Problem #PRU-100654

Problems Algebra Number theory. Divisibility Divisibility rules Divisibility tests for 3 and 9

Problem

In a country far far away, there are only two types of coins: 1 crown and 3 crowns coins. Molly had a bag with only 3 crown coins in it. She used some of these coins to buy herself hat and she got one 1 crown coin back. The next day, all of her friends were jealous of her hat, so she decided to buy identical hats for them. She again only had 3 crown coins in her purse, and she used them to pay for 7 hats. Show that she got a single 1 crown coin back.