**T**** he Main Challenge**

Your task is to arrive at the target numbers **66**, **77**, **88** and **99** by using the five numbers **1**,** 2**,** 3**,** 4 **and** 5** once in each calculation, and with + – × ÷ available.

**T****he**** 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid of 49 different numbers, ranging from **2 **up to **84**.

The 4th & 7th rows contain the following fourteen numbers:

3 4 10 11 24 27 30 32 35 44 54 60 70 77

What is a quarter of the highest multiple of 10?

**T****he Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every 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).

Show how you can make **181**, in EIGHT different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **6** and **12** once each, with + – × ÷ available, which are the FIVE target numbers it is possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target ****Challeng****e**

Can you arrive at **181** by inserting **8**, **9**, **10** and **11** into the gaps on each line?

- ◯×(◯+◯)+◯ = 181
- ◯×(◯+◯)–◯ = 181

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

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