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

Add together the 7th prime number, the 7th square number, the 7th 2-digit number and the 7th whole number that contains a **7**. What is your answer?

**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

Which two numbers listed have a sum of 101?

**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 TWO ways to make **12 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **4**, **5** and **10 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

40 41 42 43 44 45 46 47 49 49

#*NumbersIn40s*

**The Target Challenge**

Can you arrive at **12** by inserting **2**, **3**, **4** and **6** into the gaps on each line?

- (◯–◯)×◯×◯ = 12
- ◯×◯–(◯+◯) = 12
- ◯÷◯×(◯+◯) = 12
- ◯²–◯×◯÷◯ = 12
- (◯²+◯³)×◯÷◯ = 12

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

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