**Th****e**** Main Challenge**

Starting with the number **7**, complete the following sixteen arithmetic steps:

- multiply by ten
- 40 percent of this
- double it
- multiply the digits together
- increase by 20 percent
- divide by three
- increase by 50 percent
- one-third of this
- double it
- square it
- five-sixths of this
- decrease by 10 percent
- divide by three
- add thirty-nine
- increase by 20 percent
- seven-ninths of this

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 1st & 3rd rows of the playing board contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

What is the difference between the sum of the odd numbers and sum of the even 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 EIGHT different ways to make **203 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **5**, **7** and **11 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

8 16 24 32 40 48 56 64 72 80

#*8TimesTable*

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

Can you arrive at **203** by inserting **3**, **4**, **7** and **8** into the gaps on each line?

- (◯×◯–◯)×◯ = 203
- (◯+◯)²–◯²–double◯ = 203
- ◯³–◯×(◯³+◯) = 203

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

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