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

If you add **1+4**, then to that answer add **9**, then keep on adding consecutive square numbers to the previous total, what is the first answer you reach that is **greater than 200**?

(Hint: Square numbers are **1** (1×1), **4** (2×2), **9** (3×3) … and so on.)

**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

What is the sum of the factors of 30 listed above?

**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 **37 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

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

2 3 5 7 11 13 17 19 23 29

#*PrimeNumbers*

**The Target Challenge**

Can you arrive at **37** by inserting **1**, **3**, **5** and **7** into the gaps on each line?

- ◯×◯+◯–◯ = 37
- (◯+◯)×◯+◯ = 37
- (◯+◯)×◯–◯ = 37
- ◯²–◯×(◯–◯) = 37
- ◯²+◯×(◯–◯) = 37

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

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