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

Your task is to arrive at the target answer of **18** by using each of the four numbers **2**, **6**, **7** and **10** exactly once each, with + – × ÷ available. Can you find TWO ways of making 18?

**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 6th & 7th rows contain the following fourteen numbers:

4 5 11 12 18 20 24 27 30 33 49 56 70 77

Which number, when 23 is added to 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 FIVE ways of making **93 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **5**, **7** and **10 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **93** by inserting **3**, **4**, **6** and **11** into the gaps on each line?

- (◯+◯)×◯+◯ = 93
- ◯²–◯²–◯²–half◯ = 93
- ◯³+◯×◯+◯ = 93

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

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