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

Using the three numbers **3**, **6** and **9** just once each, with + – × ÷ available, THREE of the following target numbers are not possible to make:

3 6 9 12 15 18 21 24 27 30 33 36

What is the sum of these three impossible numbers?

**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

Which number on the list, when multiplied by 5, has its result also on the list?

**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 THREE ways of making **33 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which is the ONLY number it is 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 **33** by inserting **2**, **3**, **4** and **5** into the gaps on each line?

- (◯+◯+◯)×◯ = 33
- (◯+◯)×◯–◯ = 33
- (◯³+◯–◯)÷◯ = 33

**A****nswers **can be found **here**.

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