**T**** h****e Main Challenge**

Your task is to make the target number of **10** by adding together five numbers. You are limited to using **1 to 5**, but these can be used any number of times in each sum.

One way to make 10 is 5+2+1+1+1 (or 52111); can you find 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 & 6th rows contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the sum of the multiples of 6?

**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 just TWO ways of making **120 **when using *Lagrange’s Theorem*. Can you find them both?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which THREE numbers are NOT 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 **120** by inserting **3**, **4**, **5** and **6** into the gaps on each line?

- (◯+√◯)×◯×◯ = 120
- (◯×◯)²×◯÷◯ = 120
- (double(◯+◯)²)×◯÷◯ = 120

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

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