Questions involving a number pattern in the form of a matrix are similar to number sequences in that you are required to find a missing value. These questions test your ability to identify directional and/or number patterns from the numbers that are grouped together. However these types of questions are different from a number group in that:

1. The numbers are not grouped but are rather individual and,
2. The directional patterns are very flexible. It may be vertical, diagonal and horizontal or the number may even jump.

The above two components are important in these types of questions, because not only do you need to consider a 'number pattern' but you also need to have due regard for a visual pattern which makes it a bit more difficult.

For these types of questions , it is important to have an open mind and not be rigid in your assumptions . Matrices do not always follow the same directional pattern. They may also be L shaped, be zigzagged or other odd directions. While it is important to look at directions, do not be fooled into one conventional direction. You will need to explore different possibilities but first, try the pattern that seems most obvious to you.

You could follow this logical step-by-step process below to solving such questions.

1. Identify the features of the matrix. That is, whether they are numbers, letters or a combination and whether they increasing or decreasing.

2. Identify the visual pattern of the matrix. See whether the numbers run horizontally, vertically, diagonally or in some other shape. A common pitfall with a matrix question is that students often believe the directional pattern must be horizontal, vertical or diagonal. This mistake often occurs as a result of students focusing on the direction rather than the figures themselves.

3. Identify the mathematical properties of number within the visual pattern. That is, whether the numbers are obtained using addition, subtraction, multiplication or division. If you are unsure of how this works, you should revise the guidelines from section 3.1 on how to find a relationship after looking at the direction (increasing or decreasing) that the numbers follow.

4. Other peculiarities. There could be 'dead' numbers – i.e. numbers that are there but don't form part of the pattern e.g. a 0 which just stays constant or a number like 123 where it doesn't mean 'one hundred and twenty three' but rather the figures, 'one', 'two' and 'three'.

Let's now go through some illustrated examples below.

EXAMPLE 1

| 49 | 42 | 35 |

| 36 | 30 | 24 |

| 25 | 20 | ? |

Let's apply the logical step-by-step process to solve the above.

1. The numbers are decreasing from left to right.
2. There is a horizontal direction.
3. The numbers in the first column can be obtained by multiplying a number by itself. The numbers in the first row are multiples of seven. The second row numbers are multiples of six and the numbers in the third row are multiples of five.

Therefore, the answer is 15.

EXAMPLE 2

| 99 | 88 | 66 |

| 77 | 55 | 33 |

| 44 | ? | 11 |

Let's apply the logical step-by-step process to solve the above.

1. The numbers are decreasing from left to right.
2. The numbers run diagonally from bottom left to top right.
3. The numbers increases by 11 from left to right diagonally. Therefore, the missing number must be obtained by subtracting 11 from 33.

Therefore, the answer is 22.

EXAMPLE 3

| 49 | 35 | 23 |

| 25 | 15 | 7 |

| 16 | 8 | ? |

EXAMPLE 4

| * | 35 | 23 |

| 25 | 15 | 7 |

| 16 | 8 | ? |

Key Rules to remember:

• The numbers are not grouped but are rather individual and,
• The directional patterns are very flexible. It may be vertical, diagonal and horizontal or the number may even jump.
• Follow the logical step-by-step process.

Now it's time to do your assignment.

1. Download the assignment question here.
2. Print it out or if you want to do it electronically, save it.
3. Complete the questions to it.
4. Then check the solutions on the video below.
5. For the answers in text instead of video, download them here.