phlegmtheorem Posted May 22, 2008 Report Share Posted May 22, 2008 My favorite riddle ever. I have not posted this yet, because it's fairly common, but just in case you have not heard it before... This one is FUN! I'm more interested in how you solved it, since the answer is easy to find online. If you are looking for the solution online, just google: Einstein's Riddle Hint: how I solved it (DONT READ IF YOU WANT TO TRY THIS YOURSELF): i used excel to map out a simple grid with each possible outcome in each row and in each column, then i read through the clues and used excel to map out what i found from each clue, identifying the positives and eliminating the negatives. be sure to create a secondary graphic to keep track of spacial relation as well, because some of the hints are relative to the position of other things. Let us say that there are five different colored houses next to each other on the same road. In each house lives a man from a different country. Every man has a favorite drink, a favorite brand of cigarettes, and keeps pets of different kinds. 1. The Englishman lives in the red house. 2. The Swede keeps dogs. 3. The Dane drinks tea. 4. The green house is just to the left of the white one. 5. The owner of the green house drinks coffee. 6. The Pall Mall smoker keeps birds. 7. The owner of the yellow house smokes Dunhills. 8. The man in the center house drinks milk. 9. The Norwegian lives in the first house. 10. The Blend smoker has a neighbor who keeps cats. 11. The man who smokes Blue Masters drinks bier. 12. The man who keeps horses lives next to the Dunhill smoker. 13. The German smokes Prince. 14. The Norwegian lives next to the blue house. 15. The Blend smoker has a neighbor who drinks water. Who keeps fish as a pet? Link to comment Share on other sites More sharing options...
Sacosphilz Posted May 22, 2008 Report Share Posted May 22, 2008 That puzzle is one of my favorite as well. How nostalgic. I agree that there's no point in spoiling the answer or the method. What's important is if you can solve it and how long it takes you. As for the method, I think you can also use paper and it won't be any harder. Link to comment Share on other sites More sharing options...
Metal Bunny Posted May 22, 2008 Author Report Share Posted May 22, 2008 Woho, after 20 minutes and pen and paper, old school baby, I figured out the answer. After a few hard, but logical steps, many easy, also logical steps, will lead you to the answer, the problem lies in the start. The answer is The german heh. Was a nice way of relaxation, never heard of it before, thanks for posting it Also, when I went to confirm my answer, I saw that Einstein said only 2% of the people would solve it. It's not that I need another confirmation (school and this sure as hell cannot be good for my already mountainous self-esteem but, OH YEAAAH! Link to comment Share on other sites More sharing options...
Trahern Posted May 22, 2008 Report Share Posted May 22, 2008 @5-point star problem, and @Sacophilz for inferring that I don't speak human The response Sacophilz posted seemed sound enough to me, but here's some human for ya... The exterior of the star consists of ten angles. The sum of the exterior angles of any polygon is 360. The sum of the interior angles of a pentagon is 540. Vertical angles are congruent. The five of the ten exterior angles that are not the "points" of the star are the vertical angles of the interior pentagon, and thus their sum is also equal to 540. The difference between 540 and 360 is 180... which is the sum of the remaining angles, the sum of the angle of the points of the star, and the answer to the problem. Link to comment Share on other sites More sharing options...
Grido Posted May 22, 2008 Report Share Posted May 22, 2008 @einstein problem, wow forgot bout that one, hant seen it in at least 5 years, so naturally had fogtton the answer and had to work it out again. It is the German, but just to fully point out , he lives in the Forth house in the row, which is Green, he likes to drink Coffee, his favourite cigarettes are Prince, and of course he has the pet Fish Link to comment Share on other sites More sharing options...
Trahern Posted May 22, 2008 Report Share Posted May 22, 2008 On my way to work this morning I was thinking about puzzles of that style and considering posting one, only to find that I was beaten to it. It's like they say I guess, "Great minds think alike." "Simple minds seldom differ." Link to comment Share on other sites More sharing options...
Sacosphilz Posted May 22, 2008 Report Share Posted May 22, 2008 @5-point star problem, and@Sacophilz for inferring that I don't speak human The response Sacophilz posted seemed sound enough to me, but here's some human for ya... The exterior of the star consists of ten angles. The sum of the exterior angles of any polygon is 360. The sum of the interior angles of a pentagon is 540. Vertical angles are congruent. The five of the ten exterior angles that are not the "points" of the star are the vertical angles of the interior pentagon, and thus their sum is also equal to 540. The difference between 540 and 360 is 180... which is the sum of the remaining angles, the sum of the angle of the points of the star, and the answer to the problem. You lost me at these two lines: The sum of the exterior angles of any polygon is 360. The difference between 540 and 360 is 180... which is the sum of the remaining angles, the sum of the angle of the points of the star, and the answer to the problem. Umm.... how? Am I misunderstanding something? Using a similar explanation, as I see it: The exterior of the star consists of ten angles. The sum of the exterior angles of any ten-sided polygon is 180*(10+2) = 2160. The sum of the interior angles of a pentagon is 180*(5-2) = 540. Vertical angles are congruent. The five of the ten exterior angles that are not the "points" of the star are the vertical angles of the interior pentagon, and thus their sum is also equal to 540. The difference between 2160 and 540 is 1620, which is the sum of the exterior angles of the points of the star. The sum of the interior angles of the points of the star, which is the answer to the problem, would then be 5*360 - 1620 = 180 Link to comment Share on other sites More sharing options...
Trahern Posted May 22, 2008 Report Share Posted May 22, 2008 You lost me at these two lines: The sum of the exterior angles of any polygon is 360. The difference between 540 and 360 is 180... which is the sum of the remaining angles, the sum of the angle of the points of the star, and the answer to the problem. Umm.... how? Am I misunderstanding something? Using a similar explanation, as I see it: The exterior of the star consists of ten angles. The sum of the exterior angles of any ten-sided polygon is 180*(10+2) = 2160. The sum of the interior angles of a pentagon is 180*(5-2) = 540. Vertical angles are congruent. The five of the ten exterior angles that are not the "points" of the star are the vertical angles of the interior pentagon, and thus their sum is also equal to 540. The difference between 2160 and 540 is 1620, which is the sum of the exterior angles of the points of the star. The sum of the interior angles of the points of the star, which is the answer to the problem, would then be 5*360 - 1620 = 180 Because "similar" and "equivalent" are similar, but not equivalent... Mine: The sum of the exterior angles of any polygon is 360. Yours: The sum of the exterior angles of any ten-sided polygon is 180*(10+2) = 2160. 360 is not equal to 2160. I'm not sure where your equation comes from, but it doesn't make much sense. It would claim that the sum of the exterior angles of a triangle would be 900, when here as well the sum is 360. One point to keep in mind about my claim is that they're also directional angles, such that "left turns" would be negative, and "right turns" would be positive, or vice versa. I simply said "the difference" to make it sound more "human" rather than go through a description of sign notation. For a visual representation of this, I like this example: http://www.mathopenref.com/polygonexteriorangles.html And for interior angles, this one is nice too: http://www.mathopenref.com/polygoninteriorangles.html Link to comment Share on other sites More sharing options...
phlegmtheorem Posted May 22, 2008 Report Share Posted May 22, 2008 Relax you two. What is the difference between a brand new crisp fifty dollar bill, and a wrinkled dirty old one...? Link to comment Share on other sites More sharing options...
Grido Posted May 22, 2008 Report Share Posted May 22, 2008 other than the obvious? different face on it? Link to comment Share on other sites More sharing options...
Trahern Posted May 22, 2008 Report Share Posted May 22, 2008 Relax you two. What is the difference between a brand new crisp fifty dollar bill, and a wrinkled dirty old one...? We're relaxed. I just have a tendancy to come off abrasive before I have my coffee. No harm intended. 49 dollars. or... the latter is married to Hillary Clinton. Link to comment Share on other sites More sharing options...
phlegmtheorem Posted May 22, 2008 Report Share Posted May 22, 2008 hahahah! and you are correct... $49 it is... Link to comment Share on other sites More sharing options...
Sacosphilz Posted May 23, 2008 Report Share Posted May 23, 2008 Because "similar" and "equivalent" are similar, but not equivalent... Mine: The sum of the exterior angles of any polygon is 360. Yours: The sum of the exterior angles of any ten-sided polygon is 180*(10+2) = 2160. 360 is not equal to 2160. I'm not sure where your equation comes from, but it doesn't make much sense. It would claim that the sum of the exterior angles of a triangle would be 900, when here as well the sum is 360. One point to keep in mind about my claim is that they're also directional angles, such that "left turns" would be negative, and "right turns" would be positive, or vice versa. I simply said "the difference" to make it sound more "human" rather than go through a description of sign notation. For a visual representation of this, I like this example: http://www.mathopenref.com/polygonexteriorangles.html And for interior angles, this one is nice too: http://www.mathopenref.com/polygoninteriorangles.html Thank you. I get it all now after reading a bit through the links you've given. Basically, I didn't know the definition of "exterior angle", specifically the definition you were using. (That math article in the links also states that the "sum of exterior angles" could mean more than one thing.) I've never learned about that concept in school, and I didn't take my math classes in English either, so there's lots of room for misunderstanding. By the way, in my last post, I just mistakenly presumed that the definition for "exterior angle" is the absolute angular span between a pair of intersecting line segments outside the enclosed area of a polygon which those line segments belong to. Relax you two. Math is one of my few ways of relaxing. No harm intended. Link to comment Share on other sites More sharing options...
Metal Bunny Posted May 23, 2008 Author Report Share Posted May 23, 2008 Lol... get back to solving riddles Like a few unsolved riddles we have left? Don't know which ones, going to put them in a structure later. Here are a few, (well known?) easy ones. You have a bottle, a coin and a cork. You put the coin in the bottle and then cork it. What do you have to do in order to get the coin out, without damaging the bottle or the cork, btw you are not allowed to take the cork out. You are stranded on an island, sucks to be you, and it's full of cannibals, sucks to be you, however they have a custom that might save your life. You are given 2 jars, one is filled with 50 black marbles and the other with 50 white ones. They will randomly pick one jar, sucks to be you, and you have to take a marble without looking, sucks to be you, if you pick a black marble you will be eaten, alive, with hot sauce in your eyes, and a pineapple shoved into your mouth, and a coconut into another orifice, sucks to be you. Your chance on survival depends on the choice you will make, as you are allowed to rearrange the marbles into the jars as you see fit, as long as all the marbles stay in the game. Also, the jars are shaken by a buttercarning vibrator afterwards, sucks to be you. What do you do to almost make sure it doesn't sucks to be you? You are stranded on an island, sucks to be you, with a rabid rabbit who has developed a taste for scrumptious human flesh, sucks to be you. The rabbit is cute and fluffy but so much more powerfull than you, sucks to be you. You however were on a trip with 39 other people, and the rabbit decided to try and eat you all, sucks to be all of you. After eating 20 of you, it is satiated and decides to have some fun. You and the other 19 are to play a game with it, sucks to be you man... You will all stand in a row, and you will only be able to see the people in front of you. So the last person can see all the other 19, but the first person cannot see anybody, because if you move your head, "glomp" and "orf with ur headz", yes all of you die, no cheating, sucks to be you. The rabbit will start at the end and will randomly put a black or a white hat on the person. Remember you cannot see the color of your hat or the of hats behind you. You are allowed to say "black" or "white", nothing else, because else, you'll be made into smelly and steamy bunny poop. If you guess correctly, you are allowed to leave with the conveniently placed submarine next to the island. The bunny gives you all 24 hours before the game starts. What is the best method to save as many people as possible? The 'opted goal' here is saving almost everybody and maybe even everybody. Link to comment Share on other sites More sharing options...
Trahern Posted May 23, 2008 Report Share Posted May 23, 2008 You have a bottle, a coin and a cork.You put the coin in the bottle and then cork it. What do you have to do in order to get the coin out, without damaging the bottle or the cork? Take out the cork, turn over the bottle, and the coin will fall out. What do you do to almost make sure it doesn't suck to be you? Take out a white marble. Your mention of cannibals got me thinking it was going to be one of those "get the people across the river" puzzles.... ****ing cannibals. Link to comment Share on other sites More sharing options...
phlegmtheorem Posted May 23, 2008 Report Share Posted May 23, 2008 cannibal marbles: rearrange the marbles so that all of the black marbles are at the bottom of each jar (half in each) and all the white marbles are on the top of each jar (half in each). then just pull a marble off the top. carnivorous bunny: start at the back of the line, the last person says the color of the hat of the person in front of him. he has a 50% chance of it being the same as his, and they have a 100% chance of survival. the third person to guess says the color of the person's hat in front of them as well. again, 50% and 100%. and so forth. Cork!: Trahern got my answer, i just wanted to make another spoiler tag! Link to comment Share on other sites More sharing options...
Trahern Posted May 23, 2008 Report Share Posted May 23, 2008 @Sacosphilz, (but for the benefit of everyone else ... I think we're both wrong... In your answer, you give this assumption: - The sum of the angles a2, v = 180 degrees; because they are on the same line. In my answer I say: - The five of the ten exterior angles that are not the "points" of the star are the vertical angles of the interior pentagon... The only requirement is that we "Draw a 5 pointed star on a piece of paper." We assumed that to do this we would draw 5 connecting lines in the fashion of a pentagram. But what if we were to draw 10 individual line segments to create a 5-pointed star? Our assumptions fall apart. Another way I can think to illustrate this is: Let M be the point in the center of our star. Create a line (or more properly, a ray) along MA. Create point F such that it lies along rayMA and that the length of AM is not equal to AF - (Don't put F on A basically). Let your new star points be FBCDE. In short, keeping points V and W in the same place, and increasing the distance of A from the center would decrease the size of angle a, and increase the size of angles v and w... Since most of the riddles and puzzles involve thinking outside of the box and abandoning our assumptions, I figured I'd mention it. Link to comment Share on other sites More sharing options...
Metal Bunny Posted May 23, 2008 Author Report Share Posted May 23, 2008 Uh... I apparently forgot to add in some things. The cork is not allowed to taken out of the bottle The jars are shaken wildly by a buttercarning vibrator, sucks to be you. And @ phlegm that's a 50%, meaning 10 people are saved, sorta... But there is a way to save more people. Heh I'll add a 'goal' for the awesomeness bunny riddleness, with the best method you should be able to save almost everybody and maybe even everbody. I also edited this into my original post. Link to comment Share on other sites More sharing options...
Trahern Posted May 23, 2008 Report Share Posted May 23, 2008 About to head to lunch, so this is more guessing than thinking it through... The cork is not allowed to taken out of the bottle Push the cork into the bottle. Turn the bottle over to remove the coin. This may involve a bit of shaking the bottle if it's empty. If it contains water, wine, etc. then the cork should float up while the coin should fall down to the opening. The jars are shaken wildly by a buttercarning vibrator, sucks to be you. Method 1, tactile detection: Place all of the black rocks out in the sun so they get nice and warm, and the white rocks in the shade. Grab a cool rock. or Dunk all the white rocks in the water (islands are surrounded by water). Grab a wet rock. (less reliable as water tends to drip) Method 2, a math guess and probably what you're after: Place all but one white rock in jar A. Place the remaining white rock in jar B. 50% chance of a white rock if they choose jar B + 49/99 chance from jar A = 148/198 chance. Link to comment Share on other sites More sharing options...
Metal Bunny Posted May 23, 2008 Author Report Share Posted May 23, 2008 @ trahern You got both right. But when you were beginning with method 1 I wanted to post an immediate "stop trying to cheat or the cannibal gods will eeeeaaat you in your sleeeep" warning. Luckily your 2nd method is correct The chance is actually 74/99 , I know it's nitpicking... Link to comment Share on other sites More sharing options...
phlegmtheorem Posted May 23, 2008 Report Share Posted May 23, 2008 Metal Bunny, you are wrong about my bunny method, there is a much greater than 50% chance of survival with the route i took. Half of the people will be saved FOR SURE, and the other half will be saved 50% of the time (roughly) giving me about a 75% survival rate. Unless there is a new rule i should know about... Also, you gave the same chance as Trahern, you just simplified it... Link to comment Share on other sites More sharing options...
Sacosphilz Posted May 23, 2008 Report Share Posted May 23, 2008 @Trahern: Yes, I thought of the same assumption we were making too, but decided to keep it because if that assumption didn't hold true, we'd just have a random 10-sided polygon with alternating convex and concave angles (please correct me if I'm using the wrong terminology again) , and there would be no point in solving it...... or is there? Example: If the "arms" of the star were made of 5 equilateral triangles of the same size, the total angle of the "points" of the star would be 60*5 = 300, which is not 180. If the assumption didn't hold, any answer between 0 and 540 would be possible. @Metal Bunny: Just when I thought we have a few good, new riddles, two of them had been solved so quickly. By the way, just asking in advance, can I borrow some of your bunnies for some future riddles? Some riddles might be in need of some psychotic, almighty entities, and I think your bunny subjects could fit perfectly roleplay properly. @canivorous bunny riddle: Cheating method #1: Starting from the backmost person, whisper the color of the hat of the person in front, then guess his or her own hat's color. But they're sooo eaten by the bunny. Cheating method #2: Develop two accents to say "white" and "black". Each accent has a hidden meaning hinting at the color of the hat of the person in front of you. But they're sooooo eaten by the bunny. Real attempt: During the given 24 preparation time, practice counting silently at the same speed. Also memorize each person's voice and their standing order just to be safe. Let's number the people #1 to #20, #1 being the person in the front who can see no hats and #20 being the person in the rear who can see 19 hats. (1) Let N be a running index starting from 20. Note that N will always be an even number. (2) Have person #N count the number of white hats and black hats among the visible hats. There should be an odd number of hats in total. (3.1) If he/she sees exactly 1 more white hats than black ones, call "white". The people in front of him/her will now know exactly how many white and black hats there are in total among them. Starting from person #N-1 to #1, count the hats in front of him/her and subtract from that total, then call out the remaining color, then the next person subtract that answer from the current total and repeat the same process. They will all be able to give the correct answers with absolute certainty. Go to step (4). (3.2) If he/she sees exactly 1 more black hats than white ones, call "black". The people in front of him/her will be able to make the correct answer with the same method as in case (3.1). Go to step (4). (3.3) Otherwise, he/she remains silent for a designated period of time (that's what the counting training was for), then subtract 2 from N and go back to step (2). (4) If there are still people who haven't given an answer (i.e. if #20 couldn't make the answer yet), repeat the whole process from (1) with the remaining people. Otherwise, all's done. Persons #1 to #19 will surely survive, and #20 has a 1/2 chance of survival. Some clarifications: - During each run, one person will eventually be able to call "white" or "black", the last turn being the turn of the second person from the front -- Because there is only 1 visible hat, there is always 1 more hat of a color than another color. (1 vs 0) - With the exception of N=20, when person #N calls "white" or "black", he/she can be sure that it's also the color of his/her hat, because if it weren't so ... that would mean there were equal number of black and white hats in #1 to #N ... which would mean that there were either exactly 1 more whites than blacks or exactly 1 more blacks then whites in #1 to #N+1 ... which would mean that person #N+2 would've already made an answer, which he/she hadn't. EDIT: That was a very good puzzle. It took me hours and I just couldn't sleep until I got it. It's 4 a.m. and I'm still typing. Link to comment Share on other sites More sharing options...
Metal Bunny Posted May 23, 2008 Author Report Share Posted May 23, 2008 @ trahern, yea sorry you're right, but it doesn't really matter anymore, because saco already gave the right answer And yes saco you're allowed to use tha almighty bunny, as long as it is in a reverend verse and you sacrifice us a daily human, prefered young and clean and especially no hobo's else you die, horribly, like, eye-gougingly, scrotum squashingly, anal-probingly, horrible... But nice to hear that it was a nice riddle I'll come up with some other riddles later Link to comment Share on other sites More sharing options...
phlegmtheorem Posted May 23, 2008 Report Share Posted May 23, 2008 A simpler method to the bunny riddle: stealing Saco's counting method... Using the 24 hours, set up the following method of telling the person in front of you what color their hat is: if you have the same color hat as them, you will answer immediately... if not, you will wait ten seconds to tell them that it is opposite. The person at the back of the line has a 50/50 shot. This is how it works in practice: the last person in line says the color of the hat of the person directly in front of them. if it just so happens to be their color, then they live. if not... oh well. everyone else will survive with 100% certainty. The next person in line has 2 options: 1) answer immediately the correct color of their own hat... but ONLY if the person in front of them has the same color hat. 2) Wait a full ten seconds before answering correctly the color of their own hat. (signaling to the person in front of them that their hat is the opposite color). I think this is easier, although much less mathmatically interesting. Link to comment Share on other sites More sharing options...
Metal Bunny Posted May 24, 2008 Author Report Share Posted May 24, 2008 Well, I did say no cheating, besides saco's method is exactly the same, just without the 10 seconds waiting, so his is better Link to comment Share on other sites More sharing options...
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