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 Civic Duty
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  • 0 posts edited
  • 249 helpful flags
  • 346 votes cast
Mar
16
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?
Feb
11
comment A ship sails to an island . Find the average sailing speed for the whole journey.
How did this become a hot question???
Dec
29
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 $8\choose 5$+$8\choose 6$+$8\choose 7$+$8\choose 8$?
Dec
27
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.
Dec
27
awarded  Civic Duty
Dec
20
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
Dec
20
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.
Dec
19
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.
Dec
19
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?
Dec
13
comment Geometry Problem about tangent lines
I assume the middle of an arc is meant to be its intersection with its bisector?
Dec
13
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?
Nov
30
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...
Nov
25
awarded  Pundit
Nov
18
awarded  Yearling
Nov
4
comment Does limit of $x_n=(1+\frac{1}{2})*(1+\frac{1}{4})*…*(1+\frac{1}{2^n})$ exist?
an increasing function is always monotonic...
Oct
28
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 $y$?
Oct
23
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?
Oct
23
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.
Oct
23
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?
Oct
16
comment improper integrals: Need help please
@mm-aops I guess you meant for $a>1$?