## Math Forum - Problem of the Week

### Galactic Exchange

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### Introduction

It's the year 2075. You take a vacation to the planet Orange. When you arrive, you notice coins of three different shapes: squares, circles, triangles. Unfortunately, no one speaks your language, and you're hungry. You find a food vending machine, but the prices are worn off! You have to try different combinations of coins to get food, and in addition, you will be able to figure out the relations between the coins.

### Questions:

1. Buy a package of zoogs. What are the fewest number and types of coins needed to purchase a package of zoogs using exact change?

2. Which coin is worth the least, and how many of it does it take to equal each of the other coins?

3. How many of the least valuable coins would it take to buy a package of zoogs?

4. Buy a package of Glorps. What are the fewest number and types of coins needed to purchase a package of Glorps using exact change? How many of the least valuable coins would it take to buy a package of Glorps?

5. Another Earthling arrives on the next shuttle and wants to try some Mushniks. Explain how you figured out the relations between the coins.

6. What are the fewest number and types of coins needed to purchase a package of Mushniks using exact change?