## Plus Blog

December 10, 2015

There are several different notions of average: the mean, the median, the mode and the range (see below for the definitions). If you work out each of these for the set of numbers 2, 5, 5, 6, 7, you'll notice something interesting — they are all equal to 5!

Can you find other sets of five positive whole numbers where mean = median = mode = range?

How many sets of five positive whole numbers are there with mean = median = mode = range = 100?

This puzzle comes from our sister site Wild maths, which encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. Visit Wild maths for more games, investigations, stories and spaces to explore!

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### Definitions

Given a list of numbers up to (ordered by size) the mean is

The median separates the lower half of the list from the higher half. It is the middle number if there are an odd number of numbers in the list, or the number half-way between the two middle numbers if there are an even number. So, assuming that The median is

if is odd and

if is even.

The mode is the number in the list that occurs most often — which means that there can be more than one mode.

The range is the difference between the largest and the smallest number in the list:

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December 9, 2015

Manjul Bhargava (centre) with Plus editors Rachel and Marianne

Manjul Bhargava's idea of mathematics is interesting: "I think that the reasons for doing maths are similar to those for doing music or art," he says. "It's about contributing to a certain understanding of the world and ourselves." Bhargava has been described as having "extraordinary creativity" and was awarded the Fields Medal in 2014, one of the most important prizes in mathematics.

Bhargava believes that one of the keys to solving hard mathematical problems is to look at them in a new way: he famously solved an old number theory problem by visualising it as a Rubik's cube. You can meet him and his work on Wild Maths, and find out more detail in the Plus articles Revealing numbers and Answers on a donut, and listen to our interview with him from 2014.

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

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December 8, 2015

We've read the book. We've bought the T-shirt. And now, finally, here it is: the movie of one of our favourite maths problems, the bridges of Königsberg. Though admittedly, we made it ourselves. We learnt several interesting lessons in the process. For example that a bin doesn't make a good supporting character and that people who shouldn't be in the frame should get out of it. But other than that, we're well on course for an Oscar! And we believe that the solution to this problem is a true example of mathematical creativity.

You can read more about the bridges of Königsberg here.

This video was inspired by content on our sister site Wild Maths, which encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

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December 7, 2015

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Can you cut up an old playing card to make a hole big enough to walk through?

Have a go! If you struggle, visit Wild Maths, where you can get some ideas and also find other things to do with paper and scissors.

Enjoy!

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

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December 7, 2015

Sometimes a piece of mathematics can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples of this is the art gallery problem.

The Guggenheim Museum in Bilbao: hard to supervise. Image: MykReeve.

Suppose you have an art gallery containing priceless paintings and sculptures. You would like it to be supervised by security guards, and you want to employ enough of them so that at any one time the guards can between them oversee the whole gallery. How many guards will you need?

Think about this for a while (go on, it's Sunday) and once you've had enough, read about the answer and its proof here. It's pure genius!

This article was inspired by Wild Maths, which encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

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December 5, 2015

Got it! a game for two players. The first player chooses a whole number from 1 to 4. After that players take turns to add a whole number from 1 to 4 to the running total. The player who hits the target of 23 wins the game.

You can play the game against a friend, or against the computer using the interactivity on Wild Maths. Can you find a winning strategy? If yes, can you describe it? And what if you change the target number to something other than 23, or the numbers you are allowed to add to something other than 1 to 4?

Have fun!

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

Return to the Plus Advent Calendar

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