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Mar
29
comment $\sin(\pi - a) = \sin (a)$. How/why?
What's your definition of $\sin$? Is it in terms of triangles or complex exponentials?
Mar
25
comment Math of password cracking
Spaces are \, or \;. Your formula looks correct, so if it overestimates then the obvious question is: why do you think it does 4 billion calculations per second? Edit: wait, I may have it. Does your program exit early when it finds the password? Your calculation is the worst case: if the password is generated uniformly and randomly then on average it will take half that time.
Mar
24
comment Number of ways to set 3 queens to attack each other
I'm not sure whether the problem statement is intended to be that each queen is attacked by at least one queen or by all other queens; and in the latter case, whether you intend to count "all in a straight line" as an exception.
Mar
24
comment $A ⊂ B$ if and only if $A − B = ∅$
The statement is incorrect. Alberto's answer proves the correct statement (with $\subseteq$ instead of $\subset$), but for some reason doesn't point out this important difference.
Mar
24
comment Do all logic problems have one solution?
The NAND operator also includes the case that neither of the operands is true. I think you're confusing it with XOR. But for the first issue, if you know what the problem is with your answer, and you know how to fix the problem, what's the question? And for the second issue, what do you mean? I can see two instances of $P(y)$ in that answer.
Mar
18
comment Growth factor problem
@DavidK, in my experience it is never a good idea to suggest to someone new to the SE network that a question would be a better fit on a different site in the network unless you explicitly mention that it can be migrated by flagging and asking a moderator to do it. Otherwise you end up with cross-posts and much irritation all round. But in this case, it seems to be pure algebraic manipulation, so I think it's a better fit here.
Mar
18
comment Growth factor problem
I've edited in the relevant formulae, but it would be helpful to have more context in terms of what you've tried and how far you get. E.g. is $\frac{d\ln g}{dt} = \frac{\dot{g}}{g}$ a useful hint to get you started, or are you already way beyond that?
Mar
16
comment Mathematical Analysis Question: Cauchy sequences proof
You must surely have tried something. If you show us what you've tried and why it doesn't work, you'll be able to get help which actually helps you.
Mar
15
comment The irreducibility of polynomials for specific cases
In your second paragraph, irreducible should say reducible.
Mar
9
comment Selection from cliques of a graph in polynomial time
Are you given that the cliques are maximal?
Mar
6
comment Examples of non-hamiltonian decomposable graphs
Either I'm misunderstanding your notation or $C_2 \times C_3 = K_6$, which is 5-regular. Note also the statement in the second MathWorld page I linked that every Hamiltonian vertex-transitive graph with no more than 31 vertices has a Hamilton decomposition except the line graphs of the Petersen and Coxeter graphs. The next smallest known non-decomposable vertex-transitive graph has 48 vertices, so if you're looking for examples which can be checked by hand you almost certainly want to look at non-vertex-transitive graphs.
Mar
5
comment Examples of non-hamiltonian decomposable graphs
Any non-hamiltonian graph, for a start. Or any graph whose number of edges isn't an integer multiple of its number of vertices. Can you narrow down a bit more what you're looking for? PS Mathworld's page on Hamilton decomposition may have what you want.
Mar
5
comment Probability of get 3 cards out of 4
One million tries seems somewhat overkill given that there are only 270725 ways of choosing 4 cards from a 52-card deck: it would probably be easy and just as fast to adapt your program to calculate the exact value you seek. But I'm not clear what it is you're calculating. What do you mean by "off-suited and off-ranked"?
Feb
27
comment Asymptotic for binomial coefficients
@BrianM.Scott, you've lost a factor of $k^k$ in the last step of the first approximation.
Feb
26
comment Multinomial theorem: Number of elements where all coefficients have even powers..
An alternative way of phrasing what you're after is the elements of $(a_1^2 + \ldots + a_n^2)^{r/2}$.
Feb
26
comment Ball-of-wacks combinations
"Never share an edge or vertex" is equivalent to "Never share a vertex", since two faces which share an edge also share two vertices. In this particular case, the structure of the faces is such that we can ignore the vertices of order 3 and the problem is equivalent to edge-colouring a regular icosahedron, which may be an easier problem to think about.
Feb
12
comment Find two numbers whose sum is 20 and LCM is 24
Depending on the conventions adopted for an LCM involving negative numbers, -4 and 24 could be another solution.
Feb
12
comment Find two numbers whose sum is 20 and LCM is 24
@AlexR, it's a question of conventions, and I'm sure there are some people who would argue that an lcm involving a negative number should be negative. But since you say it's 24, that's a counterexample to your earlier claim.
Feb
12
comment Find two numbers whose sum is 20 and LCM is 24
@AlexR, that depends on what you consider to be the value of $\textrm{lcm}(-4, 24)$.
Feb
10
comment Is the language “substrings of an even-lengthed regular language” also regular?
@j6m8, I think he's answering the question in the title rather than the question in the body. Maybe you should edit the title to something like "Is the language of 50%-prefixes of words in a regular language also regular?"