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

From the numbers **1-30** inclusive, delete:

- multiples of 5
- factors of 36
- numbers containing a ‘7’
- prime numbers
- even numbers

Which is the only number that remains?

**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 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

Which three different numbers on the list have a sum of 100?

**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 SIX ways of making **123 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

12 24 36 48 60 72 84 96 108 120

#*12TimesTable*

**The Target Challenge**

Can you arrive at **123** by inserting **3**, **9**, **10** and **12** into the gaps on each line?

- ◯×◯+◯÷◯ = 123
- ◯×◯+half(◯×◯) = 123
- (◯+◯)×◯+half◯ = 123

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

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