Ordering and Arrangement Questions in NSW OC and Selective Thinking Skills

Ordering and arrangement questions are a common part of both NSW OC and Selective Thinking Skills. They may involve people sitting in a row, runners finishing a race, houses in a street, train stops, objects on shelves or events happening in sequence.

The story changes, but the underlying skill is the same:

Can the student turn several conditions into one consistent arrangement?

These questions appear in different forms across the published Thinking Skills papers, including race rankings, seating positions, house arrangements and route order.

They are relevant to both NSW OC practice tests and NSW Selective practice tests.

What do these questions test?

Students are usually given several clues such as:

• A is before B.

• C sits immediately beside D.

• E is in the middle.

• F is two places away from G.

• H cannot be at either end.

They then need to work out what must be true, could be true or cannot be true.

The mathematics is usually simple. The challenge is organising the information accurately.

The best approach is often to stop treating the clues as a paragraph and turn them into a line, blocks, arrows or a small grid.

Start with the strongest clues

Not every clue is equally useful.

For example:

• Mia is somewhere to the right of Jack.

• Zoe sits at one end.

• Ava sits immediately to the left of Ben.

“Zoe sits at one end” gives a fixed position.

“Ava sits immediately to the left of Ben” gives a fixed pair:

[Ava][Ben]

These are usually more useful than a broad clue such as “Mia is somewhere to the right of Jack”.

A good order is:

1. fixed positions such as first, last or middle

2. immediate relationships

3. before or after chains

4. negative clues such as “not beside” or “cannot be third”

This reduces the number of possibilities quickly.

Turn “immediately” into a block

Students need to distinguish between:

A is before B

and

A is immediately before B.

The first may allow other people between them:

A _ _ B

The second means:

[A][B]

Treating immediate pairs as one temporary block can make the arrangement much easier.

The same idea applies to:

• immediately after

• directly beside

• next to

Build chains

Suppose:

A is before B.
B is before C.
C is before D.

Instead of storing three separate facts, combine them:

A < B < C < D

The same method works with ages, race positions, arrival times and rankings.

Selective papers use this kind of reasoning in problems involving station order and arrival order, where several “before”, “after” and “between” conditions need to be combined.

Relative order does not always mean exact position

If:

A finishes before B

we do not know that A is first or B is second.

Possible arrangements could include:

A B C D

or

C A D B

Students sometimes give a clue more information than it actually contains.

This is why it is useful to separate:

fixed position
from
relative position.

Be careful with “between”

Suppose:

B is between A and C.

This could mean:

A ... B ... C

or:

C ... B ... A

unless another clue gives the direction.

If we later learn that A is before C, then we can write:

A ... B ... C

The key is to combine clues rather than solving each sentence separately.

More difficult arrangement questions

Some questions involve several categories at once.

For example, five houses might each have:

• one person

• one favourite sport

• one type of transport

A clue may say:

The cyclist lives in the middle house.

Another may say:

Emma lives next to the person who likes tennis.

The Selective sample includes a five-house problem combining residents, sports and transport with clues about neighbouring houses, the middle position and relative distances.

For this type, a small grid is usually more effective than trying to remember everything mentally.

Students can fill in certain information first and use elimination for the remaining spaces.

Use negative clues at the right time

A clue such as:

Mia is not in position 4.

may not be very useful at the beginning.

But if other clues later narrow Mia to positions 3 or 4, it becomes decisive:

Mia = position 3.

This is why negative clues often become more useful after stronger clues have reduced the possibilities.

Common mistakes

One of the biggest mistakes is trying to keep the entire arrangement in the student’s head.

Even a simple line helps:

1 | 2 | 3 | 4 | 5

Other common errors include:

• confusing “before” with “immediately before”

• starting with a weak clue instead of a fixed one

• forgetting to combine clues into chains

• assuming a relative position is an exact position

• continuing to solve the whole puzzle when enough information is already available

That last point is important.

Sometimes several full arrangements are possible, but the answer to the question is still fixed.

If the question asks who must be in the middle, students only need enough information to prove that middle position.

“Must”, “could” and “cannot”

These words change the solving strategy.

For “must be true”:

Try to find a counterexample.

Ask:

Can I create a valid arrangement where this option is false?

If yes, eliminate it.

For “could be true”:

You only need one valid arrangement where the option works.

For “cannot be true”:

Try the options and see which one breaks one of the conditions.

This is often faster than completing the entire arrangement.

A quick worked example

Five children, Ava, Ben, Chloe, Daniel and Ella, sit in a row.

• Ava sits immediately to the left of Ben.

• Daniel sits somewhere to the right of Ben.

• Ella sits at the right end.

• Chloe sits beside Daniel.

Start with:

[Ava][Ben]

Ella must be position 5.

If Ava and Ben were in positions 3 and 4, Daniel would need to be to the right of Ben, but position 5 is already Ella.

So Ava and Ben must be earlier in the row.

The remaining clues can then be used to place Chloe and Daniel.

The important point is not the final arrangement. It is the method:

place the strongest clue, reduce the possibilities, then apply the next clue.

A fast method for the test

Students can use this process:

1. Draw the positions.

2. Place fixed positions first.

3. Turn immediate relationships into blocks.

4. Build before/after chains.

5. Use negative clues to eliminate remaining possibilities.

6. Stop when you have enough information to answer the question.

It also helps to abbreviate names.

Instead of writing:

Charlotte sits immediately before Benjamin.

write:

[CB]

Instead of:

William is somewhere after Olivia.

write:

O < W

This saves time and makes the logic easier to see.

Why these questions are worth practising

Ordering and arrangement questions test several important Thinking Skills abilities:

• extracting conditions accurately

• organising information

• distinguishing fixed and relative positions

• combining clues

• eliminating impossible arrangements

• recognising what must, could or cannot happen

The context may change from houses to runners, train stations or seating arrangements, but the underlying method stays very similar.

The key lesson is:

Do not keep the arrangement in your head. Put it on paper.

Once the information is converted into slots, blocks, arrows or a grid, many complicated-looking questions become much more manageable.

At Selective Journey, students can practise Thinking Skills together with Mathematical Reasoning, Reading and Writing.

For Selective preparation, explore the NSW Selective practice tests.

For Opportunity Class preparation, explore the NSW OC practice tests.

You can also register for a free trial.

Related guides:

Whose Reasoning Is Correct?

Strengthen, Weaken and Support Questions

Venn Diagrams and Set Relationships