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!


Advice for parents and carers

'A mathematician, like a painter or a poet, is a maker of patterns.'
G.H Hardy, 'A Mathematician's Apology'

'Pure mathematics is, in its way, the poetry of logical ideas’.
Albert Einstein

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Shake to Solve

Sometimes real progress in maths comes when you find a way of looking at a problem in two different ways. Here is a great example of this.

Suppose you have $10$ people in a room and each person shakes hands with each other person once. How many handshakes do you get in total? The first person shakes hands with $9$ other people, the second shakes hands with the $8$ remaining people, the third shakes hands with $7$ remaining people, etc, giving a total of

$$9+8+7+...+2+1$$ handshakes.

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Always a Multiple?

 

Think of a two-digit number.
Reverse the digits and add your answer to your original number. 

For example, Alison chose 42 and added 24 to get 66.

Try a few examples.
Can you explain why your answer is always a multiple of 11?

 

 Alison and Charlie came up with their own explanations:

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Dropping Eggs

Imagine you make egg-shaped ornaments, and you want to tell customers how high the eggs can be safely dropped from, without breaking them!

If you had an egg to test by dropping it from each floor of a 100 storey building, you'd need to start by dropping it from the first floor, and if it didn't break, go up to the second floor, and if it didn't break, go up to the third floor...

In the worst case scenario, you might have to do 100 tests to find out where it breaks!

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Equal and Unequal Averages: Zach's Solution

Thanks to Zach for submitting this solution in response to the problem Unequal Averages  on NRICH.

The question says you can input any five positive integers and that the output must be a single digit number. This means that the output must also be positive and lie in the range 1-9.

$\text{sum of quantities} = \text{mean} \times \text{number of quantities}$

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