It's better for you, LeonGeeste, to assume that there is no solution so that you can get on with your life, whatever that entails. Feel free to continue spinning to your desire. I'm sure it's entertaining for all of us.
Ok, you want real world? No matter the solution, the king and prisoners will live at least a day longer than after the prisoners solve the puzzle and are set free. I never said these were humans.:)
k is not undefined. k is a number that the king and prisoners know ahead of time. This should be obvious, as the problem does indeed say there is a solution.
This problem is fundamentally different from that one. It won't help you much to know how to do that one, and is more likely to make you sure of a wrong solution than to get you to a right solution.
" Pain in the neck...wanted to go to sleep an hour ago, but now I have to figure this one out:)"
I brought the productivity of the entire student work force at Sandia Natl Labs down to zero this summer by posting this problem on their message boards.:)
Just so you know, the only person who I know legitimately solved this problem (none of the students at SNL could get it) worked at it for a couple weeks before getting the solution, albeit not the optimal solution.
There is a king and there are his n prisoners. The king has a dungeon in his castle that is shaped like a circle, and has n cell doors around the perimeter, each leading to a separate, utterly sound proof room. When within the cells, the prisoners have absolutely no means of communicating with each other.
The king sits in his central room and the n prisoners are all locked in their sound proof cells. In the king's central chamber is a table with a single chalice sitting atop it. Now, the king opens up a door to one of the prisoners' rooms and lets him into the room, but always only one prisoner at a time! So he lets in just one of the prisoners, any one he chooses, and then asks him a question, "Since I first locked you and the other prisoners into your rooms, have all of you been in this room yet?" The prisoner only has two possible answers. "Yes," or, "I'm not sure." If any prisoner answers "yes" but is wrong, they all will be beheaded. If a prisoner answers "yes," however, and is correct, all prisoners are granted full pardons and freed. After being asked that question and answering, the prisoner is then given an opportunity to turn the chalice upside down or right side up. If when he enters the room it is right side up, he can choose to leave it right side up or to turn it upside down, it's his choice. The same thing goes for if it is upside down when he enters the room. He can either choose to turn it upright or to leave it upside down. After the prisoner manipulates the chalice (or not, by his choice), he is sent back to his own cell and securely locked in.
The king will call the prisoners in any order he pleases, and he can call and recall each prisoner as many times as he wants, as many times in a row as he wants. The only rule the king has to obey is that eventually he has to call every prisoner in an arbitrary number of times. So maybe he will call the first prisoner in a million times before ever calling in the second prisoner twice, we just don't know. But eventually we may be certain that each prisoner will be called in ten times, or twenty times, or any number you choose.
Here's one last monkey wrench to toss in the gears, though. The king is allowed to manipulate the cup himself, k times, out of the view of any of the prisoners. That means the king may turn an upright cup upside down or vice versa up to k times, as he chooses, without the prisoners knowing about it. This does not mean the king must manipulate the cup any number of times at all, only that he may.
Assume that both the king and the prisoners have a complete understanding of the game as I have just explained it to you, and that the prisoners were given time beforehand to come up with a strategy. The king was able to hear the prisoners discuss, however, so also assume that if there is a way to foil a strategy, the king will know it and exploit the weakness. The prisoners must utilize a strategy that works in absolutely every single possible case.
Now you must figure out not only how to keep the prisoners alive, but how to also ensure their eventual freedom. When can any one of them be certain they've all been in the central chamber of the dungeon at least once? And how? Don't try to imagine any trickery like scratching messages in the soft gold of the chalice. The problem is as simple as it sounds. The prisoners have absolutely no way of communicating with each other except through the two orientations of the chalice. If any of them attempts any trickery at all they will all be beheaded. All the prisoners can do is turn the chalice upside down or right side up, as they choose, whenever they are called into the chamber.
Slashdot Mirror
It's better for you, LeonGeeste, to assume that there is no solution so that you can get on with your life, whatever that entails. Feel free to continue spinning to your desire. I'm sure it's entertaining for all of us.
Ok, you want real world? No matter the solution, the king and prisoners will live at least a day longer than after the prisoners solve the puzzle and are set free. I never said these were humans. :)
Your solution requires that the king ask the prisoners a different question from the question that he actually asks them, according to the problem.
0^0 is an indeterminate form. Its logarithm is 0*infinity.
You've misunderstood the problem. Eventually the leader must be called out again.
How do you propose they get to infinity?
"Stupid, stupid."
Yes, you are. k is not undefined. k is a number that the king and prisoners know ahead of time.
Finally, someone who understands the English language.
k is not undefined. k is a number that the king and prisoners know ahead of time. This should be obvious, as the problem does indeed say there is a solution.
You need to read the problem again. n is the number of prisoners
You've got the right idea, but it's nowhere near that simple.
One thing I notice everyone doing is assuming that the chalice starts out rightside up.
"Am I close? :)"
Nope.
" The answer is always yes..."
You're the 3rd person to suggest that. You might want to try reading the problem again.
This problem is fundamentally different from that one. It won't help you much to know how to do that one, and is more likely to make you sure of a wrong solution than to get you to a right solution.
Everything is known to everyone before the game begins.
"the king can do is to always make sure the chalice is rightside up"
No, he can't.
" Pain in the neck...wanted to go to sleep an hour ago, but now I have to figure this one out :)"
:)
I brought the productivity of the entire student work force at Sandia Natl Labs down to zero this summer by posting this problem on their message boards.
Just so you know, the only person who I know legitimately solved this problem (none of the students at SNL could get it) worked at it for a couple weeks before getting the solution, albeit not the optimal solution.
"just so I'm sure, you can't bash the kings brains in out of frustration using the chalice, right?"
The king knows Kung Fu.
"That's the solution, isn't it?"
:)
Not even close.
Again:
"Since I first locked you and the other prisoners into your rooms, have all of you been in this room yet?"
RTFP
"Since I first locked you and the other prisoners into your rooms, have all of you been in this room yet?"
You won't find it anywhere on Google. Although there are countless possible solutions, I only know of 2 people who have solved it.
There is a king and there are his n prisoners. The king has a dungeon in his castle that is shaped like a circle, and has n cell doors around the perimeter, each leading to a separate, utterly sound proof room. When within the cells, the prisoners have absolutely no means of communicating with each other.
The king sits in his central room and the n prisoners are all locked in their sound proof cells. In the king's central chamber is a table with a single chalice sitting atop it. Now, the king opens up a door to one of the prisoners' rooms and lets him into the room, but always only one prisoner at a time! So he lets in just one of the prisoners, any one he chooses, and then asks him a question, "Since I first locked you and the other prisoners into your rooms, have all of you been in this room yet?" The prisoner only has two possible answers. "Yes," or, "I'm not sure." If any prisoner answers "yes" but is wrong, they all will be beheaded. If a prisoner answers "yes," however, and is correct, all prisoners are granted full pardons and freed. After being asked that question and answering, the prisoner is then given an opportunity to turn the chalice upside down or right side up. If when he enters the room it is right side up, he can choose to leave it right side up or to turn it upside down, it's his choice. The same thing goes for if it is upside down when he enters the room. He can either choose to turn it upright or to leave it upside down. After the prisoner manipulates the chalice (or not, by his choice), he is sent back to his own cell and securely locked in.
The king will call the prisoners in any order he pleases, and he can call and recall each prisoner as many times as he wants, as many times in a row as he wants. The only rule the king has to obey is that eventually he has to call every prisoner in an arbitrary number of times. So maybe he will call the first prisoner in a million times before ever calling in the second prisoner twice, we just don't know. But eventually we may be certain that each prisoner will be called in ten times, or twenty times, or any number you choose.
Here's one last monkey wrench to toss in the gears, though. The king is allowed to manipulate the cup himself, k times, out of the view of any of the prisoners. That means the king may turn an upright cup upside down or vice versa up to k times, as he chooses, without the prisoners knowing about it. This does not mean the king must manipulate the cup any number of times at all, only that he may.
Assume that both the king and the prisoners have a complete understanding of the game as I have just explained it to you, and that the prisoners were given time beforehand to come up with a strategy. The king was able to hear the prisoners discuss, however, so also assume that if there is a way to foil a strategy, the king will know it and exploit the weakness. The prisoners must utilize a strategy that works in absolutely every single possible case.
Now you must figure out not only how to keep the prisoners alive, but how to also ensure their eventual freedom. When can any one of them be certain they've all been in the central chamber of the dungeon at least once? And how? Don't try to imagine any trickery like scratching messages in the soft gold of the chalice. The problem is as simple as it sounds. The prisoners have absolutely no way of communicating with each other except through the two orientations of the chalice. If any of them attempts any trickery at all they will all be beheaded. All the prisoners can do is turn the chalice upside down or right side up, as they choose, whenever they are called into the chamber.
(written by a former roomate)
That's the way to go. My family's last 2 cats came from a parking lot and a trash can.
"..." means "goes on forever" 1/3 = 0.333... = 0.333bar
Feel free to argue my proof, but it is correct, as has been shown countless times before. Just Ask Dr. Math, or take Calculus.