New PuzzlesPuzzles and riddles submitted to BrainDen.com - Brain Teasers Forums.
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Fri, 23 Jan 2015 16:24:12 +00005Braindencom-NewPuzzleshttps://feedburner.google.comSubscribe with My Yahoo!Subscribe with NewsGatorSubscribe with My AOLSubscribe with BloglinesSubscribe with NetvibesSubscribe with GoogleSubscribe with PageflakesConditionally conflicting
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<p><span style="font-family:verdana, geneva, sans-serif">What word has the opposite meaning of "if"?</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/mZPyvGMRjJk" height="1" width="1" alt=""/>Fri, 23 Jan 2015 16:24:12 +0000http://brainden.com/forum/index.php/topic/17291-conditionally-conflicting/http://brainden.com/forum/index.php/topic/17291-conditionally-conflicting/Ascending anagrams
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<p><span style="font-family:verdana, geneva, sans-serif">I drew five letters from the Scrabble pile.</span></p>
<p><span style="font-family:verdana, geneva, sans-serif">Amazingly, they were the five vowels, a e i o u.</span></p>
<p><span style="font-family:verdana, geneva, sans-serif">I discarded two, at random, and drew two different consonants.</span></p>
<p><span style="font-family:verdana, geneva, sans-serif">Playing with these five letters,</span></p>
<p> </p>
<p><span style="font-family:verdana, geneva, sans-serif">I arranged them into a 1-syllable word</span></p>
<p><span style="font-family:verdana, geneva, sans-serif">I rearranged them into a 2-syllable word</span></p>
<p><span style="font-family:verdana, geneva, sans-serif">I rearranged them again, into a 3-syllable word.</span></p>
<p> </p>
<p><span style="font-family:verdana, geneva, sans-serif">What were my five letters, and what were the words?</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/A8YmL-7nVNo" height="1" width="1" alt=""/>Fri, 23 Jan 2015 15:59:49 +0000http://brainden.com/forum/index.php/topic/17290-ascending-anagrams/http://brainden.com/forum/index.php/topic/17290-ascending-anagrams/Reflect on this
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<p>You find four snips of paper on which are written these numbers: 13, 14, 95 and 62.</p>
<p>You see a fifth snip of paper. What number is written on it?</p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/RSlt3RTUXBk" height="1" width="1" alt=""/>Fri, 23 Jan 2015 15:42:51 +0000http://brainden.com/forum/index.php/topic/17288-reflect-on-this/http://brainden.com/forum/index.php/topic/17288-reflect-on-this/Pour over this
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<p><span style="font-family:verdana, geneva, sans-serif">You have two 10-liter beakers filled with water, and two empty beakers, of capacity 4 and 5 liters, respectively. You may pour from one beaker to another, in such a way that either the source beaker is emptied, or the receiving beaker is filled. The object is for the two smaller beakers each to contain 2 liters of water. No water is to be wasted, and no more than none pourings is allowed.</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/HslAO_-D3Bw" height="1" width="1" alt=""/>Thu, 22 Jan 2015 04:46:04 +0000http://brainden.com/forum/index.php/topic/17287-pour-over-this/http://brainden.com/forum/index.php/topic/17287-pour-over-this/The mutilated tetrahedron
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<p><span style="font-family:verdana, geneva, sans-serif">A solid in the shape of a regular tetrahedron had uniform density and a mass of 1 kg. It was mutilated by the removal of its vertices, each made by a planar cut, parallel to its opposite face. The solid now has eight faces, whose areas are 1, 2, 3, 4, 5, 6, 7 and 8 square units, in some order. What is the area of its original faces? </span><span style="font-family:verdana, geneva, sans-serif">What is the mass of the resulting solid?</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/IfwwNaqd8M4" height="1" width="1" alt=""/>Thu, 22 Jan 2015 04:03:00 +0000http://brainden.com/forum/index.php/topic/17286-the-mutilated-tetrahedron/http://brainden.com/forum/index.php/topic/17286-the-mutilated-tetrahedron/A tourist in Moscow
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<p><span style="color:rgb(0,0,51);font-family:Times;font-size:medium">The tourist has come to the Moscow by train. All-day-long he wandered randomly through the streets. Than he had a supper in the cafe on the square and decided to return to the station only through the streets that he has passed an odd number of times. </span></p>
<p> </p>
<p><span style="color:rgb(0,0,51);font-family:Times;font-size:medium">Prove that he is always able to do that.</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/RHyEwCuMw4U" height="1" width="1" alt=""/>Tue, 20 Jan 2015 19:01:51 +0000http://brainden.com/forum/index.php/topic/17285-a-tourist-in-moscow/http://brainden.com/forum/index.php/topic/17285-a-tourist-in-moscow/A circle in a square hole.
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<p><span style="color:rgb(0,0,51);font-family:Times;font-size:medium">Given 120 unit squares arbitrarily situated in the 20x25 rectangle. </span></p>
<p><span style="color:rgb(0,0,51);font-family:Times;font-size:medium">Prove that You can place a circle with the unit diameter without intersecting any of the squares.</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/j2kofQ7btsk" height="1" width="1" alt=""/>Tue, 20 Jan 2015 18:52:46 +0000http://brainden.com/forum/index.php/topic/17284-a-circle-in-a-square-hole/http://brainden.com/forum/index.php/topic/17284-a-circle-in-a-square-hole/Product makes the sums
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<p>Does their exist four distinct natural numbers (a,b,c,d) where a*b, c*d is equivalent to the sum of all four numbers?</p>
<p> </p>
<p>What if i add the condition that a*d also equals the sum of all four numbers?</p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/WCQ3oKD7ebw" height="1" width="1" alt=""/>Mon, 19 Jan 2015 16:15:52 +0000http://brainden.com/forum/index.php/topic/17283-product-makes-the-sums/http://brainden.com/forum/index.php/topic/17283-product-makes-the-sums/Illuminating a Convex Solid At Higher Dimensions
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<p>This is a follow-up to <a href='http://brainden.com/forum/index.php/topic/17281-illuminating-a-convex-solid/' class='bbc_url' title=''>Illuminating a Convex Solid</a>. I do not know the answer to this problem.</p>
<p> </p>
<p><em>How many lights are necessary to completely illuminate a convex solid in N </em><em>dimensions?</em></p>
<p style="margin-left:0px"> </p>
<p style="margin-left:0px">Same conditions as before:</p>
<ul><li>We are working in an otherwise empty N-dimensional space.</li>
<li>The lights are point sources.</li>
<li>The solid is illuminated at every point on its surface where a straight line can be drawn uninterrupted between it and a light source.</li>
</ul><p style="margin-left:0px">Let me also add:</p>
<ul><li>Lights cannot be placed "at infinity".</li>
</ul><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/O5rrbua7JHw" height="1" width="1" alt=""/>Thu, 15 Jan 2015 14:34:40 +0000http://brainden.com/forum/index.php/topic/17282-illuminating-a-convex-solid-at-higher-dimensions/http://brainden.com/forum/index.php/topic/17282-illuminating-a-convex-solid-at-higher-dimensions/Illuminating a Convex Solid
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<p>I'm not sure if this has been posted yet, but it is a nice puzzle.</p>
<p> </p>
<p><em>Can three lights always be placed outside of any convex solid such that the solid is completely illuminated?</em></p>
<p> </p>
<p>You can assume that:</p>
<ul><li>We are working in an otherwise empty three-dimensional space</li>
<li>The lights are point sources.</li>
<li>The solid is illuminated at every point on its surface where a straight line can be drawn uninterrupted between it and a light source.</li>
</ul><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/cSN9gPndKA4" height="1" width="1" alt=""/>Thu, 15 Jan 2015 12:08:38 +0000http://brainden.com/forum/index.php/topic/17281-illuminating-a-convex-solid/http://brainden.com/forum/index.php/topic/17281-illuminating-a-convex-solid/The n-gon eats out
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<p><span style="font-family:verdana, geneva, sans-serif"><em><span style="font-family:georgia, serif"><strong>n</strong></span></em> people party at a restaurant, sitting at the vertices of an <span style="font-family:verdana, geneva, sans-serif"><em><span style="font-family:georgia, serif"><strong>n</strong></span></em></span>-gon-shaped dinner table. Their orders have been mixed up -- in fact, none of them have received the correct entree. Show that the table may be rotated so that at least two people are sitting in front of the correct entree.</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/PoSH8uO8Bp8" height="1" width="1" alt=""/>Thu, 15 Jan 2015 11:50:15 +0000http://brainden.com/forum/index.php/topic/17280-the-n-gon-eats-out/http://brainden.com/forum/index.php/topic/17280-the-n-gon-eats-out/The average chord, revisited
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<p><span style="font-family:verdana, geneva, sans-serif">The <a href='http://en.wikipedia.org/wiki/Bertrand_paradox_%28probability%29' class='bbc_url' title='External link' rel='nofollow external'>Bertrand paradox</a> asks the probability of a random chord being longer than the side of an inscribed equilateral triangle. At least three (see link) answers are possible depending on how "random" is employed in drawing the chord. Jaynes argues that one of the answers is "best." Here's a cute question, not of my making, that might also lead to a preferred answer from among the three. Or maybe not.</span></p>
<p> </p>
<p><span style="font-family:verdana, geneva, sans-serif">The question first notes that the sum of the lengths of all sides and diagonals emanating from a vertex of a regular n-gon inscribed in the unit circle is 2 cot (pi/2n) and then asks us to use this fact to find the <span style="font-family:georgia, serif"><strong>average length</strong></span> of a chord of the unit circle.</span></p>
<p> </p>
<p><span style="font-family:verdana, geneva, sans-serif">Does the answer to this question give credence to one of the three answers (again see link) over the other two? Is it Jaynes' choice?</span></p><img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/P7M4OwJ5D_I" height="1" width="1" alt=""/>Thu, 15 Jan 2015 11:34:11 +0000http://brainden.com/forum/index.php/topic/17279-the-average-chord-revisited/http://brainden.com/forum/index.php/topic/17279-the-average-chord-revisited/P(A)
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find a formula for the perimeter of a regular polygon as a function of its area. It needs to be shown that as the number of sides of a polygon of given area increases, the perimeter of the figure <br>
decreases.<img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/aY0tZPcgZm4" height="1" width="1" alt=""/>Wed, 14 Jan 2015 13:02:39 +0000http://brainden.com/forum/index.php/topic/17278-pa/http://brainden.com/forum/index.php/topic/17278-pa/Knight moves
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Put a knight on a 4x4 chessboard that is able to make standard moves only. How many moves must it take until it is able to land on every square? Does it matter where it begins? What if the board was 5x5?<img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/FmQ3gm0ylRA" height="1" width="1" alt=""/>Wed, 14 Jan 2015 12:51:41 +0000http://brainden.com/forum/index.php/topic/17277-knight-moves/http://brainden.com/forum/index.php/topic/17277-knight-moves/From my calculus class
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Here is a calculus problem from a class i teach. The problem itself illustrates the benefits of recognizing the fluidity and openness one can take in mathematics as the direct approach is ugly and messy but there is a simpler and elegant indirect way of solving this one too. Enjoy.<br><br><br><br>
Find the equation of the line tangent to the ellipse b^2*x^2 + a^2*y^2 = a^2*b^2 in the first quadrant that forms with the coordinate axes the triangle of smallest possible area (a & b are positive constants)<img src="//feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/PQAevjHebEk" height="1" width="1" alt=""/>Wed, 14 Jan 2015 12:46:27 +0000http://brainden.com/forum/index.php/topic/17276-from-my-calculus-class/http://brainden.com/forum/index.php/topic/17276-from-my-calculus-class/