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

Your task is to arrive at the target number of **20** by adding together five numbers. You are limited to using digits **1 to 5** but these can be used any number of times in each calculation.

One way of making 20 is 4+4+4+4+4 (but you can write your answer as 44444 to save time). Can you list the other FIVE ways?

**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

What is the sum of the multiples of 7?

**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 TWO ways of making **31 **when using *Lagrange’s Theorem*. Can you find them both?

**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?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **31** by inserting **1**, **5**, **6** and **6** into the gaps on each line?

- ◯×◯–◯×◯ = 31
- ◯²÷◯+◯²÷◯ = 31
- (◯÷◯+◯)×◯ = 31

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

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