**The Main**** Challenge**

Starting from **2**, list the first seven even numbers that are NOT multiples of 3, 5 or 7. What is the 7th number in your list?

**T****he 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 multiples of 8?

**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 **13 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target Challenge**

Can you arrive at **13** by inserting **1**, **2**, **3** and **4** into the gaps on each line?

- ◯×◯+◯–◯ = 13
- ◯×(◯+◯)+◯ = 13
- (◯²+◯²+◯)÷◯ = 13

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

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