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

Simply add together the first seven positive square numbers and the first seven prime numbers. What is the total of these 14 numbers?

**T****he**** 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 4th & 7th rows contain the following fourteen numbers:

3 4 10 11 24 27 30 32 35 44 54 60 70 77

Which three numbers become square numbers when 5 is added to them?

**T****he Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every 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).

Show how you can make **183**, in SEVEN different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **6** and **12** once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

12 24 36 48 60 72 84 96 108 120

#*12TimesTable*

**The Target ****Challeng****e**

Can you arrive at **183** by inserting **1**, **5**, **8** and **14** into the gaps on each line?

- (◯+◯)×◯+◯ = 183
- half ((◯+◯)²+◯+half◯) = 183

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

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