# Identify the Mystery Number using Multiple Number Operations

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.

 Pssstt!! Here's a handy hint to help you reach superstar status: look out 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 a number puzzle detective!

Look at the sets of numbers below:

72 (9) 9        54 (10) 6

How do the numbers outside the brackets work together, along with a secret invisible number, to make the middle numbers?

(Left number + right number) x 2

(Left number x right number) - 2

(Left number ÷ right number) + 1

(Left number ÷ right number) - 2

Look at the numbers below.

Which rule creates the number inside the brackets by using the two outside numbers? Check that the rule works for both sets of numbers.

8 (26) 9        7 (15) 4

(Left number x right number) + 2

(Left number ÷ right number) - 4

Left number + right number + right number again

Left number + right number + left number again

Look at the numbers below:

5 (20) 100        8 (3) 24

How do the numbers on the outside of the brackets work together to create the number on the inside of the brackets?

Left number ÷ right number

Right number ÷ left number

Left number + right number + 7

(Left number x right number) - 4

How are you getting on, number detective?

Which rule helps us make the middle numbers here?

5 (12) 4        7 (21) 11

(Left number x right number) + 3

Left number + right number + 3

Left number ÷ right number

Left number - right number - 4

Right detective, you're ready to work out some mystery numbers.

Look at the number sets below:

9 (84) 3        6 (40) 4

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

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

(Left number x right number) + 3

Left number + right number + 3

Left number ÷ right number

Left number - right number - 4

Look at the number sets below:

48 (15) 4        60 (9) 10

The rule here is 'left number ÷ right number + 3'.

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

(Left number x right number) + 3

Left number + right number + 3

Left number ÷ right number

Left number - right number - 4

Right detective, let's make things a bit more interesting.

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

7 (63) 9        12 (96) 8        11 (?) 12

132

23

1.09

122

Keep going, number detective - you're doing really well.

Look at the sets of numbers below:

Work out the rule to create the number on the inside of the brackets. Then use this rule to work out the mystery number in the third set.

3 (15) 6        4 (24) 10        9 (?) 15

24

6

39

135

Look at the numbers below:

21 (14) 3        16 (7) 5        30 (?) 4

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

120

34

26

22

Hooray! The last question, number detective! It's time to put all of your number puzzling skills to the test and solve one final number puzzle.

Look at the number sets below:

2 (32) 15        6 (30) 4        7 (?) 3

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

28

24

13

17

• Question 1

I need your help with a number puzzle detective!

Look at the sets of numbers below:

72 (9) 9        54 (10) 6

How do the numbers outside the brackets work together, along with a secret invisible number, to make the middle numbers?

(Left number ÷ right number) + 1
EDDIE SAYS
Hey detective! Did you find the rule here? With these rules, the section in brackets must be carried out first. This follows the rules of BODMAS (or you may know it as BIDMAS). The numbers on the left side of the brackets are divided by the numbers on the right side of the brackets, and then we add a secret invisible 1 to the answer. Let's look at the first number set: 72 (9) 9 72 ÷ 9 = 8 and if we add the extra 1, we get 9. Does it work for the second set too? 54 (10) 6 54 ÷ 6 = 9 and if we add the invisible 1 to the 9, we get 10. 10 is the middle number so we've cracked the rule! Make sure that the rule you select works for both sets of numbers.
• Question 2

Look at the numbers below.

Which rule creates the number inside the brackets by using the two outside numbers? Check that the rule works for both sets of numbers.

8 (26) 9        7 (15) 4

Left number + right number + right number again
EDDIE SAYS
I hope you've got your lefts and rights the right way round for this activity! We'll be using them a lot. The rule here is 'left number + right number + right number again'. Let's look at how this works in the first set: 8 (26) 9 8 (left number) + 9 (right number) + 9 (right number again) = 26. Can you see how this works with the second set of numbers too? Keep your eyes peeled for more rules. They rule!
• Question 3

Look at the numbers below:

5 (20) 100        8 (3) 24

How do the numbers on the outside of the brackets work together to create the number on the inside of the brackets?

Right number ÷ left number
EDDIE SAYS
Did you notice a relationship between the numbers on the outside of the brackets and the numbers on the inside here? The rule is 'right number ÷ left number'. Can you see how this works for the first set? 5 (20) 100 100 ÷ 5 = 20 I know that 10 ÷ 5 = 2 and this division fact helped me work out 100 ÷ 5. It also works for the second set: 8 (3) 24 24 ÷ 8 = 3
• Question 4

How are you getting on, number detective?

Which rule helps us make the middle numbers here?

5 (12) 4        7 (21) 11

Left number + right number + 3
EDDIE SAYS
Did you notice that the numbers on the inside of the brackets were bigger than the outside numbers? This is a clue that we are adding, multiplying or squaring. As the numbers aren't loads bigger this suggests that we are adding. Let's look at the first set: 5 (12) 4 5 + 4 = 9. How can we get from 9 to the middle number 12? 9 + 3 = 12. The rule could be 'left number + right number + 3'. Does it work for the second set? 7 (21) 11 7 + 11 = 18 and 18 + 3 = 21. Jackpot it works! It's now your turn to find some mystery numbers...
• Question 5

Right detective, you're ready to work out some mystery numbers.

Look at the number sets below:

9 (84) 3        6 (40) 4

The rule is 'left number squared + right 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 set of numbers? We need to square the number on the left side of the brackets. This means that we have to multiply it by itself. 5² = 25 Then we have to do 25 + the number on the right. 25 + 6 = 31 This makes 31 the mystery number.
• Question 6

Look at the number sets below:

48 (15) 4        60 (9) 10

The rule here is 'left number ÷ right number + 3'.

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

EDDIE SAYS
Did you follow the rule to get 8 here? 30 (left number) ÷ 6 (right number) = 5 5 + 3 = 8 This makes 8 the mystery number. It's time to face your next challenge...
• Question 7

Right detective, let's make things a bit more interesting.

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

7 (63) 9        12 (96) 8        11 (?) 12

132
EDDIE SAYS
In this type of question, we need to work out the rule for the first two sets of numbers first. The numbers in the middle of the brackets are quite a bit larger than the numbers on the outside. This is a clue that multiplication is involved. Let's look at the first set of numbers: 7 (63) 9 7 x 9 = 63 The rule could be 'left number x right number'. We need to check that it works for the second set too. 12 (96) 8 12 x 8 = 96 Jackpot! This rule works for both sets which means that we can use this rule to work out the mystery number: 11 (?) 12 11 x 12 = 132 This makes 132 the mystery number. It took a while but it's worth it to get the right answer!
• Question 8

Keep going, number detective - you're doing really well.

Look at the sets of numbers below:

Work out the rule to create the number on the inside of the brackets. Then use this rule to work out the mystery number in the third set.

3 (15) 6        4 (24) 10        9 (?) 15

39
EDDIE SAYS
Did you spot the rule here? The numbers in the middle of the brackets are bigger than the outside numbers. This means that we are adding or multiplying. Let's look at the first set: 3 (15) 6 3 + 6 = 9 How can we get from 9 to 15? We add another 6 (the right number). The rule could be 'left number + right number + right number again'. Does it work for the second set? 4 (24) 10 4 + 10 + 10 = 24 It works! Now let's use the rule 'left number + right number + right number again' to work out the mystery number: 9 (?) 15 9 + 15 + 15 = 39. The mystery number is 39. We did it!
• Question 9

Look at the numbers below:

21 (14) 3        16 (7) 5        30 (?) 4

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

22
EDDIE SAYS
Did you notice that the numbers inside the brackets were smaller than one of the numbers on the outside of the brackets? This is a clue that we're subtracting. The rule is 'left number - right number - 4'. Let's look at how this works for the first set: 21 (14) 3 21 - 3 = 18 and if we subtract the extra 4, we get 14. Can you see how this works for the second set of numbers too? Now we can use the rule to work out the mystery number: 30 (?) 4 30 - 4 = 26 and 26 - 4 = 22. This makes 22 the mystery number. One more number puzzle and then your mission is complete!
• Question 10

Hooray! The last question, number detective! It's time to put all of your number puzzling skills to the test and solve one final number puzzle.

Look at the number sets below:

2 (32) 15        6 (30) 4        7 (?) 3

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

28
EDDIE SAYS
We had multiplication in our rule here! The clue was that the numbers in the brackets were quite a lot bigger than the numbers on the outside. 2 (32) 15 2 x 15 = 30 and if we add the number on the left again (2) we get 32. So the rule could be 'left number x right number + left number'. Does it work for the second set? 6 (30) 4 6 x 4 = 24 and if we add the number on the left again (+6) we get 30. Now let's use this rule to work out the mystery number: 7 (?) 3 7 x 3 = 21 21 + 7 (left number) = 28. Well done and thank you for all of your excellent number puzzling skills in this activity! You have developed your ability to identify number patterns using multiple number operations, both basic and more advanced.
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