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Aug
19
comment The Day Camp Stacking Game
Is rule 4 a repetition of rule 2 or is it trying to say something additional? (I assume that "clockwise" and "left" mean the same thing here).
Aug
6
comment Deformable circle from a cubic Bezier approximation
What do you mean by "smoothness"? Do you want C2 continuity? G2? Something else?
Jul
31
comment Lower bound for a relative of the central binomial coeff
@Raphael, can you explain why there's a singularity at $-2+\sqrt{5}$? I see singularities at $-2-\sqrt{5}$ and $\frac{1}{4}$.
Jul
30
comment Lower bound for a relative of the central binomial coeff
@GerryMyerson, the central binomial coefficient has a rather neat product representation which allows an easy ad hoc proof of the bound. The only way I can see to get a similar product representation is to factor out a central binomial coefficient from each of the binomial coefficients in the second sum. Then bounding with $\frac{1}{\sqrt{m-2j-1}}\ge\frac{1}{\sqrt{m}}$ I get a non-Gosper-summable hypergeometric, and crudely bounding the terms to get a summable geometric sequence gives a worse bound than simply taking the first term of the original sum.
Jul
30
comment Prove equivalence of Diffie-Hellman shared secret
@codeomnitrix, $a \equiv b\pmod c$ is a shorthand notation for $\exists k : a - b = ck$
Jul
23
comment Transforming a latin square into a sudoku
@EwanDelanoy, that was my first thought for a counterexample, but just permuting the rows to give leading column $147258369$ suffices.
Jul
23
comment Transforming a latin square into a sudoku
And similarly for the 9x9 case it should suffice to fix the top-left 6x6 block.
Jul
18
comment What is the count of the strict partitions of n in k parts not exceeding m?
The answer to "How many different sets $X_1, \ldots, X_m$...?" would seem to be $m$...
Jul
16
comment “I have found a dead body on my car.”
This seems to be more a question about the English language than about mathematical logic.
Jul
13
comment common multiple polynominal time
What is a common multiple of two real numbers? Or, as an alternative phrasing, why is $1$ not always a solution?
Jul
12
comment The number of partitions of $n$ and the $n$th Fibonacci number.
The main difference would seem to be that the first is correct notation and the second is meaningless. When $\operatorname{mod}$ is used as an infix function from $\mathbb{Z}\times\mathbb{N}^+$ to $\mathbb{N}$ you shouldn't separate it from its first argument. $(P_n \operatorname{mod} F_n) = P_n$ looks like a bizarre way of writing $0 \le P_n < F_n$, but $P_n = P_n \pmod{F_n}$ just looks like a tautology with a typo of $=$ for $\equiv$.
Jul
12
comment Describing all points 4000 miles from the north pole
It's impossible to answer the underlying question without first determining the model of the globe and the metric. I think that you're modelling the globe as a sphere (as opposed to an ellipsoid such as the WGS84) and measuring the 4000 miles in Euclidean 3-space (as opposed to geodesics on the surface of the globe). Is this correct?
Jul
9
comment Difficulty parsing combinatorics exercise
I read this as counting pairs of partitions ($\lambda$ is a partition into distinct parts of $k$, $\mu$ is a partition into distinct parts of $l$) such that $k+l=m$, $\lambda$ has $n$ more parts than $\mu$ with the complication of the $0$s.
Jul
3
comment Finding double root of $x^5-x+\alpha$
And then we have $\gcd(x^5 - x + \alpha, 5x^4 - 1)$ $= \gcd(5x^4 - 1, 4x - 5\alpha)$ $= \gcd(4x - 5\alpha, \frac{3125}{256}\alpha^4 - 1)$, so in order for that GCD to be linear we require $\frac{3125}{256}\alpha^4 - 1 = 0$.
Jun
27
comment Looking for different proofs of “Discrete Liouville's Theorem”.
Can you think of a suitable title which includes some non-LaTeX text? Pure LaTeX titles cause some problems.
Jun
27
comment This should be a piece of cake… right?
It wouldn't have cut more than one piece of cake at once, taking the natural meaning of simultaneously. I've edited to remove that adverb and make other clarifications. There's one remaining ambiguity, which I didn't want to resolve because I didn't know in which direction to resolve it: "the cuts may be done however you want" seems to directly contradict "to make it simple, let's say you have a straightedge and a compass".
Jun
27
comment This should be a piece of cake… right?
If I put the cakes side-by-side and cut through them all parallel to the table in one motion, is that one cut or $n$?
Jun
25
comment The expected outcome of a random game of chess?
@mjqxxxx, I think it's because the chess library considers the game to be over when neither player has enough material to mate, and so breaks the loop, but doesn't consider it to be a stalemate, so it wasn't being counted correctly.
Jun
19
comment A game with numbers from MEMO $2013$
Surely the simplest first two moves for B are $0,0$.
Jun
12
comment How do you create a nonlinear game that the player can always win?
The way to maximise the non-linearity is to minimise the interdependence of the puzzles. The point I'm hoping that you'll take away is that you need to rethink your goal.