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

This is a number puzzle taken from my scrapbook of brainteasers, a favourite of mine, and used regularly as a mental maths starter in my workshops over the years!

You have a 6-sector dartboard containing the numbers **16**, **17**, **23**, **24**, **39** and **40**. Your task is to achieve **EXACTLY 100** when adding your scores together. This can be done by throwing any number of darts, each of which can land in any sector more than once.

There is only ONE way of achieving a score of **100**. How can it be done?

**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 4th & 5th rows of the playing board contain the following fourteen numbers:

3 6 7 10 16 21 32 35 44 50 54 60 81 84

List two pairs of numbers that differ by 19.

**T****he 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).

Show how you can make **192**, in just TWO different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **4** and **12** once each, with + – × ÷ available, which are the only TWO numbers is it possible to make from the list below?

10 20 30 40 50 60 70 80 90 100

#*10TimesTabl**e*

**The Target ****Challeng****e**

Can you arrive at **192** by inserting **4**, **6**, **8** and **10** into the gaps on each line?

- (◯+◯)×(◯+◯) = 192
- (◯×◯–◯)×◯ = 192
- double(◯×(◯+◯))–◯ = 192

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

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