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

What is the biggest integer (whole number) less than 630,000 that can be written using all six digits from **1 to 6**?

**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

From the list, find three different numbers that have a sum of 100.

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

**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?

9 18 27 36 45 54 63 72 81 90

#*9TimesTables*

**The Target Challenge**

Can you arrive at **48** by inserting **4**, **4**, **5** and **8** into the gaps on each line?

- ◯×◯+◯+◯ = 48
- ◯×◯×(◯–◯) = 48
- ◯²+◯–(◯×◯) = 48

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

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