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

Start with the number **13**, then follow these ten arithmetic steps:

–2 +5 ÷2 ×5 –4 ÷9 +1 ×5 –1 ÷4 = **?**

What is your final answer?

**T****he**** 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid of 49 different numbers, ranging from **2 **up to **84**.

The 1st & 6th rows contain the following fourteen numbers:

2 5 9 12 14 15 18 20 22 33 40 49 56 72

Which four different numbers, when added together, have a total of 100?

**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 FIVE ways of making **75 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **4**, **6** and **12 **once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target Challenge**

Can you arrive at **75** by inserting **3**, **4**, **5** and **10** into the gaps on each line?

- (◯+◯)×◯+◯ = 75
- ◯²×(◯–◯–◯) = 75
- ◯×◯+◯²+◯² = 75

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

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