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

Apart from **987631** (9+8+7+6+3+1), can you find the other FOUR ways to make **34** when adding together six unique digits from **1-9**?

**The 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 2nd & 6th rows contain the following fourteen numbers:

5 8 12 17 18 20 28 33 48 49 55 56 63 64

What is the sum of the multiples of 6?

**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 **146**, in NINE different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using the three digits **2**, **6** and **9** once each, with + – × ÷ available, which are the only THREE numbers it’s possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **146** by inserting **8**, **9**, **11** and **14** into the gaps on each line?

- (◯+◯)×◯–◯ = 146
- ◯²+◯+◯+√◯ = 146

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

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