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

By using the four numbers **0.5**, **2**, **2** and **2** exactly once each, can you arrive at the target answer of **7** with the four arithmetical operations + – × ÷ available to use?

**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 & 2nd rows of the playing board contain the following fourteen numbers:

2 8 9 14 15 17 22 28 40 48 55 63 64 72

From the list, find the sum of the multiples of 7.

**T****he 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 different ways to make **215 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **4**, **6** and **9 **once each, with + – × ÷ available, which are the SIX numbers it is 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 **215** by inserting **4**, **15**, **20** and **40** into the gaps on each line?

- ◯×◯+◯+double◯ = 215
- (◯×◯)÷◯+◯ = 215
- quarter(◯×◯+◯×◯) = 215

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

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