# Identify Number Relationships to Find the Mystery Number

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!

Hey there detective! We need your help to solve these number puzzles.

In this question, the three numbers in each group are related in some way.

Work out the rule that creates the middle numbers by using the outside numbers and use this rule to work out the mystery number in the final set.

4 (18) 10       20 (48) 8      19 (?) 7

43

44

45

46

47

Look at the numbers below.

3 (90) 9       5 (146) 11          6 (?) 4

Work out the relationship between the numbers in the first two sets.

Then, use this rule to work out the mystery number in the final set.

51

52

53

54

55

Look at the numbers below.

8 (27) 1        2 (21) 5        5 (?) 6

Work out the relationship between the numbers in the first two sets.

Then, use this rule to work out the mystery number in the final set.

30

33

36

39

42

Look at the numbers below.

21 (22) 65        45 (25) 95        16 (?) 58

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

19

20

21

22

23

You're halfway there, number detective!

Look at the numbers below.

56 (32) 24        93 (55) 38        72 (?) 40

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

22

32

42

52

62

Look at the numbers below.

30 (48) 9        12 (42) 15        14 (?) 13

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

37

38

39

40

41

Look at the numbers below.

3 (13) 4          6 (43) 7          9 (?) 10

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

91

81

85

95

92

Look at the numbers below.

10 (9) 50        8 (12) 64        6 (?) 72

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

13

14

15

16

17

Look at the numbers below.

9 (18) 4        6 (15) 5        4 (?) 12

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

21

22

23

24

25

It's now time for your final number puzzle mission.

Look at the numbers below.

8 (44) 3        3 (20) 2        7 (?) 1

Work out the relationship between the numbers on the outside of the brackets and the numbers on the inside of the brackets.

Use this relationship to work out the mystery number.

32

36

40

44

48

• Question 1

Hey there detective! We need your help to solve these number puzzles.

In this question, the three numbers in each group are related in some way.

Work out the rule that creates the middle numbers by using the outside numbers and use this rule to work out the mystery number in the final set.

4 (18) 10       20 (48) 8      19 (?) 7

45
EDDIE SAYS
Hey detective! I hope you've got your number puzzle hat on. Here, we had to find a way to make the number inside the brackets by using the two numbers either side. Sometimes we might square one of the numbers, use an extra invisible number or use one of the numbers twice. Let's look at the first set of numbers: 4 (18) 10 The number in the middle is bigger than the outside numbers so we are likely to be adding or multiplying. 4 + 10 = 14 and if we add the number 4 again, we get 18. The rule could be 'left number + right number + left number'. Let's see if it works for the second set. 20 (48) 8 20 (left number) + 8 (right number) + 20 (left number) = 48 (middle number). It works! Now we can work out the mystery number. 19 + 7 + 19 = 45 45 is our mystery number!
• Question 2

Look at the numbers below.

3 (90) 9       5 (146) 11          6 (?) 4

Work out the relationship between the numbers in the first two sets.

Then, use this rule to work out the mystery number in the final set.

52
EDDIE SAYS
We had squaring in our rules here. The rule is 'left number squared + right number squared'. Let's look at how this works for the first set: 3 (90) 9 3² (9) + 9² (81) = 90 The rule must work for the second set before we use it to find the mystery number. 5 (146) 11 5² (25) + 11² (121) = 146 It works for both sets so now we can work out the mystery number. 6 (?) 4 6² (36) + 4² (16) = 52 This makes 52 the mystery number.
• Question 3

Look at the numbers below.

8 (27) 1        2 (21) 5        5 (?) 6

Work out the relationship between the numbers in the first two sets.

Then, use this rule to work out the mystery number in the final set.

33
EDDIE SAYS
Did you notice that both of the numbers inside the brackets are in the three times table? This could be a clue... Let's look at the first set of numbers: 8 (27) 1 How many 3s go into 27? There are nine 3s in 27 and can we make 9 with the outside numbers? Yes we can, 8 + 1 = 9. This means that the rule could be '(left number + right number) x 3'. We have to do the part of the rule in brackets first. Let's try out this rule with the second set: 2 (21) 5 2 (left number) + 5 (right number) = 7 and 7 x 3 = 21. We've found the rule! Now we can work out the mystery number. 5 (?) 6 5 + 6 = 11 and 11 x 3 = 33 33 is our mystery number.
• Question 4

Look at the numbers below.

21 (22) 65        45 (25) 95        16 (?) 58

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

21
EDDIE SAYS
Did you spot the relationship here, detective? The numbers inside the brackets are smaller than at least one of the outside numbers. This is a clue that we could be subtracting or dividing. Let's look at the first set: 21 (22) 65 65 (right number) - 21 (left number) = 44 How can we get from 44 to the middle number 22? Half of 44 is 22. This means that the rule could be '(right number - left number) ÷ 2' Let's try it out with the second set of numbers: 45 (25) 95 95 (right number) - 45 (left number) = 50 and 50 ÷ 2 = 25 (the middle number). Now that we know the rule works for both sets, we can work out the mystery number in the final set. 16 (?) 58 58 - 16 = 42 and 42 ÷ 2 = 21. This makes 21 the mystery number.
• Question 5

You're halfway there, number detective!

Look at the numbers below.

56 (32) 24        93 (55) 38        72 (?) 40

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

32
EDDIE SAYS
Did you notice that we were subtracting here? The rule here is 'left number - right number' and there weren't any sneaky invisible numbers this time! Let's follow this rule for the final set of numbers: 72 (left number) - 40 (right number) = 32 The mystery number is 32.
• Question 6

Look at the numbers below.

30 (48) 9        12 (42) 15        14 (?) 13

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

40
EDDIE SAYS
Did you spot the relationship here? The numbers inside the brackets are bigger than the numbers on the outside. This is a clue that we are adding, multiplying or squaring. Let's try adding first, as the numbers aren't loads bigger. 30 (48) 9 30 + 9 = 39. If we add another lot of 9 to 39 we get 48. The rule could be 'left number + right number + right number'. Does it work with the second set? 12 (42) 15 12 (left number) + 15 (right number) + 15 (right number) = 42. The rule works! Now let's work out the mystery number: 14 (?) 13 14 + 13 + 13 = 40 We found the missing number! Nice work detective!
• Question 7

Look at the numbers below.

3 (13) 4          6 (43) 7          9 (?) 10

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

91
EDDIE SAYS
You may have tried multiplying or adding first here. Remember if your rule doesn't work for both sets of numbers, you'll need to find another rule. This rule involved squaring. It was 'left number squared + right number'. Can you see how this works for the first number set? 3 (13) 4 3² + 4 = 13 This also works for the second set so now we can work out the mystery number. 9 (?) 10 9² (81) + 10 = 91. It helps to know your squared numbers off by heart for these questions as it speeds things up.
• Question 8

Look at the numbers below.

10 (9) 50        8 (12) 64        6 (?) 72

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

16
EDDIE SAYS
Did you notice that the number on the left of each set of brackets goes perfectly into the number on the right? We call these numbers 'factors'. This is a clue that we are dividing. Let's look at the first set: 10 (9) 50 50 ÷ 10 = 5. How can we get to the middle number 9 from 5? We add 4. The rule could be '(right number ÷ left number) + 4' Does it work for the second set? 8 (12) 64 64 ÷ 8 = 8 and 8 + 4 = 12. Yay! The rule works for both sets so now we can work out the mystery number. 6 (?) 72 72 ÷ 6 = 12 and 12 + 4 = 16. The mystery number is 16.
• Question 9

Look at the numbers below.

9 (18) 4        6 (15) 5        4 (?) 12

Work out the relationship between the numbers in the first two sets.

Use this rule to work out the mystery number in the final set.

24
EDDIE SAYS
The numbers in brackets are bigger than the outside numbers here so let's try multiplying. 9 (18) 4 9 x 4 = 36 36 seems way too big! But what happens if we halve 36? We get 18! So the rule could be '(left number x right number) ÷ 2', as dividing by 2 is the same as halving. Does this work with the second set? 6 (15) 5 6 x 5 = 30 and 30 ÷ 2 = 15 Yippee! The rule works. It's a good feeling isn't it? Now let's work out the mystery number. 4 (?) 12 4 x 12 = 48 and 48 ÷ 2 = 24. 24 is our mystery number.
• Question 10

It's now time for your final number puzzle mission.

Look at the numbers below.

8 (44) 3        3 (20) 2        7 (?) 1

Work out the relationship between the numbers on the outside of the brackets and the numbers on the inside of the brackets.

Use this relationship to work out the mystery number.

32
EDDIE SAYS
Hey detective! Did you notice that the numbers inside the brackets are in the 4 times table? This is a clue... 8 (44) 3 How many 4s are in 44? There are 11 and can we make 11 with the two outside numbers? Yes we can! 8 + 3 = 11 The rule could be '(left number + right number) x 4' Does it work for the second set? 3 (20) 2 3 + 2 = 5 and 5 x 4 = 20. The rule works! Now let's work out the mystery number: 7 (?) 1 7 + 1 = 8 and 8 x 4 = 32. We found the mystery number- fantastic focus detective! You should now feel confident when asked to identify relationships between numbers in order to find a missing value.
---- OR ----