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

You’ve rolled the numbers **1**, **3** and **3** with three dice. Using these once each, with + – × ÷ available, find the TWO target numbers from **1-10** that it is NOT possible to make.

**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 5th & 6th rows of the playing board contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the sum of the multiples of 5 on the list?

**T****he 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 ELEVEN different ways to make **222 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **4**, **6** and **9 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

2 4 6 8 10 12 14 16 18 20

#*EvenNumbers*

**The Target Challenge**

Can you arrive at **222** by inserting **3**, **5**, **6** and **8** into the gaps on each line?

- (◯×◯–◯)×◯ = 222
- ◯³+◯+◯–◯ = 222

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

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