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

Using each of the numbers **0.1**, **0.5**, **3** and **6** once each, and with the four arithmetical operations available, can you arrive at the target answer of **7** in two different ways?

**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 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

Which three different numbers have a sum that is also on the list?

**The 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 THREE ways of making **51 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **8**, **9** and **10 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

2 3 5 7 11 13 17 19 23 29

#*PrimeNumbers*

**The Target Challenge**

Can you arrive at **51** by inserting **4**, **5**, **6** and **7** into the gaps on each line?

- (◯+◯)×◯+◯ = 51
- ◯²+(◯+◯)÷◯ = 51
- ◯×◯+◯+◯ = 51
- ◯×(◯+√◯)–◯ = 51
- (◯–◯)²×◯+◯ = 51

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

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