In 1984, Australia introduced a $100 note, bringing the number of notes in common circulation to 7, being: $1, $2, $5, $10, $20, $50 and $100.

If a person has exactly one of each of these notes, how many different values (excluding $0) can they create?For this question, we are investigating different strategies or techniques for working out how many different total sums can be made using just the seven notes provided. This is to show how the different strategies or techniques work - you will not be penalised if you do not obtain the correct solution.

Choose any THREE different strategies / techniques. All of these should allow you to find the solution, but some may be inefficient to complete.

For each of the selected strategies / techniques:

i. Name the strategy / technique and describe how it could be used to find the number of different total sums these notes can make.

ii. Demonstrate how to approach solving the problem using this strategy / technique. Document and clearly explain what you are doing throughout the process. Show all of your working.

Note: If the strategy / technique you are demonstrating takes a lot of time to complete, show enough of how to apply the strategy / technique to make it clear you understand how to use it, and then comment that the working out would continue as shown.

After attempting all three selected strategies / techniques:

iii. Reflect on the suitability of these strategies for this task. Compare how effective each of these strategies were for the task. Which would you recommend using to obtain a solution? Justify your response.