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Making change

By David Shaw, 3 October 2018

Australia has six coins that are commonly used – 5 cents, 10 cents, 20 cents, 50 cents, $1 and $2.

How many different ways can you make exactly 50 cents in Australian coins?

Scroll down for the answer!

Brainteaser answer

This problem takes a bit of organising to make sure you cover all the possibilities. One way is to start with big coins and work down.

First, the easiest solution: one 50 cent coin

Next, there are two solutions with two 20 cent coins:
• 20, 20, 10
• 20, 20, 5, 5

There are four solutions with one 20 cent coin:
• 20, 10, 10, 10
• 20, 10, 10, 5, 5
• 20, 10, 5, 5, 5, 5
• 20, 5, 5, 5, 5, 5, 5

And finally, six solutions with no 20 or 50 cent coins:
• 10, 10, 10, 10, 10
• 10, 10, 10, 10, 5, 5
• 10, 10, 10, 5, 5, 5, 5
• 10, 10, 5, 5, 5, 5, 5, 5
• 10, 5, 5, 5, 5, 5, 5, 5, 5
• 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

So all up, there are 13 ways to make 50 cents!

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