The irrationality of sqrt(2) is one of the more famous easy proofs in mathematics, and one of the typical examples often given of proof by contradiction. (In other words, we assume that sqrt(2)=a/b, an irreducible fraction, and prove that it leads to a contradiction.) I was thinking if this could be generalized. So the hypothesis is: The square root of any non-square integer is irrational. But the approach to this might not be as simple as with the special case of sqrt(2). I couldn't get far with this.
My views on diversity may be confusing because I have a right-wing concept of diversity—diversity of skills or strengths. A good example is Masterjun's SMW ACE, which requires a completely different skillset than the two starred SMW TASes. The left-wing concept of diversity is based on identity, like when Coca Cola Kid or Jetpack got a star solely because they are on 'underrepresented' systems (admit it). Or OoT doesn't get a star because it is part of the Zelda franchise—as if all Zelda TASes were the same just because they share the name Zelda. The site tries to do both but clearly prioritizes the left-wing idea. The starman page says to star 5% for each platform, unless the system is full of garbage games. Why 5%? Where does this number come from? The first part wants to assume, for whatever reason, that exactly the top 5% of each system is starworthy, but then it shifts to acknowledging the arbitrariness of this number since many systems will have <5%. Every system is different. You know Atari has zero starworthy games. The NES could have more than 5% that are worthwhile. Even so, the NES is actually underrepresented according to this 5% rule right now (NES should have 25 instead of 21 stars.) My earlier criticism was not against overrepresenting NES games but instead saying that some mediocre NES TASes got stars partly because the NES is a great system rather than because the TAS itself is great. A top 100 is a specific cap and thus by definition an antonym of 'arbitrary' and gives a star more allure. More and more TASes competing for a limited number of stars is a good thing. Star value would increase over time. Only the most awesome would get one, rather than some awesome and some not-so-great-but-at-least-we-have-diversity.
Is there really no one who finds it absurd that Coca Cola Kid has a star for the sake of diversity while the 3rd-highest rated TAS on the site does not?
Does anyone have any information regarding sub-subpixels? I remember Mister or ISM taking about it a long time ago, but I can't seem to find the post about it. It's an explanation for oscillating speeds and acceleration in general in smw.
Has it been discussed before which video has the largest discrepancy between input time : time till game completion? Because this seems like it could be a contender.
Oh and also we probably need to replace SMB3 warps with something, because the overdose of Mario is quite deadly atm. Maybe with one of these? [1297] SNES EarthBound by pirohiko in 1:10:00.95 [2592] SNES Chrono Trigger by keylie in 2:17:08.86
y=log x is upside-down and y=sin x is back-to-front.
Don't they have Super Mario Advance 4 on GBA TAS of 2017?
Oh My God,Why Judge Is Cancelling All My TASes? are People HATE ME?????
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Hey Amaraticando,How To I Use Scripts,Like the walljump glitch script?
The dwarf puzzle is (mostly) recycled from a similar puzzle with-- if I remember correctly-- 100 seats on an airplane. (I think there may have even been one other riddle of the same form.) The answer to the first question is directly from the previous riddle.
Just a note: Desert Bus wasn't accepted.
You said that right, there are few sections that require actual optimization, across the whole 17:52.19. And also note that the frame precision is just eating away a ridiculously tiny amount of frames. The game is trivial, and the run is as well.
No Funny TAS of 2017?
This is a problem I came up with a little while back and have enjoyed kicking around, especially if I have time to kill and not much around to help kill it. I initially thought of this in an airport when I noticed some patterns in the floor tile. The initial problem: You are given a 3x3 square grid in the plane, through which you may draw as many straight "piercing lines" as you would like. A particular square on the grid is considered "pierced" if it contains one or more piercing lines within the area defined by its edges. The goal is to "skewer" the grid: pierce all the squares in this grid. (Note: piercing lines drawn exactly along a border between two rows/columns of squares do not count as piercing any squares - otherwise the problem becomes trivial). You can clearly do this in 3 lines, by drawing a line through each row or each column. Can you do it with just 2 lines? How about 1 line? Can you prove the lowest value (prove that a solution with less than a certain number of lines does not exist)? Larger grids: How about a 4x4 or a 5x5 grid? Do they follow similar patterns from the 3x3 case? How about an NxN grid? Can you come up with an algorithm for the general case to get an upper bound less than N? Can you prove that this is indeed the lowest number of lines possible? Grids in higher dimensions: Given a 3x3x3 grid of cubes, define piercing lines in a similar way: a cube is pierced if it contains one or more piercing lines within the volume defined by its edges. We can clearly skewer this grid in at least 3 times the optimal solution for the 3x3 grid, as we could draw piercing lines for each "slice" of the third dimension. Can it be done with fewer lines? From here the problem can continue to expand into higher dimensions and larger sizes. I haven't solved all of the aspects of the problem which I've put forth below, but they've been fun to think about. Formalizing geometric stuff into constructs that are more mathematically.. uh, generalizable(?) is not my strong suit, so I haven't gotten very far with any of the proofs.
I don't think I fully understand question 10 (15:00). Had they intended to write that K is an integer? I see that the solution is K = 17^2, corresponding to y = 1000 (or y = 1017). But what's wrong with y = 1008 (or y = 1009), giving K = 1? What's really being asked here?
Question 16 (22:00) annoyed me because the problem statement is ambiguous as to whether the empty set is included. I included it and obtained an answer of 50, instead of the "correct" answer of 49.
Question 24 (30:30) confused me. I figured that two of the numbers being squared had to be zero and the third had to be one. There are five ways to make zero in each of those two squared numbers and three places to put them, totaling 75. I now see that there are eight ways to produce 1 in the remaining term, which is where I miscounted.
I got stuck on question 26 (34:30). I was able to simplify it to the sum over n>1 of 1/(n*(n+3)), but that looks too much like the Basel problem to me. I have no idea how this slight modification turned pi^2/6 into 13/36. Can someone help me?
Question 42 (46:30) stumped me. I wasn't able to come up with a simple expression for the area of a kite, probably because the kite is not uniquely defined by the length of its sides. Of course, the kite of maximal area is uniquely defined by the length of its sides. Could someone explain the quick-and-dirty approach that was likely used to solve the problem?