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

Here’s a 10-step number trail involving all four arithmetical operations together with the numbers **1**, **2** and **3**.

Starting with **10**, carry out the following steps:

- add 2
- ×1
- ÷3
- –2
- multiply by 3
- +1
- subtract 3
- divide by 1
- ×2
- take away two

What is your final answer?

**Th****e**** 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 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

Find two separate pairs of numbers that each have a difference of 44.

**The 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** (4+1+1+1).

Show how you can make **158**, in SIX different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using the three digits **3**, **5** and **8** once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **158** by inserting **7**, **8**, **10** and **11** into the gaps below?

- ◯×◯+◯×◯ = 158

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

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