** Th****e Main Challenge**

Insert the 12 numbers **1 1 2 2 2 3 5 5 6 7 8** and **8** so that all three lines work out arithmetically:

◯ + ◯ = 6 = ◯ – ◯

◯ + ◯ = 14 = ◯ × ◯

◯ + ◯ = 5 = ◯ ÷ ◯

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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 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 difference between the highest and lowest odd numbers?

**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 is only ONE way of making **14 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

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

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **14** by inserting **2**, **4**, **5** and **5** into the gaps on each line?

- ◯+◯+◯+√◯ = 14
- ◯²–(◯+◯+◯) = 14
- (◯+◯÷◯)×◯ = 14

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

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