combinatorics
https://plus.maths.org/content/taxonomy/term/653
enHow many melodies are there?
https://plus.maths.org/content/how-many-melodies-are-there
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Oli Freke </div>
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<p>Given there's a finite number of notes on a scale, can we still find a brand new melody? Perhaps they've all been written already!</p>
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<p>The equivalent of a writer staring at a blank page, wondering how to fill it, is a composer staring at the 88 black and white notes on a piano wondering how to compose a melody that's never been heard before. How can one possibly take the eight notes of a standard scale and write a brand new melody when so many great melodies have already been written? Perhaps they've all been taken!</p>
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<p>How many combinations are there?</p><p><a href="https://plus.maths.org/content/how-many-melodies-are-there" target="_blank">read more</a></p>https://plus.maths.org/content/how-many-melodies-are-there#commentscombinatoricsmathematics and artmathematics and musicThu, 06 Nov 2014 10:19:57 +0000mf3446213 at https://plus.maths.org/contentFriends and strangers
https://plus.maths.org/content/friends-and-strangers-0
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Imre Leader </div>
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<p>Can we always find order in systems that are disordered? If so, just how large does a system have to be to contain a certain amount of order?</p>
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Can we always find order in systems that are disordered? If so, just how
large does a system have to be to contain a certain amount of order?
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Let's consider a concrete example. Suppose there is a
room with six people in it. We are interested in whether
people in this room know each other or not. Let's call two
people friends if they know each other, strangers if they
don't.
</p><p><a href="https://plus.maths.org/content/friends-and-strangers-0" target="_blank">read more</a></p>https://plus.maths.org/content/friends-and-strangers-0#commentscombinatoricscreativitygraph theoryRamsey theoryThu, 27 Mar 2014 15:01:00 +0000Rachel6062 at https://plus.maths.org/contentHow to make a marriage stable
https://plus.maths.org/content/nobel-prize-stable-marriages
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/15_oct_2012_-_1431/rings.jpg?1350307905" /> </div>
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<p>How do you best allocate students to universities, doctors to hospitals, or kidneys to transplant patients? It's a tough problem that has earned this year's Memorial Prize in Economics.</p>
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<p>We've always got our finger on the pulse here at <em>Plus</em>.
This year's <a
href="http://www.nobelprize.org/nobel_prizes/economics/laureates/2012/press.html">Sveriges
Riksbank Prize in Economic Sciences in Memory of Alfred Nobel</a> has
been awarded for work closely related to something we covered in an <a href="https://plus.maths.org/content/mixed-doubles-matching-pairs">article</a> back
in August. The Prize was announced this morning and the laureates are
<a href="http://scholar.harvard.edu/roth">Alvin E.<p><a href="https://plus.maths.org/content/nobel-prize-stable-marriages" target="_blank">read more</a></p>https://plus.maths.org/content/nobel-prize-stable-marriages#commentscombinatorial game theorycombinatoricsgame theoryNobel prizeMon, 15 Oct 2012 13:03:34 +0000mf3445797 at https://plus.maths.org/contentMixing doubles
https://plus.maths.org/content/mixed-doubles-matching-pairs
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Ellen Hetland Fenwick </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/9_aug_2012_-_1419/icon.jpg?1344518346" /> </div>
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<p>Andy Murray and Laura Robson made a good team at London 2012, bringing home silver in the mixed doubles. But how do you make sure that the competing pair is the best you can pick from the team?</p>
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<p>Andy Murray and Laura Robson took silver at Wimbledon in the London 2012 Olympics. Image: <a href="http://commons.wikimedia.org/wiki/File:Andy_Murray_and_Laura_Robson_-Wimbledon,_London_2012_Olympics-3Aug2012.jpg">Christopher Johnson</a>.</p><p><a href="https://plus.maths.org/content/mixed-doubles-matching-pairs" target="_blank">read more</a></p>https://plus.maths.org/content/mixed-doubles-matching-pairs#commentscombinatorial game theorycombinatoricsgame theorymathematics in sportolympicsTue, 14 Aug 2012 10:00:07 +0000mf3445760 at https://plus.maths.org/contentA molecule's eye view of water
https://plus.maths.org/content/os/latestnews/may-aug10/ice/index
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/13%20Jul%202010%20-%2014%3A15/icon.jpg?1279026952" /> </div>
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<p>Water is essential for life on Earth, and it is a resource we all take for granted. Yet it has many surprising properties that have baffled scientists for centuries. Seemingly simple ideas such as how water freezes are not understood because of water's unique properties. Now scientists are utilising increased computer power and novel algorithms to accurately simulate the properties of water on the nanoscale, allowing complex structures of hundreds or thousands of molecules to be seen and understood.</p>
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Water is essential for life on Earth, and it is a resource we all take for granted. Yet it has many surprising properties that have baffled scientists for centuries. Seemingly simple ideas such as how water freezes are not understood because of water's unique properties. Now scientists are utilising increased computer power and novel algorithms to accurately simulate the properties of water on the nanoscale, allowing complex structures of hundreds or thousands of molecules to be seen and understood.
</p><p><a href="https://plus.maths.org/content/os/latestnews/may-aug10/ice/index" target="_blank">read more</a></p>https://plus.maths.org/content/os/latestnews/may-aug10/ice/index#commentscombinatoricsmaths insidepublic understanding of mathematicsFri, 25 Jun 2010 12:00:00 +0000mf3445244 at https://plus.maths.org/contentJuggling, maths and a beautiful mind
https://plus.maths.org/content/juggling-maths-and-beautiful-mind
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Burkard Polster </div>
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Many mathematicians find the pure and tight patterns of juggling as irresistible as those of mathematics. <b>Burkard Polster</b> explains how to get to grips with the bewildering range of juggling possibilities and invites you to do your own virtual juggling. </div>
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<div class="pub_date">September 2009</div>
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<p>The movie <i>A Beautiful Mind</i> contains a memorable transition: the mathematician John Nash (played by Russell Crowe) rides his bicycle in an infinity sign, which slowly solidifies into part of a mathematical formula from the next scene.</p>
<p>Watching the movie the other day, there occurred to me another way to effect this transition. Imagine John juggling the basic three ball pattern. Then the balls in this pattern automatically trace an infinity sign...</p><p><a href="https://plus.maths.org/content/juggling-maths-and-beautiful-mind" target="_blank">read more</a></p>https://plus.maths.org/content/juggling-maths-and-beautiful-mind#comments52combinatoricsmathematics of jugglingSat, 05 Sep 2009 23:00:00 +0000plusadmin2371 at https://plus.maths.org/contentKissing the frog: A mathematician's guide to mating
https://plus.maths.org/content/kissing-frog-mathematicians-guide-mating
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John Billingham </div>
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What's your strategy for love? Hold out for The One, or try and avoid the bad ones? How long should you wait before cutting your losses and settling down with whoever comes along next? <b>John Billingham</b> investigates and saves the national grid in the process. </div>
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<div class="pub_date">September 2008</div>
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<p>When you were small, you probably heard the fairytale <i><a href="http://en.wikipedia.org/wiki/The_Frog_Prince_(story)">The Frog Prince</a></i>. The original version of the story is rather more complicated.</p><p><a href="https://plus.maths.org/content/kissing-frog-mathematicians-guide-mating" target="_blank">read more</a></p>https://plus.maths.org/content/kissing-frog-mathematicians-guide-mating#comments48combinatoricsdatingmathematical modellingsecretary problemstatisticsSun, 31 Aug 2008 23:00:00 +0000plusadmin2339 at https://plus.maths.org/contentWhat do you think you're worth?
https://plus.maths.org/content/what-do-you-think-youre-worth
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Steven J. Brams </div>
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Bonuses are a fact of business life. Last year the Guardian newspaper calculated that the cash rewards paid to London's financial chiefs comfortably outstripped the UK's entire transport budget. With such large sums at stake, envy is bound to raise its ugly head, nver a good thing for company morale. So how should you decide who gets how much? <b>Steven J. Brams</b> suggests a method that's not only
fair, but also encourages honesty. </div>
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<p><i>Bonuses are a fact of business life. Last year the <a href="http://www.guardian.co.uk/business/2007/aug/28/money.executivepay">Guardian newspaper</a> calculated that the cash rewards paid to London's financial chiefs comfortably outstripped the UK's entire transport budget. With such large sums at stake, envy is bound to raise its ugly head, never a good thing for company morale. So how
should you decide who gets how much? Steven J.<p><a href="https://plus.maths.org/content/what-do-you-think-youre-worth" target="_blank">read more</a></p>https://plus.maths.org/content/what-do-you-think-youre-worth#comments46combinatoricsfair divisionSat, 01 Mar 2008 00:00:00 +0000plusadmin2322 at https://plus.maths.org/contentRubik success in twenty-six steps
https://plus.maths.org/content/rubik-success-twenty-six-steps
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Computer scientists prove how long it should take you to solve Rubik's cube </div>
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<div class="pub_date">05/06/2007</div>
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<p><em>Since this article was published the result has been improved to 20.</em></p><p><a href="https://plus.maths.org/content/rubik-success-twenty-six-steps" target="_blank">read more</a></p>https://plus.maths.org/content/rubik-success-twenty-six-steps#commentscombinatoricsgroup theorypermutationRubik's cubeMon, 04 Jun 2007 23:00:00 +0000plusadmin2554 at https://plus.maths.org/contentRunning a lottery, for beginners
https://plus.maths.org/content/running-lottery-beginners
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John Haigh </div>
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There are many different types of lottery around the world, but they all share a common aim: to make money. <b>John Haigh</b> explains why lotteries are the way they are. </div>
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<p><i>To appreciate why Lottery formats are what they are, consider how you would design an ongoing Lottery from scratch. Your aim is to maximise the total profit, within the legal constraints that all tickets are treated equally.</i></p><p><a href="https://plus.maths.org/content/running-lottery-beginners" target="_blank">read more</a></p>https://plus.maths.org/content/running-lottery-beginners#comments30combinatoricslotteryrandomnessFri, 30 Apr 2004 23:00:00 +0000plusadmin2247 at https://plus.maths.org/contentThe UK National Lottery - a guide for beginners
https://plus.maths.org/content/uk-national-lottery-guide-beginners
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John Haigh </div>
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In the early days of the UK National Lottery, it was quite common to see newspaper articles that looked back on what numbers had recently been drawn, and attempted to identify certain numbers as "due" or "hot". Few such articles appear now, and <b>John Haigh</b> thinks that perhaps the publicity surrounding the lottery has enhanced the nation's numeracy. </div>
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<p><i>The UK National Lottery began in November 1994. Optimistic statisticians hoped that the surrounding publicity might increase interest in ideas of chance and probability, and perhaps even enhance the nation's numeracy.</i></p><p><a href="https://plus.maths.org/content/uk-national-lottery-guide-beginners" target="_blank">read more</a></p>https://plus.maths.org/content/uk-national-lottery-guide-beginners#comments29combinatoricslotteryrandomnessMon, 01 Mar 2004 00:00:00 +0000plusadmin2243 at https://plus.maths.org/content