Solving a problem by making a List

Question

Suppose you are an engineer programming the automatic gate for a 50-cent toll. The gate should accept exact change only. It should not accept pennies. How many coin combination must you program the gate to accept?

Answer 1

Your options are a half-dollar coin, quarter, dime and nickel.  The various combinations include:

 

50-cent coin

 

25-cent coin  25-cent coin 

 

25-cent coin  10-cent coin  10-cent coin  5-cent coin

 

25-cent coin  10-cent coin  5-cent coin  5-cent coin  5-cent coin

 

25-cent coin  5-cent coin    5-cent coin  5-cent coin  5-cent coin   5-cent coin

 

10-cent coin  10-cent coin  10-cent coin  10-cent coin   10-cent coin

 

10-cent coin  10-cent coin  10-cent coin  10-cent coin   5-cent coin  5-cent coin

 

10-cent coin  10-cent coin  10-cent coin   5-cent coin    5-cent coin  5-cent coin   5-cent coin

 

10-cent coin  10-cent coin    5-cent coin   5-cent coin    5-cent coin  5-cent coin   5-cent coin  5-cent coin

 

10-cent coin   5-cent coin     5-cent coin   5-cent coin    5-cent coin  5-cent coin   5-cent coin  5-cent coin  5-cent coin

 

5-cent coin (10 times)

 

So, you see you have a choice of 11 combinations