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

You’ve rolled the numbers **4**, **5** and **5** with three dice. Using these once each, with + – × ÷ available, find the only FOUR target numbers from **1-10** that it is possible to make.

**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 of the playing board contain the following fourteen numbers:

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

Which even number, when halved, becomes a cube number?

**T****he 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 NINE different ways to make **235 **when using *Lagrange’s Theorem*. How many of them can you find?

**The Mathematically Possible Challenge**

Using **2**, **4** and **8 **once each, with + – × ÷ available, which is the ONLY number that is NOT possible to make from the list below?

2 4 6 8 10 12 14 16 18 20

#*EvenNumbers*

**The Target Challenge**

Can you arrive at **235** by inserting **2**, **4**, **6**, **8** and **10** into the gaps below?

- treble◯×◯–(◯+◯)÷◯ = 235

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

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