** The Main Challenge**

Here is an introductory **Mathelona** challenge taken from the front cover of Volume 1 of my pocket book series.

◯ + ◯ = 3 = ◯ – ◯

◯ + ◯ = 4 = ◯ × ◯

◯ + ◯ = 5 = ◯ ÷ ◯

Can you insert the digits **1 1 1 1 2 2 2 3 3 4 5** and **6** into the 12 gaps above so all three lines work out arithmetically?

**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 & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

What is the sum of the odd numbers listed above?

**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 **28 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **28** by inserting **2**, **4**, **6** and **8** into the gaps on each line?

- ◯×◯+◯–◯ = 28
- ◯×◯÷◯+◯ = 28
- ◯×◯+◯×√◯ = 28
- ◯×◯+◯÷◯ = 28
- (◯+◯)×◯–◯ = 28
- (◯+◯)×◯÷◯ = 28
- (◯+◯)×◯+◯ = 28

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

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