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Dec
22
comment Kings on a chessboard
@Serkan, I'm not sure what you're counting there. The more obvious criticism is that the last sentence of my comment talks about "reducing" to a problem class which already contains the original problem.
Dec
20
comment Kings on a chessboard
Not a complete answer, but it might help: divide the board into 9 $2\times 2$ tiles. Each such tile can contain at most one king, so this gives an easy (but very loose) upper bound of $5^9$. Moreover, this approach reduces the problem to a 2D analogue of combinatorics on words: counting grids which avoid forbidden subgrids.
Dec
15
comment Calculate how many ways to get change of 78
What's wrong with the various programs that people supplied you in answer to your earlier question?
Dec
10
comment combinatorics - fixed point permutations
Wolfram Alpha suggests not. If there were a closed form then Petkovšek's algorithm should find it, and I would be very surprised if Alpha doesn't implement it.
Dec
7
comment Polynomials with rational zeros
In addition to saying what you've tried - homework is given to help you learn by doing - it would help to say where you encountered this. What theorems did your course just cover?
Dec
4
comment Closed form expression for unusual sum of binomial coefficients
The way computer algebra systems derive the closed form expression is by using knowledge about what the answer looks like. Specifically, if your expression has an indefinite sum then it's the term multiplied by a rational polynomial, and it's possible to bound the degrees of the numerator and denominator. See Gosper's algorithm
Dec
2
comment Determining Ambiguity in Context Free Grammars
An even simpler ambiguous string is $()$.
Nov
25
comment Prove that every practical number is either a power of two or a power of two times a non-trivial polygonal number
@half-integerfan, I've added lists of 1000 and 1000000 practical numbers to my personal site at cheddarmonk.org/maths/practical_numbers/… and obvious substitution. I will refresh my memory on the current comment submission process for OEIS at a later date.
Nov
8
comment Representing everywhere a camera can see as a matrix
you can test a point $Q=(x_Q, y_Q, z_Q)$ against the near and far planes by simply comparing $z_Q$ to the near and far clipping distances; you can clip against the side planes by comparing $x_Q / z_Q$ to $\pm\tan (\theta_w/2)$ where $\theta_w$ is the angular width; and you can clip against the top and bottom planes by comparing $y_Q / z_Q$ to $\pm\tan (\theta_h/2)$ where $\theta_h$ is the angular height.
Nov
8
comment Representing everywhere a camera can see as a matrix
@Imray, the frustrum is bounded by 6 planes. Testing which side of a plane a point is on comes down to looking at the sign of a dot product. (E.g. if the plane is defined by a point $P$ in the plane and its normal $N$ then you can test which side a point $Q$ is by looking at the sign of $(Q-P).N$). It wouldn't surprise me, though, if actual implementations take a different approach. If you transform the world such that your camera is positioned at the origin and looks along the $z$-axis, with the up vector pointing along the $y$-axis, then (cont)
Nov
7
comment Probabilty to win in die rolling game
Thanks for editing to add your ideas. The point at which you're going wrong is to interpret the question as asking for a probability which relates to a single die roll. It's actually asking for the probability that you lose on the first die roll (which you correctly state to be $k/N$), or that you lose on your next die roll, or a subsequent one. I hope that makes it clearer what you should be recursing on.
Nov
5
comment Dead presidents
I think the only reasonable answer to this question is that it's not well posed. If you're supposed to pretend you don't know the death dates, shouldn't you also pretend that you don't know how many are still alive? So the person who posed it should specify precisely what information you have as prior knowledge.
Nov
4
comment is this operating procedure an Abelian Group?
@K.L., yes, each element is self-inverse.
Nov
2
comment Generator of a subgroup of a cyclic group
The title is the only thing about the question which shows in most contexts, so it's worth having a title which gives a clue as to what the question is about.
Nov
1
comment What is the official proof (if there is any) for the area of a circle of radius 'r'?
Related question: math.stackexchange.com/q/44631/5676
Oct
31
comment How to show that the order in which multiple sums are performed does not matter
Probably not sufficiently rigorous for your purposes, but the first of Knuth's Two notes on notation is relevant.
Oct
31
comment Probability to find A
The answers to all three questions are A, axiomatically.
Oct
26
comment Freeman Dyson's example of an unprovable truth
That fills the gap nicely. Thanks.
Oct
26
comment Freeman Dyson's example of an unprovable truth
I don't see the relevance of your comments on "unlikely" true statements. The contrapositive of "it seems likely, so it must be true" is not "it seems unlikely, so it must be false".
Oct
24
comment Show that if $F$ is multiplicative, then $f$ is multiplicative
How do you justify $$\sum_{d\mid n_1n_2} \mu(d)F(n_1n_2/d) = \sum_{d\mid n_1n_2} \mu(d)F(n_1/d)F(n_2/d)$$?