Warwick Challenges
https://blogs.warwick.ac.uk/warwickchallenges
A blog for Warwick Maths Challenges and Writing Challenges on Twitteren-GB(C) 2019 Eleanor Lovellhttps://blogs.law.harvard.edu/tech/rssEleanor LovellEleanor LovellWarwick Blogs, University of Warwick, https://blogs.warwick.ac.uk120Maths Challenge #9 - Ring a-Ring a-Ringroad by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_9/
<p>The M25 motorway completely encircles London, and in Britain we drive on the left. So if you travel clockwise around the M25 you stay on the outside carriageway, whereas travelling anti-clockwise keeps you on the inside carriageway, which is shorter. But how much shorter?</p>
<p>The total length of the M25 is 188km (117 miles), so the advantage of being on the inside carriageway outght to be quite a lot – shouldn’t it?</p>
<p>Suppose that two cars travel around the M25, staying in the outside lane – one going clockwise and one going anti-clockwise. Also suppose that the distance between these two lanes is always 10 metres (to make it specific).</p>
<p>How much further does the clockwise van travel than the anti-clockwise one? You should also assume that the roads all lie in a flat plane.<br />
</p>MathschallengeMon, 15 Jun 2009 10:22:48 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_9/#comments094d739921cf952e0121e370c8ce05309Maths Challenge #8 - Family Occasion by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_8/
<p>'It was a wonderful party,' said Lucilla to her friend Harriet.<br />
'Who was there?'<br />
'Well - there was one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law and one daughter-in-law.'<br />
'Wow! Twenty-three people!'<br />
'No, it was less than that. A lot less.'<br />
<br />
What is the <em>smallest </em>size of party that is consistent with Lucilla's description?</p>MathschallengeMon, 08 Jun 2009 11:53:20 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_8/#comments094d7399212fe7ed0121bfb72a6a30d310Maths Challenge #7 - How Deep is the Well? by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_7/
<p><span class="status-body"><strong></strong><span class="entry-content">I drop a rock down a well, and it takes 6s to reach the bottom. If gravity is 10m/s², how deep is the well? </span></span></p>MathschallengeMon, 01 Jun 2009 10:22:22 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_7/#comments094d7399212fe7ed01219b575dc4205b5Maths Challenge #6 - What Day is It? by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_6/
<p>Yesterday, Dad got confused about which day of the week it was. 'Whenever we go on holiday, I forget,’ he said.<br />
‘Friday,’ said Darren.<br />
‘Saturday,’ his twin sister Delia contradicted.<br />
‘What day is tomorrow, then?’ asked Mum, trying to sort out the dispute without too much stress.<br />
‘Monday,’ said Delia.<br />
‘Tuesday,’ said Darren.<br />
‘Oh, for Heaven’s sake! What day was it yesterday, then?’<br />
‘Wednesday,’ said Darren.<br />
‘Thursday,’ said Delia.<br />
'Grrrrr!’ said Mum, ‘each of you has given one correct answer and two wrong ones.’<br />
<br />
What day is it today?<br />
</p>MathschallengeTue, 26 May 2009 09:32:25 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_6/#comments094d7399212fe7ed01217c437b16142616Maths Challenge #5 - Après-le-Ski by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_5/
<p>The little-known Alpine village of Après-le-Ski is situated in a deep mountain valley with vertical cliffs on both sides. The cliffs are 600 metres high on one side and 400 metres high on the other. A cable runs from the foot of each cliff to the top of the other cliff, and the cables are perfectly straight.<br />
</p>
<p><img src="/images/warwickchallenges/2009/05/18/apresleski.jpg?maxWidth=500" alt="Apres-le-Ski" border="0" /><br />
At what height above the ground do the two cables cross?</p>
<p>(Picture not to scale)<br />
</p>MathschallengeMon, 18 May 2009 10:02:48 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_5/#comments094d7399212fe7ed01215329caf107be9Maths Challenge #4 - How Old Was Diophantus? by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_4/
<p>Diophantus’ childhood lasted one sixth of his life. His beard grew after one-twelfth more. He married after one-seventh more. His son was born five years later. The son lived to half his father’s age. Diophantus died four years after his son. <strong>How old was Diophantus when he died?</strong></p>
<h6>Who was Diophantus?</h6>
<p>"Diophantus was probably Greek and he lived in ancient Alexandria. Some time around AD 250 he wrote a book about solving algebraic equations - with a slight twist: the solutions were required to be fractions, or better still, whole numbers. Such equations are called <em>Diophantine equations</em> to this day."</p>
<p>Find out more in <a href="http://www.amazon.co.uk/Professor-Stewarts-Cabinet-Mathematical-Curiosities/dp/1846680646"><em>Professor Stewart's Cabinet of Mathematical Curiosities</em></a> by Ian Stewart</p>
<p><br />
</p>MathschallengeMon, 11 May 2009 11:11:19 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_4/#comments094d73991f407a3f01212f5e9fe0343a6Maths Challenge #3 - Scrabble Oddity by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_3/
<p class="answer">Writing about web page <a href="http://www2.warwick.ac.uk/newsandevents/audio/more/mathschallenge/?podcastItem=scrable_odity_question_master.mp4" title="Related external link: http://www2.warwick.ac.uk/newsandevents/audio/more/mathschallenge/?podcastItem=scrable_odity_question_master.mp4">http://www2.warwick.ac.uk/newsandevents/audio/more/mathschallenge/?podcastItem=scrable_odity_question_master.mp4</a></p>
<p>Scrabble Oddity: Which positive integer is equal to its letter score in scrabble?</p>
<p> <script type="text/javascript"><!--
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<br />
</p>MathschallengeTue, 05 May 2009 10:34:59 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_3/#comments094d73991f4078a501211057368b37853Maths Challenge #2 - Pig in a Field by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_2/
<p>A pig tied to the corner of a 100m-sided equilateral triangle field can cover half its area. How long is the rope?</p>MathschallengeMon, 27 Apr 2009 12:18:29 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_2/#comments094d73991f4078a50120e78318122a094Maths Challenge #1 - Digital Century by Eleanor Lovell
https://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_1/
<p>Place 3 maths symbols between the digits 123456789, in that order, so that the result = 100<br />
<br />
</p>MathschallengeMon, 27 Apr 2009 12:07:38 GMTEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_1/#comments094d73991f4078a50120e7792aca2a021