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 **5²** (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: **3²** 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!