** T****h****e Main Challenge**

What is the sum of the 50 integers (or whole numbers) from **1 through to 50** inclusive?

**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 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the sum of the factors of 24 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 only TWO ways of making **16 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **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 **16** by inserting **3,** **4**, **6** and **8** into the gaps on each line?

- ◯×◯×◯÷◯ = 16
- ◯²–◯×(◯–◯) = 16
- ◯÷◯×³√◯×◯ = 16

**Ans****wers **can be found **here**.

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