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

Can you arrive at the target answer of **7** by using each of the numbers **0.2**, **0.5**, **2** and **2.5** 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 1st & 6th rows contain the following fourteen numbers:

2 5 9 12 14 15 18 20 22 33 40 49 56 72

What is the sum of the factors of 36?

**T****he 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 **178**, in TWELVE different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **6** and **12** once each, with + – × ÷ available, which SEVEN target numbers from the list below can be made?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

** The Target Challenge**

Can you arrive at **178** by inserting **10**, **11**, **16** and **20** into the gaps on each line?

- ◯×◯+◯÷◯ = 178
- ◯×◯+double(◯–◯) = 178

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

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