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

You have SIX each of **7puzzleland**‘s brand-new **4p** and **7p** coins. Your task is to try and make various amounts from 20p and above with these coins.

As shown here, the first few have been done for you:

**20p**can be made from 5 × 4p coins,**21p**from 3 × 7p coins,**22p**from 2 × 7p coins and 2 × 4p coins . . .

From 20p upwards, what is the lowest amount you CANNOT make from your 12 coins?

**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 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

What is the difference between the highest multiple of 11 and lowest multiple of 7?

**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 EIGHT ways of making **126 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

40 41 42 43 44 45 46 47 48 49

#*NumbersIn40s*

**The Target Challenge**

Can you arrive at **126** by inserting **2**, **3**, **6** and **9** into the gaps on each line?

- ◯×◯×(◯–◯) = 126
- ◯×(◯×◯–◯²) = 126
- ◯²×◯+◯×◯ = 126
- ◯³×◯–◯²×◯ = 126
- ◯²×◯+double(◯×◯) = 126

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

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