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

With the four arithmetical operations + – × ÷ available, use all four numbers **1**, **1.5**, **3** and **4** once each in your attempt to arrive at 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

Which four different numbers from the above list have a sum of 100?

**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 SEVEN ways of making **129 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **3**, **6** and **10 **once each, with + – × ÷ available, which SIX numbers is it 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 **129** by inserting **3**, **8**, **9** and **12** into the gaps on each line?

- ◯²+◯–◯×◯ = 129
- ◯×(◯+◯)–√◯ = 129
- double(◯²)+◯÷(◯+◯) = 129

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

**Click Paul Godding for details of online maths tuition.**