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

Can you arrive at the target number **55** by using the five numbers **1**, **2**, **3**, **4** and **5** exactly once each, and with + – × ÷ available?

**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 5th & 7th rows contain the following fourteen numbers:

4 6 7 11 16 21 24 27 30 50 70 77 81 84

What is the sum of the factors of 42?

**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 **136 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

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

13 26 39 52 65 78 91 104 117 130

#*13TimesTable*

**The Target Challenge**

Can you arrive at **136** by inserting **4**, **6**, **7** and **8** into the gaps on each line?

- (◯×◯–◯)×◯ = 136
- (◯+◯+◯)×◯ = 136

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

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