**The Main Challenge**

This is a very special challenge personally endorsed by Robert Sun, inventor of the world-famous maths card game, *24game*^{®}*.*

The idea is very simple; to make 24 from the card below by using the four numbers exactly once each, and with + – × ÷ available.

(The three dots in each corner signifies a hard level of challenge)

Can you also make 24 from the following two combinations using the same rules?

- 1 5 5 5
- 4 4 7 7

**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

What is the sum when adding together all the multiples of 7?

**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 **191**, in FOUR different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

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

9 18 27 36 45 54 63 72 81 90

#*9TimesTabl**e*

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

Can you arrive at **191** by inserting **7**, **11**, **19** and **25** into the gaps on each line?

- ◯×◯+◯–◯ = 191
- ◯×◯+double(◯–◯) = 191

**Answers **can be found **here**.

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