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

What is the sum of the multiples of **0.5** in the range **10 to 20** inclusive?

**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 2nd & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

How many multiples of 3 are on the list?

**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 FOUR ways of making **83 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which is the ONLY number that 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 **83** by inserting **2**, **5**, **8** and **9** into the gaps on each line?

- (◯+◯)×◯–◯ = 83 (2 different ways)
- ◯²+◯×◯+◯ = 83
- ((◯+◯)²–√◯)÷◯ = 83

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

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