**The Main Challenge**

One simple rule – multiply two numbers together, then either add or subtract the third number to achieve your target number of **10**. The three numbers used in each calculation must be unique digits from **2-9**.

As an example, one such way of arriving at 10 is by (4×3)–2. Can you find the FIVE other ways of making **10** using this rule?

[Note: (4×3)–2 = 10 and (3×4)–2 = 10 would count as just one way!]

**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 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

What is the sum of the multiples of 8?

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every positive integer can be made by adding up to four square numbers.

For example, **7** can be made by **2²+1²+1²+1²** (or 4+1+1+1).

There are THREE ways of making **25 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

50 51 52 53 54 55 56 57 58 59

#*NumbersIn50s*

**The Target Challenge**

Can you arrive at **25** by inserting **2**, **5**, **10** and **20** into the gaps on each line?

- ◯²×◯×◯÷◯ = 25
- ◯+◯+◯÷◯ = 25
- ◯÷◯×(◯–◯) = 25

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

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