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

Firstly, allocate each letter of the English alphabet a numerical value as follows, A=1 B=2 C=3 . . . Z=26. If the value of the word DOG is 26 by calculating 4+15+7, for example, which TWO of the following 3-letter words have the same value?

AXE AND BUT COT EAR MOP SAW TOP WOK ZOO

**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 & 4th rows contain the following fourteen numbers:

2 3 9 10 14 15 22 32 35 40 44 54 60 72

How many square numbers are present on the list?

**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 THREE ways of making **38 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

30 31 32 33 34 35 36 37 38 39

#*NumbersIn30s*

**The Target Challenge**

Can you arrive at **38** by inserting **4**, **6**, **8** and **10** into the gaps on each line?

- ◯×◯+◯–◯ = 38
- ◯²–◯²–◯+◯ = 38
- ◯²+◯+◯–◯ = 38

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

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