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

Instead of being numbered **1-12**, a traditional clock had **√1**, **√4**, **√9** . . . **√144** around its circumference. Every digit is represented on the clock, except one.

What is this missing digit?

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

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the sum of the factors of 40 listed above?

**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 SEVEN ways of making **118 **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?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **118** by inserting **1**, **2**, **4** and **5** into the gaps on each line?

- ◯³+◯–◯×◯ = 118
- (◯³–◯×◯)×◯ = 118

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

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