be done without using any coins with a value of more than 11 finbars.
1. Show that at least siz demoninations are needed to enable payment for all purchases from 1 to 29 finbars.