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

Firstly, allocate numerical values to the following fifteen letters in the English alphabet:

E=3 F=9 G=6 H=1 I=–4 L=0 N=5 O=–7 R=–6 S=–1 T=2 U=8 V=–3 W=7 X=11

You’ll see that **O+N+E **adds up to** 1** and **T+W+O=2** and so on, but what is the biggest number it will make before this amazing trick stops working? A must for you and your kids to try!

**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 & 6th rows contain the following fourteen numbers:

5 8 12 17 18 20 28 33 48 49 55 56 63 64

Which number, when halved, is also on the list?

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every integer can be made by adding up to four square numbers.

For example, **7** can be made by **2²+1²+1²+1²** (4+1+1+1).

Show how you can make **147**, in EIGHT different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using the three digits **2**, **6** and **9** once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?

10 20 30 40 50 60 70 80 90 100

#*10TimesTable*

**The Target Challenge**

Can you arrive at **147** by inserting **2**, **4**, **7** and **10** into the gaps on each line?

- ◯²×(◯+◯)÷◯ = 147
- (◯+◯)²+◯–◯ = 147
- ◯²+◯²+◯–◯ = 147

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

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