**T**** he Main Challenge**

From the list of ten numbers below, find FOUR combinations that total **50**, where each combination must contain three different numbers.

The numbers are allowed to appear in more than one combination:

7 9 10 11 16 17 18 24 25 28

**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 & 4th rows of the playing board contain the following fourteen numbers:

3 10 13 25 32 35 36 42 44 45 54 60 66 80

What is the product of the two prime numbers listed?

**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 FIVE different ways to make **216 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **4**, **6** and **9 **once each, with + – × ÷ available, which are the only TWO numbers it is 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 **216** by inserting **3**, **6**, **8** and **9** into the gaps on each line?

- ◯×◯×(◯–◯) = 216
- (◯×◯+◯)×◯ = 216

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

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