**T**** he Main Challenge**

Using the numbers **3**, **4** and **5** just once each, and with + – × ÷ available, only FOUR of the numbers on the list below are possible to achieve. Which ones are they?

1 3 6 9 10 12 15 18 21 24 27 30

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

2 4 9 11 14 15 22 24 27 30 40 70 72 77

Which multiple of 5, when subtracting 4 from it, becomes a square number?

**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 SEVEN ways of making **125 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which TWO numbers is it 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 **125** by inserting **5**, **10**, **15** and **20** into the gaps on each line?

- ◯×◯+◯+◯ = 125
- ◯×◯–◯×◯ = 125
- ◯²–◯×(◯–◯) = 125
- (◯+◯)×(◯–◯) = 125
- ◯×◯+◯+double◯ = 125

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

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