Supergrunch

Well, generally it's only students and so on, but occasionally more famous people (like Paul Erdős) have got irritated about the proofs. Neither of those answers is correct. And yes, if they can make a deduction, they make it instantly, but that doesn't mean that there aren't deductions that cannot be made until something has happened.

Well, generally it's only students and so on, but occasionally more famous people (like Paul Erdős) have got irritated about the proofs. Yep. And it's directed at everyone.

Alrighty, time for another well-known but awesome problem, although the setting is a bit contrived: There is an island with 201 people on it, each of whom are "perfect logicians" - if there is a logical deduction that can be made, they make it instantly. 100 of them have blue eyes, 100 have brown, and 1 has green. They are not aware of these proportions, but are of course capable of seeing what colour eyes other people have. If a person works out what colour eyes they have, they must leave the island that night. On day 1, the green eyed person speaks to everyone, saying: "I can see someone with blue eyes." Aside from this, no communication is possible between anyone, and people can't check their eye colour in mirrors or anything similarly stupid. The question is: Who leaves the island, and when?

Hmm, I interpreted it the other way. For your interpretation, n! would be right.

Yep, the joys of Pascal's triangle, which has all sorts of crazy properties. Well, the actual solution is no longer debated as you can computationally demonstrate it, but some people (including mathematicians) aren't really happy with any of the proofs. It's just so counterintuitive.

You and several maths professors at first, but the answer wiki gives as correct is provably right, although it's hell to explain why - I'm sure wiki gives better explanations than I ever could. You can also compuationally model the game show, and if you do enough trials, the success rate converges on the counterintuitive answer.

It's a famous probability problem, and no it's not a trick question (I'll delete such questions from this thread, they don't belong here). And your answer is wrong Moogle.

Moogle and Danny are presumably guessing the solution is n!, which is provably not the case - just look at line 3, where 3! gives 6 ways but there are only 4. In fact, I'm pretty sure the solution is just

I kept wondering about reproduction all the way through that film. Having now googled it, it seems that it's actually just like humans, only with the hair connection thing as well. How unimaginative. That's like the Shakespearean Pulp Fiction thing that's been floating around from a while:

All I mean is that the first ant is as far down the rod as it can possibly be, so there's a length of L between the ant and the wall. It's of course facing the wall, as indicated in the diagram, sorry if that was misleading. And in case anyone is confused, we're treating the ants as points, so their dimensions don't come into it. Yep, in terms of the variables I gave - I can substitute them for real numbers if you want but it doesn't change the problem, and the answer is very simple either way, so there's no need to worry about complex expressions. And thanks for explaining my formulation Chair - I'm too used to giving these types of problems to mathsy people, so I actually now find mathematical notation easier to handle. But it's the problem rather than the notation that's important. I'll give one clue, as I was a little cruel last night - the prime numbers are a red herring, and won't help you solve the problem. Sorry if you think that makes it a trick question, but it just makes things more fun, and isn't a trick in the sense of xkcd 169. Oh, and as Chair implied, n is greater than or equal to 1 (i.e. there is at least one ant), and L > 0 (the rod isn't of zero length).

So, I'm feeling vaguely sleepless and have decided to make this thread as a counterpart to the riddles thread - here, people can post problems that have absolute unarguable solutions, requiring deduction to solve. As a general rule, it's probably a good idea to keep to problems that don't require any advanced knowledge, and that are in some way fun or interesting (subjective of course, but you know what I mean ), rather than just being brute computation or whatever. I'll start things going with one of my favourite problems, that looks a lot more mathematical than it actually is: There is a rod of length L attached to a wall with n ants (a1, a2, ... an) unevenly distributed along it, with the first ant sitting at the far end of the rod, away from the wall. The distance from the first ant to the second is x1, from the second the the third x2, and so on. All ants walk at speed v, and when they collide, they turn around instantly and carry on in the other direction at the same speed (what's known as a perfect elastic collision). The prime numbered ants start off facing away from the wall, and the non-prime ants (including the first) face towards it. When an ant reaches the end of the rod it falls off. Some of this information is shown in the diagram below (red indicates initial direction): How long before all the ants fall off the rod? The solution to this problem is both awesome and far easier than it looks, requiring no knowledge of advanced maths whatsoever. It's not a trick question - this thread isn't about trick questions, it's about clever solutions. Similarly, saying the ants decide to crawl somewhere else or whatever is not a valid approach - as far as this problem is concerned, the rod forms a one-dimensional system and the ants behave exactly as stated. There is enough information given here to work out a genuine answer. I'll see how this goes, anyway. If people don't like this particular problem I might try something that sounds less mathsy.

There aren't many things that instantly demand my money, but that's one of them.

I completely forgot about all this stuff - I had pretty much all the 3D bugs things, loads of the How My Body Works, and a few Dinosaurs to top it off.

Wow craziness, the use of the term gender just seems to be confusing everyone. Starting with what we agree on: sex is an anatomical (and to some extent physiological) term, that's usually binary but by no means always. Hence it's probably best to say it's continuous and one-dimensional, although even that's a bit of a simplification. Now this is where it gets confusing. The term gender actually originates from linguistics, where just refers to a particular category of nouns for a given language. It just so happens that many Indo-European languages, and so most of the "gendered" languages English-speakers are familiar with, have masculine and feminine genders (and sometimes neuter). This is by no means necessary - to use a commonly cited crazy example, the Aboriginal language Dyirbal has one gender for women, fire, dangerous things, non-dangerous birds, and "unique" animals like echidnas and platypuses. But returning to languages like French: over time the linguistic genders take on roles in the culture, and what are effectively stereotypes of male attributes and female attributes are formed, with the gender terms being descriptors. This is the point where the word gender gets adapted, and begins to describe cultural ideas relating to sex rather than anything to do with language. And thus the gender you consider yourself to have really is about stereotypes, as its basically defined by the way in which you identify yourself with the cultural views attached to sex. Thankfully in recent times gender has become a lot more complex than being binary, and as a mental and cultural property, it only really makes sense to view it as continuous and multi-dimensional. This also shows what's wrong with the race example - while you can choose whether or not to subscribe to the cultural properties associated with your race, whether you are of that race is usually genetic rather than cultural. There are grey areas here, however, such as when races become culturally rather than physically defined, and in these cases race becomes more like gender than like sex.

To quote John Gruber:

Hmm, crazy. Maybe your oven is crap (like my one in Cambridge where you generally have to triple the given time), or mine is some kind of furnace. 6 minutes usually seems fine for me. Oven pizzas are too fickle to have a Platonic form.

The general rule of oven pizzas is that the timing given on the packet is a load of rubbish, and you should cook it for just over half that. Don't trust anything but your eyes.

It's not so much non-linear as a random collection of stories written by different people at different times, that have been shoe-horned into all being about the same deity. Anyhoo. Might be seeing The Road tonight. I hope it manages to be better than most post-apocalyptic things are (haven't read the book and so am seeing it in ignorance).

(Somewhat late) congrats to MBAndo! So I submitted my dissertation today, after much frenzied work over the last week. I'm still not entirely happy with a little bit of it, but it'll have to do now. And yay now it's done - I've been working on it for about 6 months now...

Everyone (read: people studying linguistics) seems to know German but me, I feel like I ought to learn it some time. Plus it's kind of archetypal verb second, which is cool. It's a bit funny how modern English is one of the few Germanic languages that isn't. My general (non-German specific) advice is to make sure you have a good grasp of the grammar.

Personally I find that otaku statistic both hilarious and expected, and it's like disruptive selection of genres. Probably doesn't make for good anime overall though.

This only applies if you go to a rich college though. *is jealous*