**Th****e Main Challenge**

Apart from 9+5+1, find the SEVEN other ways you can make **15** when combining and adding together three unique digits from **1-9**.

**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 5th & 7th rows contain the following fourteen numbers:

4 6 7 11 16 21 24 27 30 50 70 77 81 84

Which two pairs of numbers both have a difference of 11?

**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 is just ONE way of making **32 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

8 16 24 32 40 48 56 64 72 80

#*8TimesTable*

**The Target Challenge**

Can you arrive at **32** by inserting **2**, **4**, **7** and **8** into the gaps on each line?

- ◯×◯+◯÷◯ = 32
- ◯×◯÷◯+◯ = 32
- (◯+◯)²÷◯+◯ = 32

**An****swers **can be found **here**.

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