**T**** h****e Main Challenge**

There are five different *24game***®** challenges below.

For each group of four numbers, your task is to arrive at the target answer of **24** by using each of the four digits exactly once, with + – × ÷ available:

- 1 2 3 4
- 2 3 4 5
- 3 4 5 6
- 4 5 6 7
- 5 6 7 8

All five challenges are possible, can you do them all?

**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 & 7th rows of the playing board contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the total when adding together all the odd numbers?

**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).

There are TEN different ways to make **229 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **2**, **4** and **8 **once each, with + – × ÷ available, which FIVE 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 **229** by inserting **2**, **3**, **4**, **5** and **7** into the gaps below?

- ◯²×◯+◯²×◯+◯ = 229

**A****nswers **can be found **here**.

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