Use 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!

Now it's over to you, to hunt down those missing numbers!

Welcome to another activity, number detective!

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.

6 (45) 7        3 (39) 12        8 (?) 11

What is the mystery number?

80

88

90

91

93

Look at the numbers below.

3 (28) 5        9 (109) 10        6 (?) 7

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

51

52

53

54

55

Look at the numbers below.

10 (23) 3        6 (21) 9        2 (?) 5

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

8

9

10

11

12

Look at the brackets below.

6 (46) 20        3 (19) 8        7 (?) 10

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

25

26

27

28

29

You're halfway through this activity, number detective!

Look at the numbers below:

10 (21) 5        4 (17) 7        16 (?) 4

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

23

22

25

21

26

Look at the numbers below.

5 (53) 10        6 (21) 3        7 (?) 4

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.

28

29

30

31

32

Look at the numbers below.

7 (32) 5        10 (14) 2        6 (?) 8

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.

71

70

72

75

69

Look at the numbers below.

5 (8) 60        7 (4) 56        10 (?) 100

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.

6

5

7

4

9

Look at the numbers below.

66 (23) 10        24 (4) 8        90 (?) 7

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

It's time for your last challenge, number detective!

Look at the numbers below.

3 (49) 4        7 (121) 4        6 (?) 3

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.

80

81

100

82

76

• Question 1

Welcome to another activity, number detective!

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.

6 (45) 7        3 (39) 12        8 (?) 11

What is the mystery number?

91
EDDIE SAYS
Hey detective! In questions like this, we need to work out the rule for the first two sets of numbers and then use this rule to work out the mystery number in the final set. Let's look at the first set of numbers: 6 (45) 7 The number in the middle is quite a lot bigger than the outside numbers. This is a clue that we are multiplying. 6 x 7 = 42 and if we add an invisible number of 3, we get 45. The rule could be 'left number x right number + 3'. We need to check that this works for the second number set. 3 (39) 12 3 x 12 = 36 and if we add the invisible 3 we get 39 which matches the middle number in this set. Jackpot, our rule works! Now that we have the rule for the first two sets of numbers, we can use this rule to work out the mystery number in the final set. 8 (?) 11 8 x 11 = 88 and then add the extra 3 to get 91. Therefore 91 is our mystery number.
• Question 2

Look at the numbers below.

3 (28) 5        9 (109) 10        6 (?) 7

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

55
EDDIE SAYS
Did you spot the rule here? The numbers in brackets are quite a lot bigger than the outside numbers. This is a clue that we're multiplying or squaring numbers. Let's look at the first set: 3 (28) 5 5² = 25 and if we add the 3, we get 28. The rule could be 'right number squared + left number'. Let's check if this works for the second set: 9 (109) 10 10² (left number) + 9 = 109 (middle number) The rule works! Now we can use this to work out the mystery number: 6 (?) 7 7² (49) + 6 = 55 55 is our mystery number. Are you getting the hang of this now?
• Question 3

Look at the numbers below.

10 (23) 3        6 (21) 9        2 (?) 5

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

9
EDDIE SAYS
Did you notice a relationship between the numbers here? The numbers in the middle of the brackets are bigger than the outside numbers but not loads bigger, which means we are probably adding, rather than multiplying. Let's look at the first set: 10 (23) 3 10 + 3 = 13 and if we add another 10 (which is the number on the left) to 13 we get 23. The rule could be 'left number + right number + left number' so let's try it out for the next set of numbers: 6 (21) 9 6 + 9 = 15 and if we add another six (left number) we get 15. Result! We cracked the rule. Now we can use it to work out the mystery number. 2 (?) 5 2 (left number) + 5 (right number) + 2 (left number) = 9 This makes 9 the mystery number.
• Question 4

Look at the brackets below.

6 (46) 20        3 (19) 8        7 (?) 10

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

27
EDDIE SAYS
Can you see a pattern here? This was a bit like the last question as we had to use one of the numbers twice. The rule was 'left number + right number + right number'. Let's look at how this works for the first number set: 6 (46) 20 6 + 20 + 20 = 46 Can you check that it works for the second group of numbers? Now we know that it works for both number sets, we can work out the mystery number. 7 (?) 10 7 + 10 + 10 = 27 Are you getting the hang of this now, detective?
• Question 5

You're halfway through this activity, number detective!

Look at the numbers below:

10 (21) 5        4 (17) 7        16 (?) 4

Work out how the numbers in brackets are related to the outside numbers and use this rule to work out the mystery number.

26
EDDIE SAYS
We had a sneaky invisible number involved in our rule here! The rule was 'left number + right number + 6'. Let's look at how this works for the first set of numbers: 10 (21) 5 10 + 5 + 6 = 21 This also works for the second set. Can you see how? Now, we need to use this rule to work out the mystery number: 16 (?) 4 16 (left number) + 4 (right number) + 6 = 26 This makes the mystery number 26! I hope you've got your lefts and rights right!
• Question 6

Look at the numbers below.

5 (53) 10        6 (21) 3        7 (?) 4

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.

31
EDDIE SAYS
Here, the numbers in brackets are a fair bit bigger than the numbers outside the brackets. This is a clue that there is squaring or multiplication involved. Let's look at the first set: 5 (53) 10 5 x 10 = 50 and how do we get to 53 from here? We add an invisible 3. The rule could be 'left number x right number + 3' Does it work for the second set? 6 x 3 = 18 and add the invisible 3 = 21. Now we know it works for both sets, we can work out the mystery number. 7 (?) 4 7 x 4 = 28 + 3 = 31 This makes our mystery number 31.
• Question 7

Look at the numbers below.

7 (32) 5        10 (14) 2        6 (?) 8

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.

70
EDDIE SAYS
This number relationship involved squaring. I do like my square numbers! Can you see which number in each set has been squared? 7 (32) 5 At first, you might have thought we were multiplying the numbers as 7 x 5 = 35. This pattern doesn't work with the next set of numbers though. We have to find a rule that works for both sets. 5² = 25 and if we + 7 (left number) we get 32. The rule could be 'right number squared + left number'. Does it work for the next set? 10 (14) 2 2² = 4 and + 10 = 14 Yes, it works! Now we can work out the mystery number. 6 (?) 8 8² = 64 and + 6 = 70 This means 70 is our mystery number.
• Question 8

Look at the numbers below.

5 (8) 60        7 (4) 56        10 (?) 100

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.

6
EDDIE SAYS
Did you spot division in the relationship here, detective? The rule is 'right number ÷ left number - 4'. Let's take a look at the first set of numbers: 5 (8) 60 60 ÷ 5 = 12 and 12 - 4 is 8. Does it work for the second set? 7 (4) 56 56 (right number) ÷ 7 (left number) = 8 and 8 - 4 = 4. Yes, it works! Now we can work out the mystery number: 10 (?) 100 100 ÷ 10 = 10 and 10 - 4 = 6. This makes 6 our mystery number.
• Question 9

Look at the numbers below.

66 (23) 10        24 (4) 8        90 (?) 7

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.

38
EDDIE SAYS
Now this was a challenge! We had to halve one of the numbers first. Can you see which number we might have to halve? 66 (23) 10 Half of 66 = 33. How can we get from 33 to the inside number of 23? We subtract 10 (the number on the right). The rule could be 'half the left number then subtract the right number'. Does it work for the second set? 24 (4) 8 Half of 24 = 12 and subtract 8 = 4. It works! Now we can work out the mystery number. 90 (?) 7 Half of 90 = 45 and subtract 7 = 38. 38 is our mystery number. Did you find that one hard? You're not alone - it was a tricky one!
• Question 10

It's time for your last challenge, number detective!

Look at the numbers below.

3 (49) 4        7 (121) 4        6 (?) 3

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.

81
EDDIE SAYS
Hey detective! Did you spot the relationship in your final mission? Did you notice that the numbers inside the brackets are both square numbers? This is a clue! The rule is '(left number + right number)²' This means that we add the left and right numbers together and square whatever the answer is. Let's look at the first set: 3 (49) 4 3 + 4 = 7 and 7² = 49 It works for the second set too: 7 (121) 4 7 + 4 = 11 and 11² = 121 Let's work out the mystery number in the final set: 6 (?) 3 6 + 3 = 9 and 9² = 81 81 is our mystery number! Excellent work on this number puzzle activity, detective! I knew I could count on you to spot patterns. You have developed your ability to spot relationships between numbers and then use this to identify the hidden mystery number.
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