** The Mai****n Challenge**

Using seven 7’s (7 7 7 7 7 7 and 7) once each, with + – × ÷ available, it is possible to make various target answers, such as **7** as shown here:

- 7+7+7+7–7–7–7 =
**7**, or perhaps - 7×(7÷7)×(7÷7)×(7÷7) =
**7**

In a similar way, show how to make the target answers **1**, **2** and **3**.

**The 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 3rd & 4th rows contain the following fourteen numbers:

3 10 13 25 32 35 36 42 44 45 54 60 66 80

What is the sum of the multiples of 4?

**The Roll3Dice Challenge**

From six of the seven groups of numbers below, it is possible to make today’s target number of **10 **when each number in the group is used once and + – × ÷ is available:

- 1 1 6
- 1 2 6
- 1 5 5
- 2 2 3
- 2 4 5
- 3 5 5
- 4 5 6

Which is the only group that CANNOT make **10**?

**The Mathematically Possible Challenge**

Using **4**, **5** and **10 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target Challenge**

Can you arrive at **10** by inserting **2**, **2**, **3** and **5** into the gaps on each line?

- (◯–◯)×◯×◯ = 10
- (◯–◯÷◯)×◯ = 10
- (◯²–◯–◯)÷◯ = 10
- ◯÷(◯–◯÷◯) = 10

**A****nswers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**