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

Use all three numbers in each of the five groups below, with + – × ÷ available, to try and make the target of **23**. But for one of the groups it is impossible. Which one?

- 1 4 6
- 2 5 5
- 3 4 5
- 3 4 6
- 3 5 6

Full details of our number & strategy board game, click **Mathematically Possible**.

**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 1st & 7th rows of the playing board contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

Which three different numbers have a sum of 77?

**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 THIRTEEN different ways to make **230 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **2**, **4** and **8 **once each, with + – × ÷ available, which is the ONLY number is it possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **230** by inserting **2**, **3**, **5**, **6** and **7** into the gaps below?

- ◯×(◯+◯)²+◯×◯ = 230

**A****nswers **can be found **here**.

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