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

Here’s seven tricky mental teasers to try:

- (18 – 5) – (7 – 17) = ?
- 128 + 294 = ?
- How many seconds are in a quarter-of-an-hour?
- How many degrees are in three-quarters of a circle?
- (16 – 8) × (13 – 8) = ?
- On four consecutive days, you spend £55, £74, £36 and £15. What is the average amount spent per day?
- What is 15% of £8?

**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

Which two numbers have a difference of 42?

**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 FOUR ways of making **107 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **1**, **4** and **9 **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 **107** by inserting **9**, **10**, **11** and **12** into the gaps on both lines?

- ◯×◯+◯–◯ = 107 (2 different ways!)
- ◯×◯+(◯–◯)³ = 107

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

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