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

Carry out the following 15-step number trail – with no calculator!

Start with **20**, then:

+1 ÷3 ×5 –7 +2 ÷6 +4 –1 ×3 ÷4 +4 –5 ×1 +3 ×6 = **?**

What is your final answer?

**The**** 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 2nd & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

Which three different numbers have a sum of 100?

**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 SIX ways of making **81 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which TWO numbers are possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **81** by inserting **2**, **3**, **6** and **9** into the gaps on each line?

- ◯×◯×◯÷◯ = 81
- ◯²×◯×◯÷◯ = 81
- ◯²+◯×(◯+◯) = 81

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

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