**Th**** e Main Challenge**

Each of the nine letters, **A-I**, in the two sections below has a subtraction calculation attached to it. Which is the only letter that has the same answer in both sections?

- Section 1

C:24–13 G:14–6 D:20–10 E:15–7 I:14–9 F:18–11 B:9–2 A:17–5 H:25–12

- Section 2

I:16–3 A:15–1 H:20–8 C:19–9 G:12–4 E:11–5 F:21–6 D:14–7 B:27–18

**T****he**** 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 4th & 7th rows contain the following fourteen numbers:

3 4 10 11 24 27 30 32 35 44 54 60 70 77

What is the difference between the highest and lowest multiples of 4?

**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 just TWO ways of making **80 **when using *Lagrange’s Theorem*. Can you find them both?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challenge**

Can you arrive at **80** by inserting **4**, **5**, **8** and **10** into the gaps on each line?

- ◯×◯+◯×◯ = 80
- ◯×◯×(◯–◯) = 80
- ◯×◯×(◯–◯)² = 80
- (◯–◯)×(◯–◯)² = 80
- ◯³+◯×◯÷◯ = 80

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

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