mmiguel

I thought this might be fun, but maybe it will flop. A person finds a magic lamp with an evil genie inside. The person may ask for any wish to be granted. The genie, spiteful for having to serve a pitiful little human with his phenomenal cosmic powers, wants to make his master regret every wish that is made. Posters, assume the role of either the genie of the human. Rules: I. Both genie and human are powerless to change these rules II. As the human , you should wish for something that most people would actually find desirable. III. Everything the human explicitly wished for must come true, and all harm (physical, mental, psychological, ...etc) that the spiteful genie inflicts should ultimately derive from a creative interpretation of the wish (e.g. deliberately ignoring common implications in speech that are not explicitly stated, or taking things out of context, ...etc). E.g. it's cheating if a person wishes for a million dollars, and the genie gives him a million dollars and also dumps a bucket of lava on his head (lava has nothing to do with the wish). It's not cheating if a person wishes for eternal life, and the genie prevents them from ever dying, but allows their body to to continue to age and weaken normally forever into some grotesque shamble that doesn't even look human - in this case, the person's eventual regret derives from making the wish in the first place. IV. The genie cannot control his master's mind. This may sound good for the master, but it prevents the genie from being able to grant wishes like: I wish to always be happy forever. V. Off limits: Wishing for more wishes, wishing for multiple things in one wish. The wish should be one thing possibly followed by further clarifications that specify the one thing. Cannot undo wishes. Challenge: Humans: Find an uncorruptible wish. Genies: Corrupt every wish Let's see who wins! Here's one to start with: "I wish to be the most intelligent person ever"

There are 3 smaller, easier puzzles that may serve as hints to building up the answer to this one. I will post the first one below. Those with pride, feel free to not look.

Hmm.... That could make things complicated because we can get into a circular: "but he knows that I know that he knows that I know that ....", which I would prefer to avoid. The correct answer allows you to identify which Gods are which regardless of what they think you are thinking.

They are omniscient. They each know which God is which. Random can provide different answers to the same question. I guess I don't see any harm in them knowing what Random will say if for example you were to use question 1 to ask what Random would say question 2 or on question 3.

A question that cannot be answered --- sounds like a paradox. Likely not to get much useful info out of a paradox. Random can always answer, since he doesn't even need to listen to your question, he can ignore you, flip a coin or roll a die and give you whatever answer he chooses.

I think this is where I would start. Still working on Q#2 and 3. Not all will answer that way with certainty, just 2 of 3.

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

try the question on me, i'll try to answer yes and we'll see if i am stopped lol

I like this topic, and those boy-girl puzzles made me think about this a lot a couple years ago. Here is what I think of it, and you may agree with me or not, either way, I find this thought provoking. I think: The fundamental difference between part A and part B above is that in that in one case, a statement was made about a specific object (part B), while in the other case, no statement was made about any specific object. I see this manifest in your solutions 3, 4, and 5 as well. In 3, we identify one of the cards i.e. the card identified as the first one drawn, and make a statement about that object. In 4, we also identify one of the cards, i.e. the card identified as the last card drawn, and make a statement about that object. In 5, we identify one of the cards i.e. the card identified as the one corresponding to heads (for example) In 6 and 7, the statement is not applied to any specific card. What I was trying to get at, is that by her "thinking" about a specific card, she has made a selection, and has thus made a statement about a specific card, i.e. the card identified as the one she thought about at this specific point in time. This concept, that making a statement about a specific object changes the probability problem is very neat to me. The real idea behind it, is being able to distinguish between objects, and the impact of that on the probability model. Here is how I think about it in a more general context than this problem: We are talking about two objects, which must differ in some way (for if they did not, how would you even know they are two objects and not one?). We can represent them as an ordered 2-tuple (x,y). When we say something about a specific object, we distinguish them in some way, and we can interpret the meaning of the index of the tuple as an indicator of any differing characteristic. Let's think of some differing characteristics, and apply them here: x is short and fat y is tall and lean you can say the index here (index 0 in the tuple is position x, index 1 in the tuple is position y), can be interpreted as an indicator of fatness. if the index is 0, the object is fat, if 1 the object is lean. you can also interpret it as an indicator of shortness. if the index is 0, the object is short, else the object is tall. the reason i'm bringing this up, is that you can apply this concept to any distinguishing characteristic. one such characteristic might be, (friend of problem solver from above problem is thinking about the object). in general terms, you can take any differing characteristic and map it into an ordering scheme for this 2-tuple. if in a probability problem, we make a statement about a specific object, then we can define a sample space of outcomes, which can be represented as tuples containing the potential states of the two objects, ordered by whatever distinguishing characteristic may be inferred from the statement about the specific object. let's say that specific object was x (i.e. the object in index 0). We may modify the sample space to remove all possible outcomes in which the element in index 0 of the tuple does not satisfy the the statement. now assume no distinguishing statement is made about either object -- this is like Part A above. for lack of a better ordering interpretation, let's use whatever ordering system we used from the case in which a statement about a specific object was made. What outcomes are we allowed to eliminate now from the sample space, given the generic statement about no specific object? We eliminate all outcomes where neither x nor y (i.e. object in index 0 nor object in index 1) satisfy the statement. This is a completely different change to the sample space than the other case, and the probability conclusions will be different in general. Thus, a small, subtle detail, changes everything. And it all comes down to being able to distinguish between objects, which in most cases is satisfied by making a statement about one concrete object, and not making the same statement about the other. Maybe that wasn't the cleanest explanation, but I think I got the meat of it in there.

well... i guess my interpretation is not inconsistent with original problem statement, if 1-on-1 is interpreted as a one-to-one mapping i.e. a pair. "Assume all encounters are 1-on-1 and random." i can definitely see how one would see this and assume that in any "round" only 2 people are selected from the population, and said to have "met". oh well, twas a good exercise of thought.

ah! haha i suppose i should spend more time reading the prompt then, i guess i was solving the wrong problem

This one is cool! http://en.wikipedia.org/wiki/Richard's_paradox The paradox begins with the observation that certain expressions in English unambiguously define real numbers, while other expressions in English do not. For example, "The real number whose integer part is 17 and whose nth decimal place is 0 if n is even and 1 if n is odd" defines the real number 17.1010101..., while the phrase "London is in England" does not define a real number. Thus there is an infinite list of English phrases (where each phrase is of finite length, but lengths vary in the list) that unambiguously define real numbers; arrange this list by length and thendictionary order, so that the ordering is canonical. This yields an infinite list of the corresponding real numbers: r1, r2, ... . Now define a new real number r as follows. The integer part of r is 0, thenth decimal place of r is 1 if the nth decimal place of rn is not 1, and the nth decimal place of r is 2 if the nth decimal place of rn is 1. The preceding two paragraphs are an expression in English which unambiguously defines a real number r. Thus r must be one of the numbers rn. However, r was constructed so that it cannot equal any of the rn. This is the paradoxical contradiction.

To make this short-lived thread more interesting, part B is below: You decide to repeat this game, and follow the same procedure as above in order to deliver her two cards to her. This time, she looks at the two cards and says: "I'm thinking of one of the cards in my hand right now, and it is a red Ace!" What is the probability that both of her cards are Aces of any color?

edit: gack, formatting.