** Th****e**** Main Challenge**

When listing the first seven whole numbers, **above 20**, that are not multiples of 3, 5 or 7 or do not contain a 3, 5 or 7 as part of their number, what is the 7th number in your list?

**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

Can you find FIVE groups of three different numbers that each total 99?

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

**The Mathematically Possible Challenge**

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

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **30** by inserting **2**, **3**, **5** and **10** into the gaps on each line?

- ◯²+◯–(◯+◯) = 30
- ◯×√(◯×◯×◯) = 30
- (◯²+◯)×◯÷◯ = 30

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

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