**The Main Challenge**

When playing **Mathematically Possible**, players analyse which target numbers can (or cannot) be made from the three numbers rolled on their dice, but this particular challenge is slightly different as you are only allowed to add and subtract (+ and –) when calculating.

Use the numbers **3**, **6** and **10** once each to find the only FOUR target numbers from **1-30** that are mathematically possible to achieve.

**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 & 3rd rows of the playing board contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

What is the sum of the multiples of 7 listed above?

**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 TEN different ways to make **201 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **5**, **7** and **11 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target ****Challeng****e**

Can you arrive at **201** by inserting **3**, **5**, **8** and **9** into the gaps on each line?

- (◯×◯–◯)×◯ = 201
- (◯+◯)²+◯–◯ = 201

**Answers **can be found **here**.

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