Peter Taylor
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 Jul3 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 $\frac{3125}{256}\alpha^4 - 1 = 0$. Jun27 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. Jun27 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". Jun27 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 $n$? Jun25 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. Jun19 comment A game with numbers from MEMO $2013$ Surely the simplest first two moves for B are $0,0$. Jun12 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. Jun11 comment Gosper summable The case $m=1$ is quite easy. The case $m>1$ seems to require showing that a set of simultaneous equations has no solution. Jun10 comment Hex game winning strategy It's not clear from the question what the board layout is (you can do ASCII art by putting 4 spaces before each line, and there are online designs for ASCII art hexagons), or what the rules of the game are. May21 comment Deterministic Push-Down Automata Is $U$ a terminal? And as a hint: have you tried building a non-deterministic push-down automaton to recognise this language? May21 comment What is one way to prove that there exists no ellipse that matches the exact curvature of the sin wave? That doesn't rule out the sine wave being less than half of an ellipse. May16 comment what is the minimum value of the angles inside these triangles? I think the question is: what is the smallest angle $\alpha$ such that there exists a dissection of the square into triangles satisfying two properties: that none of the triangles has an internal angle greater than $\alpha$; and that no vertex of a triangle touches another triangle except at a vertex. If so, there's an easy lower bound of 67.5 degrees. May6 comment Calculate the Probability for Binary Matrix I assume that the second sentence means that each element of the matrix is $1$ with probability $p$, but is the third sentence talking about independence of random variables or about linear independence (i.e. the matrix is non-singular)? Apr23 comment Repeating cycles in the $3n-1$ problem Your cycles have a very close link with the cycles of $3n+1$ starting with negative $n$. Apr19 comment Return of the lost ant 3D That such paths exist isn't an problem. Whether or not they have a length is another matter. Apr17 comment Maximum number of edges in a (n,n) bipartite graph, that doens't have a complete bipartite subgraph $K_{r,r}$ $c=0$ works for every $r$. Apr17 comment Maximum number of edges in a (n,n) bipartite graph, that doens't have a complete bipartite subgraph $K_{r,r}$ There's a trivial solution: let $c=0$. If $r=1$ then that's tight. Apr17 comment Prove that there are two frogs in one square. Harry Dunlop's answer already provides a solution: this is essentially just Hilbert's Hotel backwards. Apr15 comment Game Theory - Voting The procedure as described doesn't seem to always select a winner. If A gets 51%, B gets 49%, C gets 0%, and D gets 0% then the first round of eliminations should ditch C and D, but neither A or B can be eliminated. Apr15 comment Proof that $12$ in a row tic-tac-toe is a tie game? Tic-tae-toe on an infinite grid can never end in a tie. Presumably you mean that neither player has a winning strategy.