TnT: Tips and Tricks in Binary Logic
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True always speaks truly, False always speaks falsely, but whether Random speaks binary logic questions tricks 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 Binary logic questions tricks, but will answer all binary logic questions tricks in their own language, in which the words for yes and no are da and jain some order. You do not know which word means which. Boolos provides the following clarifications: Boolos credits the logician Raymond Smullyan as the originator of the puzzle and John McCarthy with adding the difficulty of not knowing what da and ja mean.
Related puzzles can be found throughout Smullyan's writings. For example, in What is the Name of This Book? He explains binary logic questions tricks "the situation is enormously complicated by the fact that although all the natives understand English perfectly, an ancient taboo of the island forbids them ever to use non-native words in their speech.
Hence whenever you ask them a yes-no question, they reply Bal or Da —one of which means yes and the other no. The trouble is that we do not know which of Bal or Da means yes and which means no. The puzzle is based on Knights and Knaves puzzles. One setting for this puzzle is a fictional island inhabited only by knights and knaves, where knights always tell the truth and knaves always lie. One version of these puzzles was popularized by a scene in the fantasy film Labyrinth. There are two doors with two guards.
One guard lies and one guard does not. One door leads to the castle and the other leads to 'certain death'. The puzzle is to find out which door leads to the castle by asking one of the guards one question. In the movie, the protagonist Sarah, does this by asking, "Would he [the other guard] tell me that this door leads to the castle? Boolos provided his solution in the same article in binary logic questions tricks he introduced the puzzle.
Boolos states that the "first move is to find a god that you can be certain is not Random, and binary logic questions tricks is either True or False". One strategy is to use complicated logical connectives in your questions either biconditionals or some equivalent construction. It was observed by Roberts and independently by Rabern and Rabern that the puzzle's solution can be simplified by using certain counterfactuals.
The reason this works can be seen by studying the logical form of the expected answer to the question. This binary logic questions tricks form Boolean expression is developed below ' Q' is true if the answer to Q is 'yes', ' God' is true if the god to whom the question is asked is acting as a truth-teller and 'Ja' is true if the meaning of Ja is 'yes':. This final expression evaluates to true if the answer is Jaand false otherwise.
The eight cases are worked out below 1 represents true, and 0 false:. Comparing the first and last columns makes it plain to see that the answer is Ja only when the answer to the question is 'yes'.
The same results apply if the question asked were instead: Each of the eight cases are equivalently reasoned out below in words:. Regardless of whether the asked god is lying or not and regardless of which word means yes and which noyou can determine if the truthful answer to Q is yes or no. The solution below constructs its three questions using the lemma described above. Boolos' third clarifying remark explains Random's behavior as follows: This does not state if the coin flip is for each question, or each "session", that is the entire series of questions.
If interpreted as being a single random selection which lasts for the duration of the session, Rabern and Rabern show that the puzzle could be solved in only two questions;  this is because the counterfactual had been designed such that regardless of whether the answerer in this binary logic questions tricks Random was as a truth-teller or a false-teller, the truthful answer to Q would be clear.
Another possible interpretation of Random's behaviour when faced with the counterfactual is that he answers the question in its totality after flipping the coin in his head, but figures out the answer to Q in his previous state of mind, while the question is being asked. Once again, this makes asking Random the counterfactual useless. If this is the case, a small change to the binary logic questions tricks above yields a question which will always elicit a meaningful answer from Random.
The change is as follows:. This effectively extracts the truth-teller and liar personalities from Random and forces him to be only one of them. By doing so the puzzle becomes completely trivial, that is, truthful answers can be easily obtained. However, it assumes that Random has decided to lie or tell the truth prior to determining the correct answer to the question — something not stated by the puzzle or the clarifying remark. Rabern and Rabern suggest making an amendment to Boolos' original puzzle so that Random is actually random.
The modification is to replace Boolos' third clarifying remark with the following: With this modification, the puzzle's solution demands the more careful god-interrogation given at the top of The Solution section. In A simple solution to the hardest logic puzzle ever B. Rabern offer a variant of the puzzle: For example, if the question "Are you going to answer this question with the word that means no in your language?
The paper represents this as his head exploding" They have but one recourse — their heads explode. In support of a two-question solution to the puzzle, the authors solve a similar simpler puzzle using just two questions.
Note that this puzzle is trivially binary logic questions tricks with three questions. Furthermore, to solve the puzzle in two questions, the following lemma is proved. Using this lemma it is simple to solve the puzzle in two questions. Rabern and Rabern use a similar trick tempering the liar's paradox to solve the original puzzle in just two questions.
Uzquiano uses these techniques to provide a two question solution to the amended puzzle. Neither True nor False can provide an answer to the following question.
Since the amended Random answers in a truly random manner, neither True nor False can predict whether Random would answer ja or da to the question of whether Dushanbe is in Kirghizia. Given this ignorance they will be unable to tell the truth or lie — they will therefore remain silent. Random, however, who spouts random nonsense, will have no problem spouting off either ja or da.
Uzquiano exploits this asymmetry to provide a two question solution to the modified puzzle. Here again neither True nor False are able to answer this question given their commitments of truth-telling and lying, respectively. They are forced to answer ja just in case the answer they are committed to give is da and this they cannot do. Just as before they will suffer a head explosion. In contrast, Random will mindlessly spout his nonsense and randomly answer ja or da. Uzquiano also uses this asymmetry to provide a two question solution to the modified puzzle.
From Wikipedia, the free encyclopedia. It is stated as follows: The Harvard Review of PhilosophyVolume 6pp. The Harvard Review of Philosophy. This is different from a god who answers 'yes' or 'no' randomly. One usual trick in solving many logic puzzles is to design a perhaps composite question that forces both a truth-teller and a liar to answer 'yes'.
For such a question, a person binary logic questions tricks randomly chooses to be a truth-teller or a liar is still forced binary logic questions tricks answer 'yes', but a person who answers randomly may answer 'yes' or 'no'. What is the Name of This Book? Englewood Binary logic questions tricks, New Jersey: The Riddle binary logic questions tricks Scheherazade.