A lot of people here seem to misunderstand the nature of the hacks that these laws are targetting. The intention here is to punish those who abuse these hacks to gain a competitive edge when playing against others, which can be extremely sizable especially for FPSes. Professional teams also rely on the in game competitive rankings to scout for new talent, so this abuse can have further ramifications apart from brusing egos.
One assumption not explicitly explained is that the prisoners can identify the boxes by their order, since they are arranged in a line. So, the prisoners first agree among themselves that box number x should correspond to which prisoner, and vice versa. So now, each box contains a name, which points to another box at a certain position, which contains another name, ad infinitum, until the prisoner finds his name. It is guaranteed that he will, because of the relationship between permutations and cycles.
It is interesting that this question is regarded as the most math intensive. I myself was spoiled the solution a few years ago, but I have the impression that the challenge is in observing the correct algorithm rather than calculating the probability. Maybe the author felt that one needs mathematical insights in order to see the solution out of the blue.
>I have the impression that the challenge is in observing the correct algorithm rather than calculating the probability
I've got a stats PhD and I guessed the solution but couldn't calculate the probability of having a max cycle length of 50 or less. To be fair, the calculation isn't hard once you see it, but it's not trivial either.
The 30% figure threw me since I know the probability of a random permutation having a fixed point is 1/e (just over 30%), so I went looking for ways to link the cycle length to the Poisson distribution.
I beg to differ. Math olympiad problems are typically short and concise, and mathematical phrasing, even when expressed in English, typically has clear bijections to equivalent terms in other languages.
Well, the motivations to attend hackathons don't seem to be about winning. Many of us students attend hackathons knowing that the chances of winning something is marginal at best, yet we still regularly attend for the singular reason of fun. It's not every day that you can just spend two days of your life, cut off from the rest of the world, working with your buddies on something you all love. Even for professionals, attending hackathons could be a means to break away from the monotony of normal work.
Interesting points, but minor correction here. Typing Chinese efficiently has to do with the input method. Using pinyin as you suggest is actually hopelessly slow as you would have to first recall the precise pronunciation of the word (the -n vs -ng for example), type the pinyin, then scroll through the (normally) massive list of words. Of course, things like fuzzy pinyin and context aware suggestions help, but adopting an input method based on the character radical composition or handwriting recognition is much faster.
> "Using pinyin as you suggest is actually hopelessly slow"
Everyone I've encountered in China seems to do it just fine. It is only hopelessly slow if you type one character at a time.
> "adopting an input method based on the character radical composition or handwriting recognition is much faster"
What character radical input method are you talking about? I can't imagine any input method using radical composition being faster, it would be comparable to using Latin roots to type out English words; there are just too many to be practical. You can actually do this on Pleco, but it takes forever, even longer than typing one character at a time in pinyin.
Handwriting could work assuming you can handwrite Chinese quickly (I would be deathly slow as I can't read a typical handwritten cursive note, much less write one). I think handwriting recognition is already pretty good, people just use pinyin because it's the easiest.
The wubi input method (五笔字形) uses radical composition or something like it -- keys represent different (semi-arbitrary) character portions, and you "build" characters by choosing the portions, and adding other keys that indicate the overall shape of the character. You can get nearly any character out there in four keys, usually much less, and it also does phrase input. It's much harder to learn, obviously, but a practiced wubi typist is supposed to be able to go faster than pinyin.
Over the years I've tried to teach myself, and I can sort of do it, but I never got fast enough to really switch away from pinyin.
Pinyin is just fine (or zhuyin in my case), but the parent is right about one thing. Structure based inputs like Cangjie and Wubi are really fast. Fewer strokes per character and zero need to select from a list mean more speed.
From what I've seen, it is mostly Southerners (南方人) or Western people taught by Southerners who have trouble with distinguishing between endings such as -n and -ng.
Also, pinyin IMEs can be fairly fast even with only minimal practice as the matching is done at the word level (and possibly some IMEs look at preceeding characters) rather than at the character level. For example, when entering 南方人, my tying sequence was "nanfangren<space>", and the IME was already suggesting the correct answer at "r", so I could have actually typed "nanfangr<space>".
There are also a lot of phrases that can be typed with just the first letter from each word, eg typing "bth" gives "不太好", "zmy" gives "怎么样", and there are endless more combinations like this.
I can't remember seeing anybody using anything but pinyin input, foreigners and locals alike. You can compose entire sentences and let the software pick the correct hanzi in bulk.
I've never seen a Chinese person using handwriting input, even though it's widely available on smartphones. They all use pinyin input because it's easiest and fastest.
I write on my iPhone and use pinyin on my Linux, Mac and Windows computers. I'd like to write Cantonese and Japanese too, but I don't do that enough to bother finding the relevant input software. Using a hiragana table is much slower for me than writing the characters using my index finger.
It is useful when you are trying to type a character that you cannot quite pronounce/pronounce erroneously. It happens quite often even with Chinese people. With this input you can simply imitate the strokes.
> first recall the precise pronunciation of the word (the -n vs -ng for example)
I am a foreigner living in China and this was never an issue for me, so I doubt the native people here find that a problem.
I rarely see any Chinese people use the handwriting character recognition on their phones. I use it sometimes just for practice, but just writing pinyin is much faster.
I could imagine skip[0] being quite efficient. I doubt any native speaker would use it, though. I have used multiple radical lookup systems before, and they are not in any way efficient. I don't speak Chinese, but I do a fair bit of writing in Japanese and phonetic input is very, very quick (especially with context sensitive completion).
Can this really be said in all fairness? What of the flashes of brilliance, the striking insights into understanding seemingly inexplicable phenomena? The discovery of the structure of benzene, the creation of the periodic table comes to mind.
I think you are a little hasty in assuming that the author had the popular misconception that Einstein was bad at math. Certainly, Einstein was much better at math than the average man, but among his fellow physicists, not to mention the handful of physicists as celebrated as he is, his mathematical skills pales in comparison.
In other words, his contributions to science arose from his exceptional physical insights, and not his mathematical brilliance.
> In other words, his contributions to science arose from his exceptional physical insights, and not his mathematical brilliance.
True about special relativity, certainly false about general relativity. Between 1905 and 1915, Einstein learned the mathematics required to formulate and write the general theory.
