The King and the Chalice
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.
Princes, Peasants, and Merchants
In the land of Gog, princes always lie, peasants always tell the truth, while merchants sometimes tell the truth and soemtimes lie. A tourist is enjoying an afternoon refreshment in one of the local pubs when the bartender (who always tells the truth) says to her: “Do you see those three men over there? One is a peasant, another a prince, and the third a merchant. You may ask them three yes/no questions, always indicating which man you wish should answer. If, after asking these three questions, you correctly identify the peasant, prince, and merchant, they will buy you a drink.” The tourist is indeed very thirsty. What questions should she ask?
Sticky Triangles
Let’s say I have a stack of sticks: all identical, inflexible, unbreakable. Sticks can touch only at their ends, not in between.
If I give you 3 sticks, you can make one triangle. If I give you 2 more sticks (5), you can make 2 triangles. If I give you another stick (6), how can you make 4 triangles?
18 Heads Up
You’re in a dark room with 50 quarters, 18 of which are heads up. You are allowed to move around the coins or flip some or all of them, if you wish. Problem is, it’s too dark to tell what you’re moving or flipping (no, you can’t figure it out by touch either). Your job is to split the coins into two groups, each of which has the same number of heads up coins. How do you accomplish this?
Where’s the father?
The mother is 21 years older than the child. In 6 years from now, the mother will be 5 times as old as the child. Question: Where’s the father?
When I solve these, I’ll put my solution in the comments section.
For those that like solving math/logic riddles, you might wanna visit Your Favorite Math/Logic Riddles?
Almost forgot about my favorite riddles site: [ wu :: riddles]
