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

With the four arithmetical operations + – × ÷ available, use all four numbers **1**, **1.5**, **2** and **6** once each in your attempt to make the target answer of **7**.

**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 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

What is the sum of the factors of 64?

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

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

1 3 6 10 15 21 28 36 45 55

#*TriangularNumbers*

**The Target Challenge**

Can you arrive at **127** by inserting **4**, **7**, **8** and **10** into the gaps on each line?

- (◯+◯)×◯+◯ = 127
- ◯²+◯×◯–√◯ = 127
- ◯²+◯+◯+double◯ = 127

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

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