# Work Out 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.

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: 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!

Look at the groups of numbers below:

5 (33) 7        6 (22) 4

How do the outside numbers of each set work together, along with an extra top secret number, to make the middle numbers?

Click on the correct rule below.

(Left number + right number) x 2

(Left number x right number) - 2

Left number + right number + 4

Left number - right number - 3

Look at the numbers below.

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

5 (22) 12        8 (25) 9

Check that the rule works for both sets of numbers.

(Left number x right number) + 2

Left number + right number + right number again

Left number + right number + left number again

Left number - right number - 3

Look at the numbers below:

53 (33) 20        19 (11) 8

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

Left number x right number + 1

Left number ÷ right number - 3

Left number - right number

Left number - right number - 4

How are you getting on so far, number detective?

Which rule helps us make the middle numbers here?

15 (8) 4        45 (32) 10

Left number x right number

Left number - right number + 4

Left number ÷ right number

Left number - right number - 3

Right detective, you seem ready to work out some mystery numbers now.

Look at the number sets below:

27 (2) 9        64 (7) 8

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

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

Left number x right number

Left number - right number + 4

Left number ÷ right number

Left number - right number - 3

Look at the number sets below:

19 (27) 4        10 (32) 11

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

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

Left number x right number

Left number - right number + 4

Left number ÷ right number

Left number - right number - 3

OK detective, it's time to make things a bit more challenging...

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

5 (21) 4        3 (28) 9        6 (?) 3

19

17

10

2

Look at the sets of numbers below.

Work out the rule to make the number 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.

3 (14) 8        7 (21) 11        10 (?) 12

123

19

25

117

Look at the numbers below:

3 (10) 4        10 (26) 6        5 (?) 8

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.

35

1

45

18

Well, number detective, it's time to put all of your new skills to the test and solve one final number puzzle.

Look at the number sets below:

4 (5) 12        3 (9) 21        5 (?) 25

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

7

3

127

123

• Question 1

Look at the groups of numbers below:

5 (33) 7        6 (22) 4

How do the outside numbers of each set work together, along with an extra top secret number, to make the middle numbers?

Click on the correct rule below.

(Left number x right number) - 2
EDDIE SAYS
Hey detective! Did you spot the rule here? The numbers on the left side of the brackets multiply by the numbers on the right side of the brackets, and then we take away the mystery number 2. This gives us the answers in the middle of the brackets. Let's look at the first number set: 5 (33) 7 5 x 7 = 35 and then if we subtract the mystery 2, we get 33. Let's check that it works for the second set: 6 (22) 4 6 x 4 = 24 and then subtract the extra 2 to give us 22. Try out all of the options until you find one that works for both sets.
• Question 2

Look at the numbers below.

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

5 (22) 12        8 (25) 9

Check that the rule works for both sets of numbers.

Left number + right number + left number again
EDDIE SAYS
Did you try out all of the rules until you came across the right one here? Let's look at the first set of numbers: 5 (22) 12 The number in the middle is bigger, so we are probably adding or multiplying. Multiplying would give us too big a number, so let's try adding. 5 + 12 = 17 and to get to 22 we add an extra 5 (this is the same as the left number). The rule could be 'left number + right number + left number'. Let's see if it works for the second set: 8 (25) 9 8 + 9 = 17 and if we add an extra 8 we get 25. We've found the rule! Prepare yourself to workout more rules. They rule!
• Question 3

Look at the numbers below:

53 (33) 20        19 (11) 8

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
EDDIE SAYS
The clue here is that the number inside the brackets is smaller than one of the numbers on the outside. This means that we are probably subtracting or dividing. Looking at the first set, 53 is a prime number so it's unlikely to be division as we can only divide 53 by 53 or 1. 53 (33) 20 53 - 20 = 33 The rule could be simply 'left number - right number'. Does it work for the second set? 19 - 8 = 11. Jackpot it works!
• Question 4

How are you getting on so far, number detective?

Which rule helps us make the middle numbers here?

15 (8) 4        45 (32) 10

Left number - right number - 3
EDDIE SAYS
Did you notice that the numbers inside the brackets were smaller than one of the outside numbers? This is our clue to subtraction or division. If we look at the first set: 15 (8) 4. I can't do 15 ÷ 4 so let's try subtraction. 15 - 4 = 11 and if we subtract the mystery number of 3 we get 8. The rule could be 'left number - right number - 3' Let's try it for the second set: 45 - 10 = 35 and subtract an extra 3 = 32. We found the rule! It's now your turn to find some mystery numbers...
• Question 5

Right detective, you seem ready to work out some mystery numbers now.

Look at the number sets below:

27 (2) 9        64 (7) 8

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

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 36 (left number) ÷ 4 (right number) = 9 and then subtract 1 = 8. This makes 8 the missing number. How good are you at following rules? It's very important here!
• Question 6

Look at the number sets below:

19 (27) 4        10 (32) 11

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

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

EDDIE SAYS
Did you follow the rule to get 19 here? 7 (left number) + 6 (right number) + 6 (right number again) = 19 (mystery middle number). I think you're ready for your next challenge...
• Question 7

OK detective, it's time to make things a bit more challenging...

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

5 (21) 4        3 (28) 9        6 (?) 3

19
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 larger than the numbers on the outside. This is a clue that we are adding or multiplying. Let's look at the first set: 5 (21)4 5 x 4 = 20 and if we add a mystery number of 1 to this we get 21. The rule could be 'left number x right number + 1' but we need to check that it works for both sets of numbers: 3 (28) 9 3 x 9 = 27 and if we add the extra 1 we get 28. Yes! The rule works for both sets, which means we can now use the rule to work out the mystery number: 6 (?) 3 6 x 3 = 18 and add the extra 1 to get 19. This makes 19 the mystery number. It's a long process, but it's worth it!
• Question 8

Look at the sets of numbers below.

Work out the rule to make the number 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.

3 (14) 8        7 (21) 11        10 (?) 12

25
EDDIE SAYS
Did you notice 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 (14) 8 The number in the middle isn't LOADS bigger, so we are probably adding. 3 + 8 = 11 and then if we add an invisible number 3 we get 14. The rule could be 'left number + right number + 3' so let's try this for the second set: 7 (21) 11 7 + 11 = 18 and then we add the invisible 3 to get 21. As the rule works for both sets, we can work out the mystery number: 10 (?) 12 10 + 12 = 22 and if we add the invisible 3 we get 25. This makes the mystery number 25. We did it! It's a good feeling when it works.
• Question 9

Look at the numbers below:

3 (10) 4        10 (26) 6        5 (?) 8

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.

18
EDDIE SAYS
Did you spot the rule here, detective? The rule was 'left number + right number + left number again'. Can you see how this works with the first two sets? 3 + 4 + 3 = 10 10 + 6 + 10 = 26 Let's do this for the final set: 5 + 8 + 5 = 18. This makes 18 the missing number. One more number puzzle and then your mission is complete!
• Question 10

Well, number detective, it's time to put all of your new skills to the test and solve one final number puzzle.

Look at the number sets below:

4 (5) 12        3 (9) 21        5 (?) 25

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

7
EDDIE SAYS
We had division in our rule here! The clue was that the number on the left goes perfectly into the number on the right. 4 (5) 12 12 ÷ 4 = 3 and if we add an invisible 2, we get 5. The rule could be 'right number ÷ left number then + 2' Let's try this for the second set: 21 ÷ 3 = 7 and then + 2 to get 9. It works! We can now use this same rule to work out the mystery number: 5 (?) 25. 25 ÷ 5 = 5 and if we add the invisible 2 we get 7. This makes the mystery number 7! Well done for using your awesome number puzzle skills, detective! You didn't give up. You should now feel confident when asked to workout mystery numbers using basic operations and more advanced operations.
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