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

What is the **7th** 2-digit whole number that is both a multiple of 5 AND contains the letter ‘F’ when written in English?

**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 3rd & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

How many pairs of numbers have a difference of 24?

**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 **29 **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?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challenge**

Can you arrive at **29** by inserting **2**, **3**, **4** and **5** into the gaps on each line?

- (◯+◯)×◯+◯ = 29 (there are two ways)
- ◯×◯×◯+◯ = 29
- ◯²+◯×◯–◯ = 29

**An****swers **can be found **here**.

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