**T**** he Main Challenge**

Using the three numbers **5**, **5** and **5** once each, with + – × ÷ available, which SEVEN target numbers from **1-30** are mathematically possible to achieve?

**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 4th & 7th rows contain the following fourteen numbers:

3 4 10 11 24 27 30 32 35 44 54 60 70 77

Which four different numbers have a sum 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 FOUR ways of making **78 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target Challenge**

Can you arrive at **78** by inserting **2**, **4**, **5** and **8** into the gaps on each line?

- ◯×◯×◯–√◯ = 78
- (◯+◯)×(◯+◯) = 78
- (◯²–◯)×◯+◯ = 78

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

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