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

How can you use six 7’s (**7 7 7 7 7** and **7**) once each, together with the four arithmetical operations + – × ÷, to arrive at the target answer of **100**?

**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 4th & 5th rows contain the following fourteen numbers:

3 6 7 10 16 21 32 35 44 50 54 60 81 84

What is the sum when adding together all the multiples of 10?

**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 **86 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

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

11 22 33 44 55 66 77 88 99 110

#*11TimesTable*

**The Target Challenge**

Can you arrive at **86** by inserting **2**, **4**, **10** and **14** into the gaps on each line?

- ◯×(◯–◯)+◯ = 86
- ◯×◯÷◯+◯² = 86
- (◯²–◯)÷◯–◯ = 86

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

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