All 19 entries tagged <em>Mathschallenge</em>Eleanor LovellJo HandfordEleanor LovellJackie GutteridgeA blog for Warwick Maths Challenges and Writing Challenges on Twitterhttps://blogs.warwick.ac.uk/warwickchallenges/tag/mathschallenge/?atom=atomWarwick Blogs, University of Warwick(C) 2019 Eleanor Lovell2019-02-18T12:15:43ZShips That Pass . . . by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/ships_that_pass__/2009-12-08T15:10:53Z2009-12-07T11:24:07Z<p>In the days when people crossed the Atlantic in passenger liners, a ship left London every day at 4.00 p.m. bound for New York, arriving exactly 7 days later.</p>
<p>Every day at the same instant (11.00 a.m. because of the time difference) a ship left New York bound for London, arriving exactly 7 days later.</p>
<p>All ships followed the same route, deviating slightly to avoid collisions when they met.</p>
<p>How many ships from London does each ship sailing from New York encounter during its transatlantic voyage, <em>not</em> counting any that arrive at the dock just as they leave, or leave the dock just as they arrive?</p><p>In the days when people crossed the Atlantic in passenger liners, a ship left London every day at 4.00 p.m. bound for New York, arriving exactly 7 days later.</p>
<p>Every day at the same instant (11.00 a.m. because of the time difference) a ship left New York bound for London, arriving exactly 7 days later.</p>
<p>All ships followed the same route, deviating slightly to avoid collisions when they met.</p>
<p>How many ships from London does each ship sailing from New York encounter during its transatlantic voyage, <em>not</em> counting any that arrive at the dock just as they leave, or leave the dock just as they arrive?</p>The Curious Incident of the Dog by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/the_curious_incident/2009-11-25T14:26:25Z2009-11-23T09:40:22Z<p>In Sir Arthur Conan Doyle’s Sherlock Holmes story ‘Silver Blaze’, we find:</p>
<p>‘Is there any other point to which you would wish to draw my attention?’</p>
<p>‘To the curious incident of the dog in the night-time.’</p>
<p>‘The dog did nothing in the night-time.’</p>
<p>‘That was the curious incident,’ remarked Sherlock Holmes. </p>
<p>Here is a sequence: 1, 2, 4, 7, 8, 11, 14, 16, 17, 19, 22, 26, 28, 29, 41, 44</p>
<p>Having taken Holmes’s point on board: what is the next number in the sequence?</p><p>In Sir Arthur Conan Doyle’s Sherlock Holmes story ‘Silver Blaze’, we find:</p>
<p>‘Is there any other point to which you would wish to draw my attention?’</p>
<p>‘To the curious incident of the dog in the night-time.’</p>
<p>‘The dog did nothing in the night-time.’</p>
<p>‘That was the curious incident,’ remarked Sherlock Holmes. </p>
<p>Here is a sequence: 1, 2, 4, 7, 8, 11, 14, 16, 17, 19, 22, 26, 28, 29, 41, 44</p>
<p>Having taken Holmes’s point on board: what is the next number in the sequence?</p>Nice Littler Earner by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/nice_littler_earner/2009-11-17T16:16:53Z2009-11-16T15:53:58Z<p>Smith and Jones were hired at the same time by Stainsbury’s Superdupermarket, with a starting salary of £10,000 per year. Every six months, Smith’s pay rose by £500 compared with that for the previous 6-month period. Every year, Jones’s pay rose by £1,600 compared with that for the previous 12-month period. </p>
<p>Three years later, who had earned more?<br />
</p><p>Smith and Jones were hired at the same time by Stainsbury’s Superdupermarket, with a starting salary of £10,000 per year. Every six months, Smith’s pay rose by £500 compared with that for the previous 6-month period. Every year, Jones’s pay rose by £1,600 compared with that for the previous 12-month period. </p>
<p>Three years later, who had earned more?<br />
</p>Target Practice by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/target_practice/2009-11-25T09:41:53Z2009-11-09T10:55:41Z<p><img style="float: right; margin-left: 5px; margin-right: 5px;" src="/images/warwickchallenges/2009/11/09/target.jpg?maxWidth=500" alt="Target Practice" border="0" /></p>
<p>Robin Hood and Friar Tuck were engaging in some target practice. The target was a series of concentric rings, lying between successive circles with radii 1, 2, 3, 4, 5. (The innermost circle counts as a ring.)</p>
<p>Friar Tuck and Robin both fired a number of arrows.</p>
<p>“Yours are all closer to the centre than mine,” said Tuck ruefully.</p>
<p>“That’s why I’m the leader of this outlaw band,” Robin pointed out.</p>
<p>“But let’s look on the bright side,” Tuck replied. “The Total area of the rings that I hit is the same as the total area of the rings you hit. So that makes us equally accurate, right?”</p>
<p>Naturally, Robin pointed out the fallacy...but:</p>
<p>Which rings did the two archers hit? (A ring may be hit more than once, but it only counts once towards the area.)<br />
</p>
<p>For a bonus point: what is the smallest number of rings for which this question as two or more different answers?<br />
</p>
<p>For a further bonus point: if each archer’s rings are adjacent – no gaps where a ring that has not been hit lies between two that have – what is the smallest number of rings for which this question has two or more different answers?<br />
</p><p><img style="float: right; margin-left: 5px; margin-right: 5px;" src="/images/warwickchallenges/2009/11/09/target.jpg?maxWidth=500" alt="Target Practice" border="0" /></p>
<p>Robin Hood and Friar Tuck were engaging in some target practice. The target was a series of concentric rings, lying between successive circles with radii 1, 2, 3, 4, 5. (The innermost circle counts as a ring.)</p>
<p>Friar Tuck and Robin both fired a number of arrows.</p>
<p>“Yours are all closer to the centre than mine,” said Tuck ruefully.</p>
<p>“That’s why I’m the leader of this outlaw band,” Robin pointed out.</p>
<p>“But let’s look on the bright side,” Tuck replied. “The Total area of the rings that I hit is the same as the total area of the rings you hit. So that makes us equally accurate, right?”</p>
<p>Naturally, Robin pointed out the fallacy...but:</p>
<p>Which rings did the two archers hit? (A ring may be hit more than once, but it only counts once towards the area.)<br />
</p>
<p>For a bonus point: what is the smallest number of rings for which this question as two or more different answers?<br />
</p>
<p>For a further bonus point: if each archer’s rings are adjacent – no gaps where a ring that has not been hit lies between two that have – what is the smallest number of rings for which this question has two or more different answers?<br />
</p>Whodunni's Dice by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/whodunnis_dice/2009-11-03T10:58:40Z2009-11-02T10:06:42Z<p>Grumpelina, the Great Whodunni’s beautiful assistant, placed a blindfold over the eyes of the famous stage magician. A member of the audience then rolled three dice.</p>
<p>"Multiply the number on the first dice by 2 and add 5,” said Whodunni. “Then multiply the result by 5 and add the number on the second dice. Finally, multiply the result by 10 and add the number on the third dice.”</p>
<p>As he spoke, Grumpelina chalked up the sums on a blackboard which was turned to face the audience so that Whodunni could not have seen it, even if the blindfold had been transparent.</p>
<p>“What do you get?” Whodunni asked.</p>
<p>“Seven hundred and sixty-three,” said Grumpelina.</p>
<p>Whodunni made strange passes in the air. “Then the dice were...”</p>
<p>What? (And how did he do it?)<br />
</p><p>Grumpelina, the Great Whodunni’s beautiful assistant, placed a blindfold over the eyes of the famous stage magician. A member of the audience then rolled three dice.</p>
<p>"Multiply the number on the first dice by 2 and add 5,” said Whodunni. “Then multiply the result by 5 and add the number on the second dice. Finally, multiply the result by 10 and add the number on the third dice.”</p>
<p>As he spoke, Grumpelina chalked up the sums on a blackboard which was turned to face the audience so that Whodunni could not have seen it, even if the blindfold had been transparent.</p>
<p>“What do you get?” Whodunni asked.</p>
<p>“Seven hundred and sixty-three,” said Grumpelina.</p>
<p>Whodunni made strange passes in the air. “Then the dice were...”</p>
<p>What? (And how did he do it?)<br />
</p>Swallowing Elephants by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/swallowing_elephants/2009-10-30T15:02:13Z2009-10-26T11:19:50Z<p>Elephants always wear pink trousers.<br />
Every creature that eats honey can play the bagpipes.<br />
Anything that is easy to swallow eats honey.<br />
No creature that wears pink trousers can play the bagpipes.</p>
<p>Therefore: Elephants are easy to swallow.</p>
<p>Is the deduction correct or not?<br />
</p><p>Elephants always wear pink trousers.<br />
Every creature that eats honey can play the bagpipes.<br />
Anything that is easy to swallow eats honey.<br />
No creature that wears pink trousers can play the bagpipes.</p>
<p>Therefore: Elephants are easy to swallow.</p>
<p>Is the deduction correct or not?<br />
</p>Digital Cubes by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/digital_cubes/2010-05-10T10:59:00Z2009-10-19T09:27:21Z<p>The number 153 is equal to the sum of the cubes of its digits:</p>
<p>1<sup>3</sup> + 5<sup>3</sup> + 3<sup>3</sup> = 1 + 125 + 27 = 153</p>
<p>There are three other 3-digit numbers with the same property, excluding numbers like 001 with a leading zero.</p>
<p> Can you find them?<br />
</p><p>The number 153 is equal to the sum of the cubes of its digits:</p>
<p>1<sup>3</sup> + 5<sup>3</sup> + 3<sup>3</sup> = 1 + 125 + 27 = 153</p>
<p>There are three other 3-digit numbers with the same property, excluding numbers like 001 with a leading zero.</p>
<p> Can you find them?<br />
</p>The Statue of Pallas Athene by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/the_statue_of/2009-10-13T13:35:41Z2009-10-12T11:20:44Z<p>According to a puzzle book published in the Middle Ages, the statue of the goddess Pallas Athene was inscribed with the following information:</p>
<p>“I, Pallas, am made from the purest gold, donated by five generous poets. Kariseus gave half; Thespian an eighth. Solon gave one-tenth; Themison gave one-twentieth. And the remaining nine talents’ worth of gold was provided by the good Aristodokos.”</p>
<p>How much did the statue cost in total? [A talent is a unit of weight, roughly one kilogram.]<br />
</p><p>According to a puzzle book published in the Middle Ages, the statue of the goddess Pallas Athene was inscribed with the following information:</p>
<p>“I, Pallas, am made from the purest gold, donated by five generous poets. Kariseus gave half; Thespian an eighth. Solon gave one-tenth; Themison gave one-twentieth. And the remaining nine talents’ worth of gold was provided by the good Aristodokos.”</p>
<p>How much did the statue cost in total? [A talent is a unit of weight, roughly one kilogram.]<br />
</p>Return of the Maths Challenge! by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/return_of_the/2009-10-05T15:40:47Z2009-10-05T15:15:26Z<p><a href="http://bit.ly/42K3fb"><img style="border: 0pt none; margin-left: 5px; margin-right: 5px; float: left;" src="http://blogs.warwick.ac.uk/images/warwickchallenges/2009/10/05/hoardofmathematicaltrasures.jpg?maxWidth=500" alt="Hoard of Mathematical Treasures" border="0" width="120" /></a>After a long summer break, the Maths Challenges will be returning to your twitter feed next week!</p>
<p>The Warwick Maths Challenges are based on the books of Professor Ian Stewart. </p>
<p>Prof Stewart’s latest book – <a href="http://bit.ly/42K3fb">Hoard of Mathematical Treasures</a> – is out now and we will bring you some of the best challenges and brain teasers every Monday morning.</p><p><a href="http://bit.ly/42K3fb"><img style="border: 0pt none; margin-left: 5px; margin-right: 5px; float: left;" src="http://blogs.warwick.ac.uk/images/warwickchallenges/2009/10/05/hoardofmathematicaltrasures.jpg?maxWidth=500" alt="Hoard of Mathematical Treasures" border="0" width="120" /></a>After a long summer break, the Maths Challenges will be returning to your twitter feed next week!</p>
<p>The Warwick Maths Challenges are based on the books of Professor Ian Stewart. </p>
<p>Prof Stewart’s latest book – <a href="http://bit.ly/42K3fb">Hoard of Mathematical Treasures</a> – is out now and we will bring you some of the best challenges and brain teasers every Monday morning.</p>Maths Challenge #10 - Perfect Square by Eleanor LovellEleanor Lovellhttps://blogs.warwick.ac.uk/warwickchallenges/entry/maths_challenge_10/2009-06-23T20:13:19Z2009-06-22T10:25:03Z<p>What is the largest perfect square number that uses each digit 123456789 exactly once?</p><p>What is the largest perfect square number that uses each digit 123456789 exactly once?</p>