bonanova

Right on. Use the elevator, make life easy.

Yes. Absolutely correct. And I did not ask the question that I intended to ask. [Where are the puzzle testers when you need them?] Restate: How many BBLs are needed to determine f with the fewest possible drops? To be sure that I mean to say when I ask what I think I mean to ask, I'll break it down. You have n bulbs; there is a strategy for determining f in the fewest drops. Phil's answer is correct for n=1, and worst case it takes 1000 drops. If you have 2 bulbs, there is a strategy for determining f with fewer than 1000 drops. Given 3 bulbs, you could get f with even fewer drops. At some point, say nf, more bulbs won't reduce the number of needed drops. What is nf ? I'll try to rescue the OP with an edit.

Y-san, I see two complications over the standard "hardest logic puzzle." The gods do not respond da or ja: each god has his own language. The third god does not randomly lie or tell the truth, he randomly says yes or no. He may thus answer any question. ThunderCloud, you don't specifically limit our questions to be of the Yes/No variety, but it seems implied?

Taking the up a few notches: When dropped from the fth floor of a building, Bonanova's Brilliant Lightbulbs uniformly will break, but not if dropped from a lower floor. You are tasked with determining f using a nearby 1000-story building. Formulate an efficient strategy for determining f, and then request only as many BBLs as are needed to carry it out, covering the strategy's worst case. Here's one strategy: Drop a BBL from randomly chosen floors. Worst case requires 1000 drops. Ask for 1000 BBLs. But you can do better. What's the number of BBL's needed to determine f with the fewest number of drops? You may assume that a 1000-story building is tall enough for this task.

More to the point of my wondering is how/when/why did any of these considerations make the scene? Something of the nature of the beast, so to speak, made a quantum leap, or the process broke. The fact that it did so is to me the interesting observation. Corollary question: Why aren't there say at least two species that wear clothes?

This is a chestnut. But since no one has jumped in with the answer, I'll give it another life.

And now for something completely different. What part of the evolutionary process involved wearing clothes?

I am giving this puzzle verbatim from a book I read long ago. These days most everything I have ever done was long ago. But I digress. I simply don't trust myself to re-cast it into scintillating banter style. So if its tenor is archaic or arcane, the onus is off me. Enjoy. A rope ran over a pulley; at one end was a monkey, at the other end a weight. The two remained in equilibrium. The weight of the rope was 4 oz/foot, and the ages of the monkey and the monkey's mother amounted to four years. The weight of the monkey was as many pounds as the monkey's mother was years old, and the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey. The weight of the weight exceeded the weight of the rope by as many pounds as the monkey was years old when the monkey's mother was twice as old as the monkey's brother was when the monkey's mother was twice half as old as the monkey's brother will be when the monkey's brother is three times as old as the monkey's mother was when the monkey's mother was three times as old as the monkey was in paragraph 1. The monkey's mother was twice as old as the monkey was when the monkey's mother was half as old as the monkey will be when the monkey is three times as old as the monkey's mother was when the monkey's mother was three times as old as the monkey was in paragraph 1. The age of the monkey's mother exceeded the age of the monkey's brother by the same amount as the age of the monkey's brother exceeded the age of the monkey. What was the length of the rope?

This is a participatory puzzle. You must participate. Write down three consecutive integers. There is no restriction, but your workload will be lighter if you pick small ones. Seriously. Write them down. I will wait. Cube them - that will give you three larger, nonconsecutive integers. Now add their digits. Example: one of your original integers was 347. Remember I said it would be easier to use smaller ones? But does anyone listen any more? 3473 is 41,781,923. 4+1+7+8+1+9+2+3 = 35. Keep going. 3+5 = 8. OK now you can stop. Do this for each of your three integers. Order the results, largest to smallest, to form a new three-digit number. Great job! You're all done. Except, now you have to read the spoiler. Your task is to debunk the rumor that I am psychic. Should not be hard.

Lol...there's the convenient 'Other Recipients' field...send as 'Invitation' to include multiple ppl... ...or are you trolling? ;P Thanks. It's amazing what one can learn simply by admitting ignorance. Scratch one excuse! Trolling? I recall, from my Norwegian heritage, learning about these delightful creatures that would not allow passage without cost. These were the first troll bridges I guess.

Interesting post. In theology Wesley defined "sin" as "willful transgression of a known law of God." So, an act could be a sin or not, based on the actor's state of knowledge or intent. Many logicians attribute the prefix "It is true that ..." or "It is the case that ..." to all declarative statements. That permits a paradox to become instead a simple contradiction. In American courts, there is a permissible disclaimer of "upon information and belief" that allows a witness to tell things as s/he knows them without saddling them with proving the truth of their statements. If we take the liar's paradox as [possibly flawed] informal conversation, we get some added "outs" from the paradox.

I agree with Failure and success need context. In A Knight's Tale, the movie, not Chaucer, William loses match after match to win the heart of Jocelyn. Granted she can't act her way out of a paper bag. But that is a successful failure I'd sign up for.

An important question to answer is, Is the judge a reliable truth-teller?. If the truth of a speaker's statements leads to a paradox, we might consider that he is a liar.

If the future that I saw did not directly involve me, then Yes. Just one look, followed by one trip to Vegas, would be very useful.

Zeno simply describes Achilles' approach to the tortoise in vanishingly small increments of distance. It does not describe what happens after that. In fact, the tortoise does not even have to be present. We could examine his separation from a fixed wall at geometrically decreasing intervals of time. The fact that an infinite number of snapshots can be taken before the time of intercept does not prove the wall will not be reached or the tortoise overtaken. It's a pseudo paradox. Any supposed difficulty here belies lack of familiarity with the nature of real numbers.

There do seem some irregularities with the site. I can see the contents. You might send a PM to Rookie1ja with your specifics. I would have, instead of this post, but I don't know how simultaneously to PM to two people.

I'm definitely on your side of the debate. There is a vague hint of the liar's paradox tho that suggests the debate is undecidable. Only for that reason, I am not marking it as solved. e.g. should we leave the word in the dictionary but without a definition? Indescribable: adj. [adding descriptive text would deny the word's meaning]

Professor bonanova peeks in, wondering if there is a clue yet. He certainly has none ...

Well done. It might be of interest if you have a concise proof?

OK that counts as over-achievement I guess. It's not the fewest trees that can make eighteen rows, but it probably is the fewest that can make twenty. Honorable mention!

Yes. Very close. It's as close as you can come and not be the minimum. That was a hint at the answer.

Well they both have a point. It's a matter of magnitude. Can we assume that if you eliminate everything that is false, all that remains is the truth? That seems reasonable. But if everything is a very large set then that is a daunting task. Especially if the truth is a very small subset of everything. Daunting or not, if we complete the task we have completed the proof. Conceivably we could assemble all the ravens and note their color. Say we did that and they all were in fact black. Q.E.D. In a fairy tale world, we could also assemble everything that is not black.It would take a while, but conceivably we could note each item's identity and confirm none of them were ravens. Q.E.D. So they are both right. It's just that the second proof [to a very much lesser extent the first proof] is in practice carried out to such a miniscule extent that it adds infinitesimally to the proof. There is nothing inherently wrong with examining things that are not remotely related to ravens in order to prove something about ravens. It's just that we have to examine everything, all things, possible ravens or not, that are not black in order to prove something about the blackness of ravens. Only their blackness, and nothing else. It's specious to point out that a white picket fence has nothing to do with ravens. It's more to the point that a white picket fence has something to do with things that might be black.

Well, we might also say that the whole is less than the sum of its parts. A set of numbers {a, b, c, d} has cardinality (4) that is less than the cardinality of the set of its subsets { {} {a} {b} {c} {d} {ab} {ac} {ad} {bc} {bd} {cd} {abc} {abd} {acd} {bcd} {abcd} } (16) and yet it contains all the members of all the subsets. Would that be a paradox?

It may or may not be a paradox. It may or may not be decidable. It may be an ill-constructed statement. It may be inadmissible to logical scrutiny. All depends on what your rules of logic, decidability and semantics are. Here are some ways out of the perceived dilemma. Do not permit self-referential statements. Tarksi's approach.Envision levels of languages, and permit statements in one level only to refer to other statements on the same level or a lower one. Simply put, "This statement is a lie" would not be permitted: it violates our rules for statements. Attach to every declarative statement the prefix: "It is true that ... " or "It is the case that ..." And have the prefix apply to the entire statement. Then we have an equivalence between these statements: [a] This statement is false This statement is true, and this statement is false. The paradox thus transforms to a contradiction. The truth value of a contradiction is False. Conclude that the sentence is not decidable. We can't determine its truth value. The strength of the liar paradox is seen in Godel's first incompleteness theorem, which kind of boils down to a crushing proof of severe limitations on mathematical logic's ability to decide things. So this thing might be escaped through linguistic dodges; it certainly challenges us to understand the meaning of statements; and, in concord with many who hated Godel for his contributions, it leaves us a little less satisfied with the richness of our analytical toolbox.