Wild Maths

Wild maths is mathematics without bounds. Here, you are free to roam and develop as a mathematician. We invite you to embark on a mathematical adventure!

Mathematics is a creative subject. It involves spotting patterns, making connections, finding new ways of looking at things and using what you already know in new contexts. Creative mathematicians play around with examples, draw pictures, have the courage to experiment and ask good questions.

We provide games, investigations, stories and spaces to explore, where we know there are discoveries to be made. Some have starting points, some a big question and others offer you a free space to investigate. Have a go at anything that catches your eye. You can find the full collection of activities, and explore challenges and investigations that are linked by some shared mathematical areas, by clicking on the 'Pathways' link in the top menu.

We'd love you to share your ideas and discoveries. You can share ideas via the comments at the bottom of each resource, or email us by clicking on the 'Share your discoveries' link at the bottom of each page.

Happy exploring!


Egyptian Fractions - How Many Ways?

You might want to take a look at Egyptian Fractions first.

Some unit fractions can be written as a sum of two different unit fractions in more than one way.
Here are the ways to write $\frac{1}{6}$:

$\frac{1}{6} = \frac{1}{7} + \frac{1}{42}$

$\frac{1}{6} = \frac{1}{8} + \frac{1}{24}$

$\frac{1}{6} = \frac{1}{9} + \frac{1}{18}$

$\frac{1}{6} = \frac{1}{10} + \frac{1}{15}$

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Dotty Grids Resources

 

Here are some resources you might find useful when working on Dotty Grids problems.

You might like to explore the problems using the interactive environment below.

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Egyptian Fractions - Writing them all

How can we write a fraction with a large numerator, such as $\frac{115}{137}$, as an Egyptian Fraction?

One way might be to write $\frac{115}{137}=\frac{1}{137}+\frac{1}{137}+...+\frac{1}{137}$ and try to find lots of different ways to write $\frac{1}{137}$ as a sum of unit fractions...

I wonder if there's a more efficient way?

 

One possibility is to try a so-called Greedy Algorithm:

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Getting Round the City

 
The grid below represents a city laid out in "blocks" with all the roads running north-south, or east-west.

Imagine two friends live where the red and blue dots are on the grid.

The animation shows three paths that one friend could choose if he wanted to visit the other.

He likes to find the shortest routes possible, so he always travels north or east, never south or west.

 

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Last Biscuit: Getting Started

Suppose it is your turn to play Last Biscuit. Ideally, you would like to leave your opponent with a configuration of biscuits from which they cannot possibly win. We will call this a losing configuration: when faced with a losing configuration the player to go next will definitely lose.

Can you find such a losing configuration for Last Biscuit? (Hint: start with as few biscuits as possible.)

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Pairwise Puzzler - Harvey's solution

Thank you to Harvey for sending us his thoughts on Pairwise Puzzler

 

Pairwise puzzler- strategy for original four numbers


I did this puzzle by using some of the strategy for the original five numbers puzzle.

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