# Workout the Mystery Number using BODMAS

In this worksheet, students will identify a rule which is used to make a number and apply this rule to find a missing number.

Key stage:  KS 2

Curriculum topic:   Verbal Reasoning

Curriculum subtopic:   Number Logic

Difficulty level:

### QUESTION 1 of 10

Hi number detective! We’ve got a new challenge that we need your help with. Are you ready?

We need to work out how the numbers on the outside of the brackets create the numbers on the inside of the brackets and then apply the same rule to the third set of brackets.

10 (23) 3        5 (16) 6         2 ( _ ) 5

Be warned:

One of the numbers could be used more than once.

A third invisible number could be used.

One or both of the numbers could be squared (multiplied by themselves).

First, we need to find a way to make 23 using 10 and 3. Remember that we will probably have to consider one of the warnings above.

If we add 10 and 3 together we get 13. Then, if we add another lot of 10, we get to 23.

So the rule could be: add the two outside numbers and then add the first number again.

Let’s try this out for the second set of numbers: 5 + 5 + 6 = 16.

We’ve found the rule! Jackpot!

Let’s use this rule to work out the missing number in the final set: 2 + 2 + 5 = 9. Therefore, the missing number is 9.

Let’s try another:

5 (28) 3        3 (16) 7        4 ( __ ) 8

First, we need to find a way to make 28 using 5 and 3. Remember that we can use one of the warnings listed above.

Let’s try 5 + 3 = 8 and add the invisible number of 20 to get to 28.

So our rule could be: add the two numbers together and then add the invisible number 20.

Let’s see if this works for the second set of numbers: 3 + 7 = 10 but we need to use a different invisible number of 8 to get to our total.

Bad news, our rule didn’t work so we need to find another.

Let’s try (this means 5 x 5) which gives us 25 and then we need to add 3 to get to 28.

So our rule could be: square the first number and then add the second.

Let’s try this for the second set: is 9 then add 7 gives us 16.

Jackpot! We’ve found the correct rule.

Let’s use this rule to work out the missing number in the final set of numbers: 4² = 16 and then add 8 gives us 24. So the correct answer is 24.

 Pssst! Here's a handy hint to help you reach superstar status: lookout for the secret number and don't worry if the first rule you find doesn't work, just stay calm and try another one!

It’s now your turn to be a number detective and hunt down those missing numbers!

I need your help with this number puzzle, detective.

Look at the groups of numbers below:

4 (19) 3        3 (16) 7

How do the outside numbers in each set create the middle numbers (the numbers in brackets) in each set?

Left number x right number + 2

Left number squared + right number

Right number squared + left number

Left number + right number + 7

Look at the numbers below.

Which rule from below creates the number inside the brackets by using the two outside numbers?

Make sure that the rule you select works for both sets of numbers.

15 (121) 4        9 (36) 3

Left number x right number

Left number squared - right number

(Left number - right number) and square the answer

(Left number - right number) x 4

You're now ready to work out some mystery numbers!

Look at the number sets below:

12 (44) 10        9 (28) 5

The rule is '(left number + right number) x 2'. This means that we add the left and right numbers together and then times the answer by 2 to get the middle number.

Use this rule to work out the mystery number in the middle of the brackets below.

Left number x right number

Left number squared - right number

(Left number - right number) and square the answer

(Left number - right number) x 4

Look at the number sets below.

6 (40) 2        5 (50) 5

The rule here is 'left number squared + right number squared'.

Use this rule to work out the mystery number in the brackets below.

Left number x right number

Left number squared - right number

(Left number - right number) and square the answer

(Left number - right number) x 4

Look at the number sets below:

45 (8) 5        80 (9) 8

The rule here is 'left number ÷ right number - 1'.

Use this rule to work out the mystery number in brackets below.

Left number x right number

Left number squared - right number

(Left number - right number) and square the answer

(Left number - right number) x 4

Let's make things a bit more challenging!

This time you need to identify the rule for the first two sets of numbers and then, use this rule to work out the mystery number in the final set.

3 (81) 6        4 (100) 6        5 (?) 3

What is our mystery number?

15

64

11

62

Nearly there, number detective - keep going!

Look at the sets of numbers below.

Work out the rule that makes the numbers on the inside of the brackets by using the two outside numbers. Then use this rule to work out the mystery number in the third set.

7 (20) 6        20 (44) 4        3 (?) 10

30

23

29

16

Look at the numbers below.

9 (85) 2        10 (136) 6        5 (?) 4

Work out the rule to make the middle number in the first two sets and use this rule to work out the mystery number in the final set.

41

9

20

14

Look at the numbers below:

72 (8) 9        56 (7) 8        120 (?) 12

Work out the rule to make the middle number in the first two sets and use this rule to work out the mystery number in the final set.

It's your final number puzzle of this set of questions!

Look at the number sets below:

13 (19) 12        36 (40) 10        15 (?) 5

Work out the rule for the first two number sets and use this rule to calculate the mystery number in the final set.

• Question 1

I need your help with this number puzzle, detective.

Look at the groups of numbers below:

4 (19) 3        3 (16) 7

How do the outside numbers in each set create the middle numbers (the numbers in brackets) in each set?

Left number squared + right number
EDDIE SAYS
Hey detective! Did you try out each rule here until you found one that worked for our number sets? The rule here was 'left number squared + right number'. Let's look at how this works for the first set: 4 (19) 3 We need to square the left number (4). This means that we have to times it by itself. 4² = 16 and then add the right number (3) to get 19 (the middle number). Let's do the same for the second set: 3 (16) 7 3² = 9 and + 7 (right number) = 16. Keep your eyes peeled for more number puzzles.
• Question 2

Look at the numbers below.

Which rule from below creates the number inside the brackets by using the two outside numbers?

Make sure that the rule you select works for both sets of numbers.

15 (121) 4        9 (36) 3

(Left number - right number) and square the answer
EDDIE SAYS
This rule was a challenge. Some parts of each rule are in brackets- these need to be worked out first as stated by the rules of BODMAS (you may know them as BIDMAS). The rule here was '(left number - right number) and square the answer'. Let's look at the the first number set: 15 (121) 4 15 (left number) - 4 (right number) = 11 and 11² = 121. This works for the second set too: 9 (36) 3 9 (left number) - 3 (right number) = 6 and 6² = 36. It's now your turn to work out some mystery numbers...
• Question 3

You're now ready to work out some mystery numbers!

Look at the number sets below:

12 (44) 10        9 (28) 5

The rule is '(left number + right number) x 2'. This means that we add the left and right numbers together and then times the answer by 2 to get the middle number.

Use this rule to work out the mystery number in the middle of the brackets below.

EDDIE SAYS
Did you follow the rule for this next set of numbers? We need to do 6 (left number) + 8 (right number) and then times the answer by 2. 6 + 8 = 14 and then 14 x 2 = 28. Are you this good at following rules at home?
• Question 4

Look at the number sets below.

6 (40) 2        5 (50) 5

The rule here is 'left number squared + right number squared'.

Use this rule to work out the mystery number in the brackets below.

EDDIE SAYS
Did you follow the rule to get 58 here? We need to square both of the outside numbers and then add these together. Remember that squaring means multiplying the number by itself. 7² = 49 3² = 9 49 + 9 = 58 Keep following those rules, detective!
• Question 5

Look at the number sets below:

45 (8) 5        80 (9) 8

The rule here is 'left number ÷ right number - 1'.

Use this rule to work out the mystery number in brackets below.

EDDIE SAYS
Let's follow the rule carefully here: 20 (?) 5 20 (left number) ÷ 5 (right number) = 4 and then if we subtract 1 we get 3. Right detective, you're now ready for your next challenge...
• Question 6

Let's make things a bit more challenging!

This time you need to identify the rule for the first two sets of numbers and then, use this rule to work out the mystery number in the final set.

3 (81) 6        4 (100) 6        5 (?) 3

What is our mystery number?

64
EDDIE SAYS
Did you notice that both of the numbers in brackets are square numbers? This is a clue that part of our rule needs to involve squaring. Let's look at the first set of numbers: 3 (81) 6 The middle number is 81. 81 is 9². How can we make 9 with the outside numbers? 3 + 6 = 9. This means that the rule could be '(left number + right number) then square the answer'. We need to check if this rule works for the second set of numbers. 4 (100) 6 4 + 6 = 10 and then 10² = 100. Jackpot! The rule works for both sets of numbers. Now, we need to use this rule to work out the mystery number. 5 (?) 3 5 + 3 = 8 and 8² = 64. Make sure that the rule you find works for both sets of numbers.
• Question 7

Nearly there, number detective - keep going!

Look at the sets of numbers below.

Work out the rule that makes the numbers on the inside of the brackets by using the two outside numbers. Then use this rule to work out the mystery number in the third set.

7 (20) 6        20 (44) 4        3 (?) 10

16
EDDIE SAYS
Did you notice the rule here? The numbers on the inside of the brackets are larger than the numbers on the outside. This is a clue that we are multiplying, adding or squaring. Let's look at the first set: 7 (20) 6 7 x 6 is 42 which is much bigger than the inside number so let's try adding. 7 + 6 = 13 If we add another 7 to the 13, we get 20, which is the middle number. The rule could be 'left number + right number + left number again'. Let's see if this works for the second set. 20 (44) 4 20 + 4 + 20 = 44. Jackpot! The rule works for both sets. Now we know the rule, we can work out the missing number in the final set. 3 (?) 10 3 + 10 + 3 = 16. 16 is our mystery number! Wow, that was a long- but worthwhile process.
• Question 8

Look at the numbers below.

9 (85) 2        10 (136) 6        5 (?) 4

Work out the rule to make the middle number in the first two sets and use this rule to work out the mystery number in the final set.

41
EDDIE SAYS
Hey detective. The rule here was 'left number squared + right number squared'. Let's look at how this works in the first set: 9 (85) 2 9² = 81 and 2² = 4 81 + 4 = 85 This also works for the second set: 10² (100) + 6² (36) = 136 Now we know the rule, we can use this to work out the mystery number in the final set: 5 (?) 4 5² (25) + 4² (16) = 41 This makes 41 our mystery number. Brilliant detecting!
• Question 9

Look at the numbers below:

72 (8) 9        56 (7) 8        120 (?) 12

Work out the rule to make the middle number in the first two sets and use this rule to work out the mystery number in the final set.

10
ten
EDDIE SAYS
Did you spot the rule here, detective? The rule was 'left number ÷ right number'. 72 (8) 9 72 (left number) ÷ 9 (right number) = 8 (middle number). 56 (7) 8 56 (left number) ÷ 8 (right number) = 7 (middle number). Now we know that the rule works for both sets of numbers, we can work out the mystery number in the final set. 120 ÷ 12 = 10 This makes 10 our mystery number.
• Question 10

It's your final number puzzle of this set of questions!

Look at the number sets below:

13 (19) 12        36 (40) 10        15 (?) 5

Work out the rule for the first two number sets and use this rule to calculate the mystery number in the final set.

14
fourteen
EDDIE SAYS
We had a mystery number involved in our rule here! The rule was 'left number + right number - 6'. Let's check this rule with the first set: 13 (19) 12 13 + 12 = 25 and subtract 6 = 19. Can you check if this works for the second set? Now we can use the rule for the final set: 15 (?) 5 15 + 5 = 20 and then subtract 6 = 14. This makes the mystery middle number 14. Great job today, number detective! You are now able to identify mystery numbers using BODMAS ordered operations.
---- OR ----

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started