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

In all four groups below, it is possible to make **24** by using the four numbers once each, with + – × ÷ available. Can you show how to achieve the target number of **24** in each case?

- 3 3 3 3
- 4 4 4 4
- 5 5 5 5
- 6 6 6 6

**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 & 4th rows contain the following fourteen numbers:

2 3 9 10 14 15 22 32 35 40 44 54 60 72

What is the sum of the multiples of 6 listed above?

**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 just TWO ways of making **40 **when using *Lagrange’s Theorem*. Can you find them both?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

70 71 72 73 74 75 76 77 78 79

#*NumbersIn70s*

**The Target Challenge**

Can you arrive at **40** by inserting **2,** **4**, **5** and **10** into the gaps on each line?

- (◯+◯–◯)×◯ = 40
- (◯–◯)×◯×◯ = 40
- ◯²×◯²×◯÷◯ = 40

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

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