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

If you multiply a certain number by 3 and then add 30, the result is the same as if you firstly added 17 to this particular number and then multiplied by 2.

Which number in the range **1 to 9 **must this be?

**The**** 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 3rd & 7th rows contain the following fourteen numbers:

4 11 13 24 25 27 30 36 42 45 66 70 77 80

What is the product of the lowest number and highest number?

**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 TWO ways of making **47 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

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

8 16 24 32 40 48 56 64 72 80

#*8TimesTable*

**The Target Challenge**

Can you arrive at **47** by inserting **2**, **6**, **7** and **10** into the gaps on each line?

- ◯×◯+◯÷◯ = 47
- ◯²–(◯+◯)÷◯ = 47
- (◯+◯)²–(◯+◯) = 47

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

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