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

What is the lowest Prime Number total it is possible to achieve when adding together SEVEN unique non-Prime Numbers?

**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 of the playing board 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 40?

**T****he 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 just THREE different ways to make **248 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **5** and **10 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

2 4 6 8 10 12 14 16 18 20

#*EvenNumbers*

**The Target**** Challenge**

Can you arrive at **248** by inserting **5**, **7**, **8**, **10** and **12** into the gaps below?

- ◯³+√(◯+◯+◯)–◯² = 248

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

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