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

Read the following facts to work out my numerical value:

- I am a single digit number,
- If you add 6 to me I become a 2-digit number,
- I am an odd number,
- I am not a square number,
- I am a factor of 30.

**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

What is the difference between the highest prime number and the highest odd number?

**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 SEVEN ways of making **134 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **3**, **6** and **10 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **134** by inserting **2**, **3**, **5** and **6** into the gaps on each line?

- ◯³+◯×◯÷◯ = 134
- (◯+◯)²+◯²+◯² = 134

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

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