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

Using each of the numbers **1.5**, **2**, **2.5** and **3** once each, and with the four arithmetical operations + – × ÷ available, can you arrive at the target answer of **7** in three different ways?

**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 2nd & 4th rows of the playing board contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

List three different numbers that have a sum of 100.

**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 EIGHTEEN different ways to make **234 **when using *Lagrange’s Theorem*. How many of them can you find?

**The Mathematically Possible Challenge**

Using **2**, **4** and **8 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1 8 27 64 125

#*CubeNumbers*

**The Target Challenge**

Can you arrive at **234** by inserting **2**, **3**, **6**, **9** and **12** into the gaps on each line?

- (◯×(◯–◯)+◯)×◯ = 234
- (◯×◯÷◯+◯)×◯ = 234

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

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