**The Main Challenge**

In this *Kakuro*-type question, can you list the only THREE ways of making **18** when adding together five unique digits from 1-9?

**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 & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

What is the sum of the factors of 120?

**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** (or 4+1+1+1).

Show how you can make **165**, in EIGHT different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **4**, **6** and **10** once each, with + – × ÷ available, which are the SIX numbers it’s possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **165** by inserting **5**, **10**, **15** and **20** into the gaps on each line?

- (◯+◯)×◯+◯ = 165
- (◯+◯)×◯–◯ = 165

**Answers **can be found **here**.

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