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

By allocating each letter of the English alphabet a numerical value as follows, A=1 B=2 C=3 . . . Z=26, the value of the word CAT would be 24, calculated by doing 3+1+20.

Following this rule, what is the value of the word **ARITHMETIC**?

**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

Find three pairs of numbers that have a sum of 54.

**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 just TWO ways of making **39 **when using *Lagrange’s Theorem*. Can you find them both?

**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?

60 61 62 63 64 65 66 67 68 69

#*NumbersIn60s*

**The Target Challenge**

Can you arrive at **39** by inserting **1**, **3**, **6** and **7** into the gaps on each line?

- (◯+◯)×◯×◯ = 39
- ◯²–(◯+◯+◯) = 39
- (◯–◯)×◯+◯ = 39

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

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