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

By following these rules, list SEVEN different positive whole numbers that total **100**:

- each number must be at least 4 away from its nearest neighbour,
- the list must contain at least three square numbers.

Can you find at least one solution?

**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 6th & 7th rows contain the following fourteen numbers:

4 5 11 12 18 20 24 27 30 33 49 56 70 77

What is the sum of the multiples of 4?

**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 THREE ways of making **92 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **5**, **7** and **10 **once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challenge**

Can you arrive at **92** by inserting **2**, **4**, **10** and **12** into the gaps on each line?

- ◯×◯×◯+◯ = 92
- ◯²–(◯+◯)÷◯ = 92
- ◯×(◯–◯)–◯= 92

**A****nswers **can be found **here**.