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

Today’s task is to arrive at the target number of **7** by using the four numbers **7**,** 7**,** 7 **and** 7** once each. All four arithmetic operations + – × ÷ are available. Can you do it?

**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

From this list, what is the sum of the square numbers?

**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 is only ONE way to make **11 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

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

2 3 5 7 11 13 17 19 23 29

#*PrimeNumbers*

**The Target Challenge**

Can you arrive at **11** by inserting **2**, **3**, **4** and **5** into the gaps on each line?

- ◯×◯+◯–◯ = 11
- ◯÷◯×◯+◯ = 11
- ◯²–√(◯×(◯+◯)) = 11

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

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