Non Verbal Reasoning – Complete the Grid (Type 6)
The Complete the Grid question type, also known as the Missing Square question, requires you to fill in the empty square based on the patterns that you identify in the other squares. These patterns are not just based on how shapes transform and rotate, but also what order the shapes are in.
Always remember that a pattern is essentially a set of rules that you apply to a shape or design. What you want to do here is build your own set of consistent rules based on the information already available to you. This will then help you apply the rules to new and future situations – it is as simple as that, no matter how complex the question is, or how many elements are involved. This is very similar to the Missing Sequence question type.
The biggest issue you have here is identifying the pattern and building out your rules. With this question type you do not get any guidance and direction other than the visual shapes that are presented to you.
What is important here is for you to study these shapes in a direct and literal way – what we mean by that is there are no trick questions and everything is the way it looks. This makes it easier for you because when studying each shape you can confidently state that Shape A did this and Shape B did that so the rule must be [write out your example rule].
Now to bring it back, what statements should you be making and how should you be looking at these shapes? It is difficult with a blank slate to find a place to start. So what you want to do is the following:
- Work from left to right in each row
- Identify each quality or characteristic of each shape e.g. is it big, is it small, has it got a border, is it coloured?
- Be detailed for each part of each shape
Once you have broken down the visual information presented to you, you can then ask questions and get answers on the following:
- Transformations – did the shape change size in any way?
- Rotations – did the shape rotate in any way?
- Changes in colour – did the shapes change colour or pattern in any way?
- Order – did the shapes move its order in any way?
- Reversals or flips – did the shape or shapes reverse or flip in any way?
- Review whether the rows are connected in any way
Now that you have a basic approach and set of questions to ask whenever you look at the Complete the Grid question type it is important to practise. Remember, practising builds your skill and confidence which makes it easier to apply your understanding. Ultimately, with a question type like this you are being tested on the following:
- Ability to take in only visual information
- Ability to look at information as a whole, but also break it down into its individual parts or elements
- Have a logical approach to determining changes and transformations
- Ability to create rules based on the information presented to you around how things are changing
- Ability to apply your rule or set of rules to predict future behaviour or fill in the gap
Essentially, when it comes to completing the grid what you are expected to do is in 2 parts or stages.
The first stage is analysing the information presented to you and demonstrating analysis skills in order to create rules that you can test and reflect the information that you are seeing. The second stage is the application of your rule to identify the shape that must complete the grid.
This question type, like most non verbal reasoning questions, focuses on testing your ability to process information and how thoroughly you do this. On top of this, how well equipped you are when it comes to asking questions about information you have never come across before.
This can only be achieved if you are ready to ask questions e.g. how has this happened or why has this happened, and then use the information to answer your questions.
What does the Complete the Grid Question Type Looks Like
As you can tell from the CGP example below, the complete the grid question type is in the following format:
- General instructions with an example
- A grid of 4, 6 or 9
- 1 grid which is empty at some point in the grid e.g. top, middle or end
- 5 answer options on the right hand side
- 1 mark per question
How do I answer this question?
As mentioned already, the complete the grid question type is all about how you understand the order of things as well as how things could change. A key thing to remember here is that not all things need or have an order and not all things need to change.
You might only get questions where you only spot changes and transformations to the shapes, or questions where there are only changes to order, or both!
What this means is that before you try to answer this question type you need to have a set of questions that you can go through step by step, and a process in place to help you understand the information in front of you.
When it comes to completing the grid, you want to know whether something has changed – whether its transformed, rotated or just changed places.
This is why things like being able to look at information as a whole, then break down information to its individual parts and having a set list of questions are so important. It is because not all your questions need be answered. But by asking questions you can start understanding what you are seeing happening, and from there you can start building rules to help you determine your answer.
This also why, just like with all other non verbal reasoning question types, there is a process that we can walk through to help you efficiently get to your answer. Lets start looking at what this process is:
- Always read the instructions
- Look at the question, is it a 4 grid, 6 or 9 grid?
- Read each row from left to right
- Identify the shapes in the grid boxes
- When looking at the shapes for each row compare them one by one to each other from left to right, and ask yourself the following questions:
- Is the same shape across multiple grid boxes?
- If it is the same shape, how is that shape changing across the grid boxes?
- Is it rotating?
- Is it transforming?
- Is the colour changing?
- Is it flipping / reversing?
- Are there different shapes across the grid boxes?
- What do these shapes look like – what qualities do they have e.g. patterned, coloured, plain?
- Do these shapes re-occur?
- If they re-occur then what is the change that is happening e.g. moving places / order, rotation, transformation, colour changing, flipping / reversing?
- Is the same shape across multiple grid boxes?
- The questions above will help you identify specific things about the shapes in the grid boxes. Use these things to now build a rule or rules.
- Apply the rule or set of rules you have created to the row of the grid that is missing a shape and select your answer (fill in the gap).
Working Example
Now that we have a process lets apply it to an example:
First of all it is clear that we have a 9 grid box, the missing grid is on the bottom row, so I am going to use all the rows, or as many, to inform my decision.
The first row has like a oval shape which is plain. Next to it there is a cup-like shape with a diagonal pattern, and in the last box there is a coloured semi-circle.
In the first row it does not seem that the shapes repeat, but there are different shapes in the different grid boxes. So instead of trying to see how shapes change, i am going to try understand how they compare and contrast with eachother.
Now looking at the second row, I can see that 2 of these shapes repeat but there is a new square shape. Where that shape came from, I am not sure.
What is visible though is the oval shape is now gone, the cup pattern shape has moved across to the left by 1, so has the semi circle coloured shape moved across by 1 to the middle.
REMEMBER : I am going row by row from left to right as thats just the general order of things and how they are presented
Now I am going to look at row 3, straight away I can that the semi circled coloured shape has moved by 1 to the left again. I have my gap and I also have a teardrop shape now which I do not know anything about.
So I have looked at the grid, the shapes and the information available to me.
I have asked as many different questions as I can about the what I see, but the only real thing I was able to determine was that the shapes move by 1 to the left and a new shape comes up on the right.
I will make this a rule to follow:
- All shapes must move across by 1 to the left on the new row to make space for the new shape on the right.
Lets now apply that rule. So in row 2 we have the cup pattern shape on the left, semi circle shape in the middle and new square shape on the right.
In row 3 we again see that the cup pattern shape has gone, semi circled coloured shape is on the left – so now, applying the rule, the square shape must now be in the middle to make space for the teardrop shape.
ANSWER : C
What if I can’t complete the grid?
Based on how open the question is, how there is little direction other than what is in the grid it is easy to see why a question like this can become confusing and difficult very quickly. It really does boil down to how you think and process visual information – but also beyond that, how you spot patterns and trends, how you see similarities and differences and finally how you compare and contrast.
To be able to demonstrate those things can be very hard, so if you are finding it do not worry. Lets slow down, and try some practical things to get us to the answer such as:
- Ask questions. There are a few tips on the kind of questions you can ask e.g. shape changes, colour changes, rotation, transformation and order, but do not feel restricted to those, ask as many questions as you want
- Remember, you are not after answers to all your questions, you are just after some answers that make logical sense e.g. the question above had no shape changes, but it did have order changes
- Where you do not get an answer move on and ask a different question – remember youre asking questions to understand the information in front of you
- Look at how shapes are changing
- Look at the order of shapes and how that is changing
- Understand only the things that make sense – there are no trick questions here, everything is on paper. What this means is that if it makes sense you should be able to see it, if you cannot see it or have to assume leave it.
- Always try to create rules for example the shapes are moving by 1 to the left or Shape A has reduced in size.
- Do not be afraid to look at things row by row, box by box
- Understand as much detail as possible
Where you are still struggling to answer the question / complete the grid, try to take a logical guess. The aim of this guess is to be as confident as you can be with the information you have infront of you. Try to set a rule or 2 and then apply that rule, if you feel you cannot set a rule ask yourself:
- What is happening to the shapes in this grid right now?
After noting down what is happening then ask:
- Can I test this change or set of changes out by applying it back over the grid?
You should be able to test a change out and see it working. The way you know it works is that it follows the same logic of the grid for example if you assume the shapes move by 1 to the left, when you apply it to any shape in the grid you will see the shape moves by 1 on the new row.
If you are sure that something seems to be working then apply that to the row with the empty grid, select your answer and at least you can be confident that you tried to apply a logical approach to answering a difficult question.