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

Follow these six steps:

- Work out the sum of
**3**and**5**, - Calculate the difference between
**3**and**5**, - Find the product of the two answers in Points 1 and 2,
- Find the square root to your answer in Point 3,
- Add the answer in Point 4 to your answer in Point 1,
- Subtract your answer in Point 2 from the answer in Point 5.

What is your answer after carrying out **Point 6**?

**The**** 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid of 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

Which pair of numbers have a difference of 49?

**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 FIVE ways of making **84 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which is the ONLY number that is possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **84** by inserting **2**, **3**, **6** and **7** into the gaps on each line?

- (◯+◯)²+◯–◯² = 84
- (◯×◯+◯)×◯ = 84
- ((◯–◯)²–◯)×◯ = 84

**An****swers **can be found **here**.

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