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

If the number sequence **2**, **5**, **8**, **11**, **14** . . . is continued, which is the ONLY number from the following list that will appear later in the sequence?

22 34 43 57 65 72 85 99

**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 & 6th rows contain the following fourteen numbers:

5 8 12 17 18 20 28 33 48 49 55 56 63 64

What is the difference between the sum of the odd numbers and the sum of the even numbers?

**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 TWO ways of making **44 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **8**, **9** and **10 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challenge**

Can you arrive at **44** by inserting **2**, **4**, **6** and **7** into the gaps on each line?

- (◯+◯)×(◯–◯) = 44
- ◯²–(◯+◯)÷◯ = 44
- (◯×◯–◯)×◯ = 44
- ◯²+(◯–◯)×◯ = 44

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

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