" The problem is that the king could choose to negate or add to any or some of the signal or not. "
Doesn't matter. Assume the king flips it k times and calls everyone but one guy so often that they each flip it their maximum number of times. Then you will have (using my previous correction that it should be (n-1)(k+1)) (n-2)(k+1)+k flips (or (nk+n-k-2)), which is one less than the (n-1)(k+1) (or nk+n-k-1) that they are looking for. Now since everyone other than the last prisoner has already flipped it their maximum number of times and the king can no longer flip it, we know that if it is flipped one more time the last guy has finally been left in the room.
The king can only flip the chalice k times, so you just need a solution that can be messed with up to k times. So if you have one guy flipping it rightside up each time he sees it upside down and all the other guys flipping it down the first k+1 times they find it up, the first guy can just count the number of times he has to flip it. Once he gets to (n-1)(k+1), I believe he knows everyone else has been in there.
" What is the degree of the angle between the hour hand and the minute hand when it is 2:15?"
I have a digital clock you insensitive clod.
"If you have a piece of paper, and you draw any quadrilateral of any size (rhombus, rectangle, or square) on that piece of paper. How can u divide that piece of paper in half so that it also evenly divides teh quadrilateral?"
I have no idea if this will work (sorry, its late), but if you were to take the point at the center of the paper and the point at the center of the quadrilateral and draw a line the hit both points, won't it divide both the drawing and the paper in half?
"If you have a 5 gallon jug and a 3 gallon jug of water, and a hose so u can refill any as u please. What are the steps to get exactly 4 gallons of water?"
I was under the impression he had to eventually call everyone x number of times for any arbitrary number x, including those greater than n(k+1). Then again its late and I should be asleep (but I can't because I'm thinking about those damn chalices).
Or while we are at it, you could always just pocket the quarters. Sure, you don't solve the problem, but you get $12.50 free. All the guy who came up with the actual solution (pull out 18 and flip all those) gets is a sense of satisfaction.
Of course this still suffers from the potential problem of the leader going insane and losing count, only now it is increased by a factor of n because the same can now happen to any of the prisoners.
How about instead of each prisoner only flipping the chalice once, they flip it the first k+1 times they get the opportunity? Then once the leader gets to n(k+1) flips, he knows everyone has been in the room and flipped it at least once.
I thought about that. The problem is the king doesn't have to flip it over at all. Thus when he hears this strategy, he can just never flip it (or just flip it less than k times) and the leader will never be able to say yes. At least not until he goes insane from sitting in a cell all day and imagines he sees the cup flipped.
Aside from the ambiguous use of the word 'flip', the misuse of the concept of entropy, and the failure to read the problem description (assuming your plan works (which, lucky for you, it likely won't), you will have an odd number of heads making it impossible to solve), you completely missed the point of the riddle. The question wasn't to find a method that "might" or even "should" end up with the correct result, but one that "would" end up in the correct state.
Dividing by zero is not "perfectly valid algebra". Division is not closed on the set of real numbers. Its not really a riddle if you lie in the problem description. Otherwise the solution to the sample problem could be "Pull out 9 of the quarters into a seperate group. I was lying when I said you couldn't see any of them."
The Romans may not have used flaming arrows, but the Greeks sure as hell knew about them. Hell Athens was supposedly burned down by flaming arrows way back during the Persian War, and then there were descriptions of the use of a flamethrower-like device in the Battle of Delium.
Yes, they had the capacity to make fire, human beings have had that for some time now. In fact fire had been used as a weapon in conflicts such as the battle of Delium and the Peloponnesian War. Just no Greek fire. Meaning it will go out as soon as it hits the water. Meaning you have to get a direct hit with your catapult to be effective, in which case why don't you just hurl a normal rock at the boat and knock a hole in it?
"The range is fixed to the focal point of the paraboloid. With a less curved paraboloid the
range increases to whatever you want it to be, but the accuracy requirements will go up quite considerably. Or failing to improve on accurracy, increase the size of the reflector."
Well, yes, its theoretical range can be whatever you design it do be, but what I was asking was what is the maximum range of one of these that could be actually built using technology available to Archimedes. My problem with the MIT device is that it is way to big to move (which is a problem since it can only harm an object at a specific point some distance away), and since the boat was not in the water it stayed perfectly still (even an anchored boat would move a little with the tide).
If I remember the show correctly, they were able to set a small model on fire from a short distance, but when they tried to scale it up it didn't work.
The only way I can think this could have been done wouild be if he had set up a few of these overnight to several fixed points out at sea, and then hope that one of the Roman ships would sail into one of the focal points (on a sunny day).
Actually I think that if they really studied history they would note that Greek Fire was probably invented in 673 AD (at least according to your wikipedia article), a number of years after Archimedes died. You might as well say this was an early incarnation of napalm.
Re:They disproved the likeliness of this ever work
on
Archimedes Death Ray
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· Score: 3, Funny
I read the article. It said
Forbidden
You don't have permission to access/2.009/www/lectures/10_ArchimedesResult.html on this server.
Not really all that interesting of a story in my opinion.
What was the range of this (or a similar) device? Could you focus the light to set a moving ship on fire lets say 100 yards away? If not, your weapon could only light a small fire on a ship sitting right next to you, which the Roman soldiers would have plenty of time to put it out while you are trying to get a sword out of your chest. And if the invasion came on a cloudy day, you can kiss your city goodbye. And I'm assuming you are using materials that were available way back then.
I still think Archimedes would be able to come up with something a little more effective. Like the grandparent said, I'm not saying the Mythbusters are always right, as shown in the episode that they are currently airing in which they revisit myths that they got complaints on (including running vs walking in the rain and driving with the windows open vs driving with the AC on, both of which they screwed up on). But setting a 2x4 on fire is a bit different than sinking a ship.
Actually the books you reference would be great citations, assuming of course you are writing on one of their subjects. Yes, they may be, lets be nice and say "controversial", but that is not a sufficient reason to ignore something. I don't know if either one is considered a primary source, but they are two of the most well known advocates of their respective theories. If your paper discusses either of those theories, what else are you going to cite? How are you going to write a paper on "The Debate between Evolution and Intelligent Design in the 21st century" without reading one side of the debate?
The problem with the Wikipedia isn't that it is controversial or may contain inaccurate facts. It is that the Internet community (the Wikipedia's author) simply is not a sufficient source of information for citation. Hell traditional encyclopedias are not considered good resources to cite. I've heard professors say that if something is in an encyclopedia, it can be considered common knowledge and doesn't need to be cited.
Even for peripheral issues, I would advise against citing the Wikipedia. Do a little research and find the paper or book that was used as the source of what you read and use that.
I doubt music videos have that great of a market either, considering not even MTV plays them anymore. I suspect the best candidate for this would be recorded TV shows, small enough in size that they can be easily stored on a hard drive player, short enough in length that they can watched casually, and you usually don't have the focus on visual effects (which, as you mention, will be less than impressive on a tiny screen).
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Doesn't matter. Assume the king flips it k times and calls everyone but one guy so often that they each flip it their maximum number of times. Then you will have (using my previous correction that it should be (n-1)(k+1)) (n-2)(k+1)+k flips (or (nk+n-k-2)), which is one less than the (n-1)(k+1) (or nk+n-k-1) that they are looking for. Now since everyone other than the last prisoner has already flipped it their maximum number of times and the king can no longer flip it, we know that if it is flipped one more time the last guy has finally been left in the room.
No, because they will get to (n-1)(k+1) on their own eventually, once all the non-leaders have flipped the chalice k+1 times.
The king can only flip the chalice k times, so you just need a solution that can be messed with up to k times. So if you have one guy flipping it rightside up each time he sees it upside down and all the other guys flipping it down the first k+1 times they find it up, the first guy can just count the number of times he has to flip it. Once he gets to (n-1)(k+1), I believe he knows everyone else has been in there.
He knows everyone has been in there when it gets to (n-1)(k+1) or he will be waiting for him to flip it as well.
I have a digital clock you insensitive clod.
"If you have a piece of paper, and you draw any quadrilateral of any size (rhombus, rectangle, or square) on that piece of paper. How can u divide that piece of paper in half so that it also evenly divides teh quadrilateral?"
I have no idea if this will work (sorry, its late), but if you were to take the point at the center of the paper and the point at the center of the quadrilateral and draw a line the hit both points, won't it divide both the drawing and the paper in half?
"If you have a 5 gallon jug and a 3 gallon jug of water, and a hose so u can refill any as u please. What are the steps to get exactly 4 gallons of water?"
I liked that movie too.
I was under the impression he had to eventually call everyone x number of times for any arbitrary number x, including those greater than n(k+1). Then again its late and I should be asleep (but I can't because I'm thinking about those damn chalices).
Or while we are at it, you could always just pocket the quarters. Sure, you don't solve the problem, but you get $12.50 free. All the guy who came up with the actual solution (pull out 18 and flip all those) gets is a sense of satisfaction.
Of course this still suffers from the potential problem of the leader going insane and losing count, only now it is increased by a factor of n because the same can now happen to any of the prisoners.
How about instead of each prisoner only flipping the chalice once, they flip it the first k+1 times they get the opportunity? Then once the leader gets to n(k+1) flips, he knows everyone has been in the room and flipped it at least once.
I thought about that. The problem is the king doesn't have to flip it over at all. Thus when he hears this strategy, he can just never flip it (or just flip it less than k times) and the leader will never be able to say yes. At least not until he goes insane from sitting in a cell all day and imagines he sees the cup flipped.
Aside from the ambiguous use of the word 'flip', the misuse of the concept of entropy, and the failure to read the problem description (assuming your plan works (which, lucky for you, it likely won't), you will have an odd number of heads making it impossible to solve), you completely missed the point of the riddle. The question wasn't to find a method that "might" or even "should" end up with the correct result, but one that "would" end up in the correct state.
Dividing by zero is not "perfectly valid algebra". Division is not closed on the set of real numbers. Its not really a riddle if you lie in the problem description. Otherwise the solution to the sample problem could be "Pull out 9 of the quarters into a seperate group. I was lying when I said you couldn't see any of them."
Spiders are not insects. And I'm sure you can find some amazing structure or protein in virtually any highly evolved organism.
That Archimedes used Greek Fire on Roman ships close to a century before it was invented? Yes, that is a total myth.
The Greeks had the technology to make a steam engine, that doesn't mean Archimedes traveled from city to city in a steamboat he built in his basement.
Neither of those examples had anything to do with the 7th century invention known as "Greek Fire".
The Romans may not have used flaming arrows, but the Greeks sure as hell knew about them. Hell Athens was supposedly burned down by flaming arrows way back during the Persian War, and then there were descriptions of the use of a flamethrower-like device in the Battle of Delium.
Yes, they had the capacity to make fire, human beings have had that for some time now. In fact fire had been used as a weapon in conflicts such as the battle of Delium and the Peloponnesian War. Just no Greek fire. Meaning it will go out as soon as it hits the water. Meaning you have to get a direct hit with your catapult to be effective, in which case why don't you just hurl a normal rock at the boat and knock a hole in it?
So is firing a cruise missile at the boat. Just neither technology was available at the time. See my previous post on the subject.
Well, yes, its theoretical range can be whatever you design it do be, but what I was asking was what is the maximum range of one of these that could be actually built using technology available to Archimedes. My problem with the MIT device is that it is way to big to move (which is a problem since it can only harm an object at a specific point some distance away), and since the boat was not in the water it stayed perfectly still (even an anchored boat would move a little with the tide).
If I remember the show correctly, they were able to set a small model on fire from a short distance, but when they tried to scale it up it didn't work.
The only way I can think this could have been done wouild be if he had set up a few of these overnight to several fixed points out at sea, and then hope that one of the Roman ships would sail into one of the focal points (on a sunny day).
Actually I think that if they really studied history they would note that Greek Fire was probably invented in 673 AD (at least according to your wikipedia article), a number of years after Archimedes died. You might as well say this was an early incarnation of napalm.
Not really all that interesting of a story in my opinion.
I still think Archimedes would be able to come up with something a little more effective. Like the grandparent said, I'm not saying the Mythbusters are always right, as shown in the episode that they are currently airing in which they revisit myths that they got complaints on (including running vs walking in the rain and driving with the windows open vs driving with the AC on, both of which they screwed up on). But setting a 2x4 on fire is a bit different than sinking a ship.
The problem with the Wikipedia isn't that it is controversial or may contain inaccurate facts. It is that the Internet community (the Wikipedia's author) simply is not a sufficient source of information for citation. Hell traditional encyclopedias are not considered good resources to cite. I've heard professors say that if something is in an encyclopedia, it can be considered common knowledge and doesn't need to be cited.
Even for peripheral issues, I would advise against citing the Wikipedia. Do a little research and find the paper or book that was used as the source of what you read and use that.
I doubt music videos have that great of a market either, considering not even MTV plays them anymore. I suspect the best candidate for this would be recorded TV shows, small enough in size that they can be easily stored on a hard drive player, short enough in length that they can watched casually, and you usually don't have the focus on visual effects (which, as you mention, will be less than impressive on a tiny screen).