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

Can you arrive at the target number **81** by using the five numbers **1**, **2**, **3**, **4** and **5** exactly once each, and with + – × ÷ available?

**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 3rd & 7th rows contain the following fourteen numbers:

4 11 13 24 25 27 30 36 42 45 66 70 77 80

List three pairs of numbers that each have a difference of 9.

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every integer can be made by adding up to four square numbers.

For example, **7** can be made by **2²+1²+1²+1²** (4+1+1+1).

Show how you can make **155**, in SIX different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using the three digits **3**, **5** and **8** once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **155** by inserting **3**, **5**, **10** and **11** into the gaps in each line below?

- ◯×◯×◯–◯ = 155
- ◯×◯+◯²×◯ = 155

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

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