PROBLEM SOLVING

Systematic Listing

Learn the reliable method for systematic listing, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Systematic listing finds every possibility exactly once.

Picture itPlan, solve, then check
2 · THE METHOD

Follow these steps

  1. Fix one choice and list all combinations with it.
  2. Change one feature at a time in a consistent order.
  3. Check for omissions and duplicates, then count the completed list.
3 · WORKED EXAMPLES

See the method in action

Example 1

There are 9 choices of routes and 4 choices of departure times. How many different journeys can be made using one of each?

  1. Each of the 9 first choices can be paired with each of the 4 second choices, giving 9 × 4 = 36 combinations.
Answer: 36
Example 2

There are 8 choices of flags and 3 choices of pole colours. How many different displays can be made using one of each?

  1. Each of the 8 first choices can be paired with each of the 3 second choices, giving 8 × 3 = 24 combinations.
Answer: 24
4 · ELEVENSPRINT TIP

A useful shortcut

Check for omissions and duplicates, then count the completed list.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.