bonanova
-
Posts
6975 -
Joined
-
Last visited
-
Days Won
66
Content Type
Profiles
Forums
Events
Gallery
Blogs
Everything posted by bonanova
-
In post 17 I explained a method for uniformly covering a triangle that is a modification of the simple problem of covering a square. Stretch the square into a rectangle, skew the rectangle into a rhombus, then cut the rhombus diagonally into a triangle. The points in the unused triangle can be discarded or reflected back into the used triangle. This method, and appropriate methods for other 2-d and 3-d shapes, can be found on Wolfram's MathWorld site
-
Well, to be clear, I don't think you can generate random points in 3-space from two RNGs. The triangle with vertices at 110, 010, 001 is still a plane surface, not a volume. That is, z is not an independent variable, it's a calculable function of x and y within their allowed ranges.,
-
It's probably not conical.
-
Another way to pick points at random on a geometrical shape:
-
In Sp's original problem, he asked that the outcomes be random in the sense of being equally likely to occur over the triangle with vertices 100, 010, 001, This might be a paraphrase of the current problem: suppose you have a way to generate equally likely outcomes of a single variable, say of x, in the interval [0,1]. How might you use that to create outcomes that are equally spaced over the triangle? That is, not clustered near, for example, the vertices, or near the center, etc. For the triangle, there are a number of "obvious" approaches that don't give a uniform distribution. If that's not what being asked, it's still an interesting exercise; it finds use in simulations where probability is not easily calculated; but by repeating a random outcome many times, and counting the desired results as a fraction of the total of the trials, the probability emerges. Hint for plasmid: Since we want uniformity over a plane surface, this should be achievable using only two applications of a one-dimensional random number generator.
-
My take on araver's discussion is that earlier solutions did not adequately rule out cases where everyone would abstain. That point, I could not see had been covered. In my that point was clear, because the 8 cases could easily be enumerated.
-
Announcement: New Forum Moderators
bonanova replied to rookie1ja's topic in Comments and Suggestions
Adding pubic congrats for Sp and Pg to earlier privates ones. -
My post was edited and quoted at the same time - matter hits antimatter - and was anihilated. Reconstructing ... The correct [and much simpler] problem has an interesting property.
-
Agree. I misread the OP as {(x,y,z)|x,y,z are real & x+y+z<=1 & 0≤x≤1 & 0≤y≤1 & 0≤z≤1}
-
-
Well the strategy can't produce a winning probability But it also can't be
-
Back of the envelope calculation for the two-dimension case.
-
I'm replying from my iPad on which spoilers don't seem available. So until I get to my desktop I'll just say it seems to admit use of uniform point picking and hence a ratio of two calculable quantities. SP, if this gives away too much, feel free to use your new powers to Spoiler it. ;-)
-
I expect that it can be shown using Green's theorem with a judiciously chosen rectangular curve. But I don't see the general result, or the back door. Interesting problem.
-
I'd hold off a bit with the answer. I just saw the problem and I think there's a theorem from my school days that may prove fruitful
-
-
Since you're looking for the score with a single deck why does speed come into play? Play the spade A then the spade J, clearing the column. Is your score 125 [50 for the AJ 21 and 75 for the black J] or 75 [21 is not scored]?
-
Hats on a death row!! One of my favorites puzzles!
bonanova replied to roolstar's question in New Logic/Math Puzzles
After two and a half years, I see that my algorithm is incomplete. -
Is the riddle title a clue?
-
I think she asks that people who did not know the answer before reading it now be given time to figure it out. Spoilers accomplish the same purpose.
-
I think the OP allows for the set of counterfeits to be {null} {H} {L} {HH} {HL} or {LL}. It doesn't say only one coin can come from each of the batches, nor, if there are two, that both must come from one of the two batches.
-
Do you ask for a definition that excludes synonyms of the word being defined? A definition might contain a collection of words, each too general to be a synonym, but taken together [logical AND] provides a sufficiently narrow description to function as a definition. But then do these broad words become classifications [as the OP uses the term]? If that's the question, it's an interesting one.
-
A->B <-> B v ^A A Knight may thus speak: "If 2+2=5 then New York is a small city."
-
Nice. OP might belong in logic/math more than word puzzle, but, it was literary so... Hope it was fun. - bn
-
Since Wilson seems reticent to supply his method, [or was it a guess?] here it is.