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

Here’s seven more mental arithmetic questions to try. Can you get all seven correct?

- (11 – 5) – (4 + 1) = ?
- What is 10 more than –4?
- 47 × 4 = ?
- 0.32 ÷ 4 = ?
- 3/4 × 2/3 = ?
- Which one is bigger: 2 cubed or 3 squared?
- You wish to buy two £30 items. Which offer would give you the best deal: (A) 15% off both items, (B) 2nd item is 40% off, (C) get 1/3 off the 2nd item, (D) 25% off 1st item, 10% off 2nd item.

**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 contain the following fourteen numbers:

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

From the list, find TWO numbers that have a sum of 111.

**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 SEVEN ways of making **108 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **1**, **4** and **9 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **108** by inserting **2**, **3**, **5** and **11** into the gaps on both lines?

- ◯²×◯²+◯–◯ = 108
- ◯×◯²+◯²+◯ = 108

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

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