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

Using the numbers **2**, **3** and **3** once each, with + – × ÷ available, can you list the ELEVEN target answers from **1-20** that are mathematically possible to achieve?

**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 & 2nd rows of the playing board contain the following fourteen numbers:

2 8 9 14 15 17 22 28 40 48 55 63 64 72

From the list, what is the total of the factors of 28?

**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 SEVEN different ways to make **212 **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 FIVE numbers it is possible to make from the list below?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target ****Challeng****e**

Can you arrive at **212** by inserting **7**, **9**, **11** and **15** into the gaps on each line?

- ◯×◯+◯×◯ = 212
- ◯×double◯+◯–◯ = 212

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

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