**The Main Challenge**

Your task is to arrive at the target number of **47** by using all five numbers **1**, **2**, **3**, **4** and **5** exactly once each. Can you arrive at 47 in two different ways?

Remember, you have + – × ÷ available to use in both calculations.

**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 1st & 7th rows of the playing board contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

From the list, how many multiples of 8 are there?

**T****he 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 TWELVE different ways to make **226 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **2**, **4** and **8 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target Challenge**

Can you arrive at **226** by inserting **4**, **5**,** 6** and **7** into the gaps on each line?

- ◯×◯×◯+◯² = 226
- ◯²×double◯+double(◯+◯) = 226

**Answers **can be found **here**.

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