New PuzzlesPuzzles and riddles submitted to BrainDen.com - Brain Teasers Forums.
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Fri, 24 Oct 2014 18:00:37 +00005Braindencom-NewPuzzleshttps://feedburner.google.comSubscribe with My Yahoo!Subscribe with NewsGatorSubscribe with My AOLSubscribe with BloglinesSubscribe with NetvibesSubscribe with GoogleSubscribe with PageflakesA simple polygon problem.
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<p><span style="font-family:verdana, geneva, sans-serif">An arbitrary convex polygon has a vector drawn from the midpoint of each of its sides.</span></p>
<p><span style="font-family:verdana, geneva, sans-serif">The vectors are perpendicular to the sides, pointed outward, and have the same lengths as the sides themselves.</span></p>
<p> </p>
<p><span style="font-family:verdana, geneva, sans-serif">What is the sum of these vectors?</span></p><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/mLAd3b61KqE" height="1" width="1"/>Fri, 24 Oct 2014 18:00:37 +0000http://brainden.com/forum/index.php/topic/17198-a-simple-polygon-problem/http://brainden.com/forum/index.php/topic/17198-a-simple-polygon-problem/Count the Flags
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<em>(Hello, friends. This is yet another puzzle from BWOC. I don't know the solution to this one yet, so I was thinking we could work on this together.)</em><br><br>
You are tasked with designing a robot to explore a large but finite maze. The maze is drawn on a square grid, and walls exist on some of the edges of the square grid. Some of the squares contain a flag.<br><br>
Your robot may interact with the world in the following ways:<br><br>
1) Check which of the 4 adjacent edges contain walls.<br><br>
2) Move to one of the 4 adjacent squares (provided there is no wall in the way).<br><br>
3) Check if there is a flag on your square.<br><br>
4) Pick up a flag (provided there is a flag on your square and the robot is not already holding a flag).<br><br>
5) Put down a flag (provided the robot is holding a flag and there is not already a flag on your square).<br><br>
6) Generate a random bit.<br><br>
7) Output a number.<br><br>
Your robot will be placed in a maze. The maze will contain some number of flags (from 100 to 1000). All flags will be reachable from the robot’s starting position. Your robot is tasked with determining the number of flags. The robot may take as long as it needs, but may only output one number and must output the correct answer eventually, with probability 1.<br><br>
The catch is that your robot is not Turing complete. It only has a finite amount of memory. You can give your robot as much memory as you need, but it must succeed on arbitrarily large mazes<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/MHn4uAViqk8" height="1" width="1"/>Fri, 24 Oct 2014 10:05:54 +0000http://brainden.com/forum/index.php/topic/17197-count-the-flags/http://brainden.com/forum/index.php/topic/17197-count-the-flags/Retirement
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<p>The retirement age in Bolandia will be raised from 66 to 67 over two years: <span style="font-family:TT6A4o00;font-size:15px">every six months the minimum age will jump up by 3 months. </span><span style="font-family:TT6A4o00;font-size:15px">Anyone over the retirement age on the date they apply will immediately get a free retired-person’s bus pass. </span></p>
<br><div><span style="font-size:11pt;font-family:TT6A4o00">How much </span><span style="font-size:11pt;font-family:TT6A3o00">younger </span><span style="font-size:11pt;font-family:TT6A4o00">could one person with a free retired-person’s bus pass be than someone not able to get one? </span></div>
<div>
<p> </p>
<p><span style="font-size:11pt;font-family:TT6A3o00">A </span><span style="font-size:11pt;font-family:TT6A4o00">It’s not possible to be younger.</span></p>
<p><span style="font-size:11pt;font-family:TT6A3o00">B </span><span style="font-size:11pt;font-family:TT6A4o00">Just under 3 months. </span></p>
<p><span style="font-size:11pt;font-family:TT6A3o00">C </span><span style="font-size:11pt;font-family:TT6A4o00">Just under 6 months.</span></p>
<p><span style="font-size:11pt;font-family:TT6A4o00">D Just under 1 year</span></p>
<p> </p>
<p>Please show workings.</p>
</div>
<p> </p><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/u0IqjfX71eY" height="1" width="1"/>Mon, 20 Oct 2014 23:27:10 +0000http://brainden.com/forum/index.php/topic/17196-retirement/http://brainden.com/forum/index.php/topic/17196-retirement/Stand and topple
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<p><a class='resized_img' rel='lightbox[340644]' id='ipb-attach-url-' href="http://brainden.com/forum/uploads/monthly_10_2014/post-53237-0-82653000-1413707786.jpg" title="roundice.jpg - Size: 17.69KB"><img itemprop="image" src="http://brainden.com/forum/uploads/monthly_10_2014/post-53237-0-82653000-1413707786.jpg" class='bbc_img linked-image' alt="roundice.jpg" /></a>
</p>
<div>A fair die was rounded on its four corners</div>
<div>just tangent to top and bottom edges.</div>
<div>On a fair throw ..will you bet for "stands" or "toppled" ? </div><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/tUhnVh7GbUs" height="1" width="1"/>Sun, 19 Oct 2014 08:37:47 +0000http://brainden.com/forum/index.php/topic/17195-stand-and-topple/http://brainden.com/forum/index.php/topic/17195-stand-and-topple/Order in a random set of alphabet letters
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Suppose you wrote all the letters to the alphabet down in a random sequence. What is the probability that you write down at least 5 letters in proper alphabetical order?<br><br>
For clarity (hopefully): for a letter to be in proper alphabetical order, the letter does not have to be moved or switched to the left past another letter in the given list. When deciding how many letters in a given random list are in order note that Letters need not be in adjacent order A,B,C,D,...) to be in proper alphabetical order. See examples below for more clarity.<br><br>
Examples:<br>
A L C E H. .... 4 letters are in proper alphabetical order (by dropping L)<br>
ZYXWU ..... 1 letter is in proper letter order, pick one<br>
HDAZV ........ 2 letters are in proper letter order, AZ for example<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/b9l1S3PGe80" height="1" width="1"/>Sat, 18 Oct 2014 12:50:30 +0000http://brainden.com/forum/index.php/topic/17194-order-in-a-random-set-of-alphabet-letters/http://brainden.com/forum/index.php/topic/17194-order-in-a-random-set-of-alphabet-letters/Easy magical Triangle
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<p>Hi dear friends...</p>
<p> </p>
<p>1- Draw an equilateral triangle ABC.</p>
<p>2- Make two points on each side to get (ABC+6point= 9 points), with 4 points on each side.</p>
<p>3- Give the numbers( 1 to 9 ) to these points, so that the sum of 4 numbers on each side is the same.</p>
<p>i.e.</p>
<p>A+point1+point2+B= B+point3+point4+C= C+point5+point6+A</p>
<p> </p>
<p> </p>
<p>have fun</p><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/IFCejBRgm3A" height="1" width="1"/>Sat, 18 Oct 2014 08:06:42 +0000http://brainden.com/forum/index.php/topic/17193-easy-magical-triangle/http://brainden.com/forum/index.php/topic/17193-easy-magical-triangle/Digit Patterns
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This is a variant of BMAD's recent post on the probability of choosing a natural number with a 1 in the digits.<br><br>
From the set of all natural numbers...<br><br>
1) What is the probability of choosing a natural number whose digits sum to an even number?<br><br>
2) What is the probability of choosing a natural number whose digits sum to a number divisible by N?<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/v2h1D5IAQ7E" height="1" width="1"/>Fri, 17 Oct 2014 14:49:24 +0000http://brainden.com/forum/index.php/topic/17192-digit-patterns/http://brainden.com/forum/index.php/topic/17192-digit-patterns/Probability of picking a natural digit
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What is the probability that you can pick a natural number that contains the digit 1 in the set of natural numbers?<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/PlDWz2y1O88" height="1" width="1"/>Fri, 17 Oct 2014 13:51:54 +0000http://brainden.com/forum/index.php/topic/17191-probability-of-picking-a-natural-digit/http://brainden.com/forum/index.php/topic/17191-probability-of-picking-a-natural-digit/Risk Battles
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In the popular board game, Risk, players try to occupy as much territory as possible by moving around their armies and attacking territory owned by other players. These battles are settled through a series of dice rolls.<br><br>
The attacker rolls up to three dice, while the defender only rolls two. First, the highest values rolled by each player are compared. If the attacker rolled a higher value, the defender loses a unit. Otherwise, the attacker loses a unit. Then, the second highest values are compared in the same manner and one of the players loses a unit. This goes on until one of the armies becomes depleted.<br><br>
If the attacker has fewer than three units, he may only roll the same number of dice as the number of units. Likewise, if the defender has fewer the two units, he may only roll one die.<br><br>
1) What is the probability that a dice roll results in a draw?<br><br>
Okay, so now pretend there is a battle where the attacker has n units, and the defender has m units.<br><br>
2) What is the probability that the attacker wins the exchange?<br><br>
3) What is the average/best/worst case running time of the entire exchange?<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/R-jsWA5xTJQ" height="1" width="1"/>Thu, 16 Oct 2014 17:14:56 +0000http://brainden.com/forum/index.php/topic/17190-risk-battles/http://brainden.com/forum/index.php/topic/17190-risk-battles/Octodad Tries To Walk Straight
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(This puzzle is based off of a student-created problem on an exam for an undergraduate Intro to Discrete Mathematics course at UC Berkeley)<br><br>
Octodad has trouble walking straight. When he takes a step, he moves one yard in any random direction.<br><br>
He decides to try and practice moving around on an xy-coordinate plane. If he starts at the origin, what will be the mean and standard deviation of his distance from the origin after taking a large number of steps?<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/YHHqQydY4Ng" height="1" width="1"/>Thu, 16 Oct 2014 16:45:13 +0000http://brainden.com/forum/index.php/topic/17189-octodad-tries-to-walk-straight/http://brainden.com/forum/index.php/topic/17189-octodad-tries-to-walk-straight/Find The Apples
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(This puzzle is taken from a blog called By Way Of Contradiction)<br><br>
Imagine the following two player game. Alice secretly fills 3 rooms with apples. She has an infinite supply of apples and infinitely large rooms, so each room can have any non-negative integer number of apples. She must put a different number of apples in each room. Bob will then open the doors to the rooms in any order he chooses. After opening each door and counting the apples, but before he opens the next door, Bob must accept or reject that room. Bob must accept exactly two rooms and reject exactly one room. Bob loves apples, but hates regret. Bob wins the game if the total number of apples in the two rooms he accepts is a large as possible. Equivalently, Bob wins if the single room he rejects has the fewest apples. Alice wins if Bob loses.<br><br>
Which of the two players has the advantage in this game?<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/7OWrL2j85aE" height="1" width="1"/>Thu, 16 Oct 2014 16:32:12 +0000http://brainden.com/forum/index.php/topic/17188-find-the-apples/http://brainden.com/forum/index.php/topic/17188-find-the-apples/Upside Down Cake
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(This puzzle is from a blog called By Way Of Contradiction.)<br><br>
Imagine you have a circular cake, that is frosted on the top. You cut a d degree slice out of it, and then put it back, but rotated so that it is upside down. Now, d degrees of the cake have frosting on the bottom, while 360 minus d degrees have frosting on the top. Rotate the cake d degrees, take the next slice, and put it upside down. Now, assuming the d is less than 180, 2d degrees of the cake will have frosting on the bottom.<br><br>
If d is 60 degrees, then after you repeat this procedure, flipping a single slice and rotating 6 times, all the frosting will be on the bottom. If you repeat the procedure 12 times, all of the frosting will be back on the top of the cake.<br><br>
For what values of d does the cake eventually get back to having all the frosting on the top?<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/jdcTAaplqVo" height="1" width="1"/>Thu, 16 Oct 2014 16:27:34 +0000http://brainden.com/forum/index.php/topic/17187-upside-down-cake/http://brainden.com/forum/index.php/topic/17187-upside-down-cake/Brain teaser help???
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<br><br>
It's Friday and you have completed your first week at work. You have been introduce to several people and have received your first company newsletter. There is a meet your employees section that features five employees; Travis, Roberto, Mike, Stephanie, Vickie. Using the clues below your goal is to figure out each persons job title, how long they have worked for the company. (1,3,5,15, or 30 years), and how they arrive to work.<br><br>
1. Travis has worked longer than the Specialist but not as long as the person who rides the bus. 2. Since she uses public transportation, Stephanie enjoys playing Candy Crush on her way to work. 3. Roberto has been at with the company exactly double the number of years as the Attorney. 4. Vickie or the person who rides the bullet train celebrated 15 years of service. 5. Mike was promoted two years ago to a Consultant. 6. A seat is not always available for the Security Officer and has to stand on the way to work at times. 7. The Project Manager position requires a minimum of six years on the job experience. 8. The Specialist can leave at any time since she does not follow a public transportation schedule. 9. Subway transportation became available eight years ago. 10. The car driver has been driving to work for more than six years. 11. During the last winter storm, only Travis and the Attorney arrived on time; the ones who travelled by bicycle, car, and bus were late.<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/SGEHOra4NVA" height="1" width="1"/>Tue, 14 Oct 2014 23:11:02 +0000http://brainden.com/forum/index.php/topic/17186-brain-teaser-help/http://brainden.com/forum/index.php/topic/17186-brain-teaser-help/more simple circles
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<p><span style="color:rgb(0,0,0);font-family:Times;font-size:medium">Place N unit circles (radius=1) together without overlapping. What is the smallest circle which can be circumscribed around the unit circles? </span></p><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/iGklc3j9Bdo" height="1" width="1"/>Tue, 14 Oct 2014 20:35:34 +0000http://brainden.com/forum/index.php/topic/17185-more-simple-circles/http://brainden.com/forum/index.php/topic/17185-more-simple-circles/simple circle
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<p><span style="color:rgb(0,0,0);font-family:Times;font-size:medium">What is the largest circle you can construct in a unit cube?</span></p><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/CkoVujJ5Xzs" height="1" width="1"/>Tue, 14 Oct 2014 20:33:12 +0000http://brainden.com/forum/index.php/topic/17184-simple-circle/http://brainden.com/forum/index.php/topic/17184-simple-circle/