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

Here’s a 12-step number trail involving + – × ÷ and the numbers **4** and **5**.

Start with the number **5**, then:

- +5
- ÷5
- multiply by 4
- subtract 4
- ×5
- add 5
- divide by 5
- add 4
- –5
- ÷4
- +4
- ÷5

What is your final answer?

**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 3rd & 6th rows of the playing board contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

How many square numbers are listed above?

**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 **238 **when using *Lagrange’s Theorem*. How many of them can you find?

**The Mathematically Possible Challenge**

Using **2**, **5** and **10 **once each, with + – × ÷ available, which are the SIX numbers it is 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 **238** by inserting **5**, **6**, **7**, **8** and **9** into the gaps below?

- ◯×◯×◯+◯–◯ = 238

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

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