New PuzzlesPuzzles and riddles submitted to BrainDen.com - Brain Teasers Forums.
http://brainden.com/forum
Thu, 30 Oct 2014 22:24:20 +00005Braindencom-NewPuzzleshttps://feedburner.google.comSubscribe with My Yahoo!Subscribe with NewsGatorSubscribe with My AOLSubscribe with BloglinesSubscribe with NetvibesSubscribe with GoogleSubscribe with PageflakesMirror Primes
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/UuPD4EW-KRU/
How many primes are the between 9 and 100 such that reversing the digits yields another prime?<br><br>
This by itself is way too easy, so try to answer this using as little brute force as possible (or try to lower the upper bound as much as possible).<img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/UuPD4EW-KRU" height="1" width="1"/>Thu, 30 Oct 2014 22:24:20 +0000http://brainden.com/forum/index.php/topic/17204-mirror-primes/http://brainden.com/forum/index.php/topic/17204-mirror-primes/Marked Hat
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/ugwdQWVhgZQ/
<div><a class='resized_img' rel='lightbox[340784]' id='ipb-attach-url-' href="http://brainden.com/forum/uploads/monthly_10_2014/post-53237-0-53776000-1414334396.jpg" title="Clockworkorange.jpg - Size: 14.06KB"><img itemprop="image" src="http://brainden.com/forum/uploads/monthly_10_2014/post-53237-0-53776000-1414334396.jpg" class='bbc_img linked-image' alt="Clockworkorange.jpg" /></a>
</div>
<div>The warden will release the 7 prisoners to be hang on</div>
<div>everyday next week if they can mark their hats with a</div>
<div>number card from a playing card deck so that anyone may</div>
<div>see and guess right the others prisoner's day and time</div>
<div>of executions. </div>
<div> </div>
<div><span style="font-size:14px">The cards shall be erected on hat through a small </span></div>
<div>straight cut on top. </div>
<div> </div>
<div><span style="font-size:14px">The schedule will be randomly drawn for everyone. </span></div>
<div> </div>
<div>No prisoner must tell his scheduled day (Sun,Mon..Sat) </div>
<div>and hour of execution (1:00,2:00,3:00 ... 12:00).</div>
<div> </div>
<div>Since these prisoners had freed themselves a couple </div>
<div>of times on this same prison it should not be hard for </div>
<div>them to agree on a plan.</div>
<div> </div>
<div> </div>
<div>What code strategy works for them?</div><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/ugwdQWVhgZQ" height="1" width="1"/>Sun, 26 Oct 2014 14:51:34 +0000http://brainden.com/forum/index.php/topic/17202-marked-hat/http://brainden.com/forum/index.php/topic/17202-marked-hat/Governors of Poker
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/418dL3BHa2M/
<div>The twenty two inhabitants of El Paso will vote for</div>
<div>their favorite poker player as the new Governor..</div>
<div>Four candidates are running for election:</div>
<div>1. Speedy Deal</div>
<div>2. Damon Blinds</div>
<div>3. Heather Raise</div>
<div>4. Clover Call</div>
<div>Each voter picks a card from an official deck as a </div>
<div>valid ballot..The first one to cast a vote at the</div>
<div>precinct place his card on ballot box in front of the </div>
<div>tally official. And to cast a vote the others place </div>
<div>their card on top of the previous voter's card. </div>
<div>If this was a sucessful electoral process.. </div>
<div>how did the voters vote?</div><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/418dL3BHa2M" height="1" width="1"/>Sat, 25 Oct 2014 17:39:03 +0000http://brainden.com/forum/index.php/topic/17201-governors-of-poker/http://brainden.com/forum/index.php/topic/17201-governors-of-poker/Six sixes to make 1,000 (modified version)
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/niwPPXD5wD0/
<p><strong>Form as many horizontal-style arithmetical expressions as possible that equal 1,000.</strong></p>
<p> </p>
<p>In order to limit the total number of possible solutions, the following rules of mine are in place:</p>
<p>----------------------------------------------------------------------------------------------------------------------------</p>
<p> </p>
<p>Use exactly six sixes.</p>
<p> </p>
<p>Use no more than one pair of parentheses.</p>
<p> </p>
<p>Use no more than one "/" symbol.</p>
<p> </p>
<p>Use no more than two decimal points.</p>
<p> </p>
<p>Use no more than one minus (subtraction) sign.</p>
<p> </p>
<p>Concatenation <strong>is</strong> allowed.</p>
<p> </p>
<p>No other symbols/characters/operations are allowed.</p>
<p> </p>
<p> </p><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/niwPPXD5wD0" height="1" width="1"/>Sat, 25 Oct 2014 17:26:19 +0000http://brainden.com/forum/index.php/topic/17200-six-sixes-to-make-1000-modified-version/http://brainden.com/forum/index.php/topic/17200-six-sixes-to-make-1000-modified-version/Removing pawns - the game
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/0aBjw6DtzJs/
<p>Here is the simple game I've invented (if someone invented it before, then I'm not aware of it):</p>
<p> </p>
<p>A pawn is placed on every square of m*n chessboard.<br>
Two players take alternate turns removing pawns.<br>
On each turn, a player removes one or more pawns.<br>
All pawns removed in a single turn have to be taken from the same row or the same column.<br>
The player who cannot make a move loses (alternatively: the player who takes the last pawn wins).</p>
<p>Let's call the player who begins the "first player" and the other one the "second player".</p>
<p>Which player (the first or the second) has a winning strategy depending on the chessboard dimensions?<br>
</p>
<p>PS The game can be played on more interesting boards. Just draw some number of crossing lines</p>
<p>on a sheet of paper and place a pawn on each point of intersection of the lines.</p>
<p>The pawns removed in a single turn should come from a single line.</p>
<p>I've tried to play this game on the pentagram (the star: five lines, ten points/pawns) with my 9 years old daughter.</p>
<p>It was fun. Determining which player wins was even bigger fun.</p><img src="http://feeds.feedburner.com/~r/Braindencom-NewPuzzles/~4/0aBjw6DtzJs" height="1" width="1"/>Sat, 25 Oct 2014 11:41:13 +0000http://brainden.com/forum/index.php/topic/17199-removing-pawns-the-game/http://brainden.com/forum/index.php/topic/17199-removing-pawns-the-game/A simple polygon problem.
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/mLAd3b61KqE/
<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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/MHn4uAViqk8/
<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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/u0IqjfX71eY/
<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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/tUhnVh7GbUs/
<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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/b9l1S3PGe80/
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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/IFCejBRgm3A/
<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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/v2h1D5IAQ7E/
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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/PlDWz2y1O88/
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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/R-jsWA5xTJQ/
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
http://feedproxy.google.com/~r/Braindencom-NewPuzzles/~3/YHHqQydY4Ng/
(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/