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

The 15 arithmetical steps below include percentage & fraction calculations as well as big additions & multiplications:

Start with the number **28**, then:

- subtract seventy-five percent
- +69
- –4
- 1/2 of this
- square root of this
- ×15
- multiply by one
- +80%
- –10
- add four hundred and sixty-five
- subtract three hundred and seventeen
- two-thirds of this
- ×0.5
- increase by 10%
- decrease by 10%

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 contain the following fourteen numbers:

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

Which of these numbers, when 65 is added to it, becomes a square number?

**The 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 SEVEN ways of making **132 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **3**, **6** and **10 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **132** by inserting **4**, **5**, **6** and **8** into the gaps on each line?

- (◯+◯)×(◯+◯) = 132
- (◯×◯–double◯)×◯ = 132

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

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