Jan Dvorak
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 Mar16 comment Cute problem a computer science classmate shared (adding non-coprimes to n smaller than n as fast as possible) Why do I feel like the part of title that's in parentheses is way more important than the part that isn't? Feb11 comment A ship sails to an island . Find the average sailing speed for the whole journey. How did this become a hot question??? Dec29 comment In a room there are eight lights. Each light can be switched on and off independently of the others. In how many ways can the room be lit with-? Why not just do $8\choose 5$+$8\choose 6$+$8\choose 7$+$8\choose 8$? Dec27 comment Is there a proof that zero multiplied by infinity = a real number Zero times infinity is undefined. There's nothing to prove here. Move on. Dec27 awarded Civic Duty Dec20 comment Best function getting 0 for odd parameter, 1 for even This should evaluate pretty fast: min(abs x', abs(x'-2)) where x' = x mod 2 Dec20 comment What are some interesting sole exceptions or counterexamples? More specifically: The function is defined as f x=sqrt(x+f x) => (f x)^2 = x + f x => f x = 1/2 +- sqrt(4*x + 1)/2 (where the upper branch is used here). This function's derivative converges to zero monotonically, which means this inequality is true for any reals > 2. x=0 is the other intersection with x=y and also a vertex of the parabola. Dec19 comment What are some interesting sole exceptions or counterexamples? Why would this be restricted to primes? This seems like a rather simple function that just happens to cross y=x at x=2. Dec19 comment Check if Sequence is Graphic: 8, 8, 7, 7, 6, 6, 4, 3, 2, 1, 1, 1 have you tried applying the handshaking lemma yet? Dec13 comment Geometry Problem about tangent lines I assume the middle of an arc is meant to be its intersection with its bisector? Dec13 comment Geometry Problem about tangent lines No problem is beautiful if it's somebody else's homework that he just needs help with. Do you mind if I consider the title kinda inaccurate? Nov30 comment The infinite sum of the reciprocal of a strictly increasing sequence is irrational if we place a limiting condition on the se quence itself izœc's suggestion still applies... Nov25 awarded Pundit Nov18 awarded Yearling Nov4 comment Does limit of $x_n=(1+\frac{1}{2})*(1+\frac{1}{4})*…*(1+\frac{1}{2^n})$ exist? Oct28 comment Are the hyperreal numbers densely ordered? What happens if you try to look at ${x+y}\over2$ as a number strictly between $x$ and $y$? Oct23 comment Best strategy for this game. [Nintendo Wii game] "the optimal strategy involves some randomness." - as I said in the comments. But what's the optimal set of probabilities, if there is any? Oct23 comment Best strategy for this game. [Nintendo Wii game] The strategy to always choose 5 sounds good if other players choose uniformly randomly (which is a bad strategy if yours clearly outperforms it). At each step you have a 8/27 ~ 1/3 chance of moving forwards, and you only need to move twice. An opponent that calls either 1 or 3 has a 4/9 ~ 1/2 chance of being uncontested, but they have to succeed 4 resp. 10 times. BUT if two different players choose that, one of the other two is sure to win. Oct23 comment Best strategy for this game. [Nintendo Wii game] There is no winning pure strategy - if everyone plays the same, noone moves. And I'm not sure if there's a single dominating probabilistic strategy. Anyone willing to do the maths? Oct16 comment improper integrals: Need help please @mm-aops I guess you meant for $a>1$?