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

Using the numbers **3**, **6** and **10** once in each calculation, together with addition and subtraction, find the only FOUR numbers from **1-30** that are mathematically possible to achieve.

**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 & 3rd rows of the playing board contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

What is the sum of the multiples of 7 listed above?

**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 TEN different ways to make **201 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **5**, **7** and **11 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

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

Can you arrive at **201** by inserting **3**, **5**, **8** and **9** into the gaps on each line?

- (◯×◯–◯)×◯ = 201
- (◯+◯)²+◯–◯ = 201

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

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