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 Apr 27 awarded Talkative Apr 27 comment How can I determine the number of unique hands of size H for a given deck of cards? I have trouble applying the formula. In my example, H=7, RS=4, C=6. This should give me $\binom{7+4-1}{4} - 4 = 206$ combinations, because I have the "standard" 210 combinations and 4 of them are invalid. Substituting in your formula gives me for $i=1$ the term $-1 \binom{4}{1} \binom{7+4-1-1(6+1)}{4-1} = -4$. For $i=2$, I get a negative term in the binomial coefficient and stop there, as suggested in your comment. This gives me a total of -4 combinations. Where did I go wrong? Apr 27 asked Combinations with up to m repetitions Jan 15 revised On a two dimensional grid is there a formula I can use to spiral coordinates in an outward pattern? changed the default spiral to start in the direction the OP posted in his example Jan 15 revised On a two dimensional grid is there a formula I can use to spiral coordinates in an outward pattern? New implementation, taking parameters for turning direction and for initial orientation Jan 15 answered On a two dimensional grid is there a formula I can use to spiral coordinates in an outward pattern? Dec 6 awarded Commentator Dec 6 comment What is a simple example of an unprovable statement? Maybe my math lessons in school oversimplified things, but I always thought that geometry cannot prove that there is only one straight line going through two points in three dimensional space. Is this the kind of answer you are looking for? (as a layperson, I cannot say if it fulfills your criteria). Jul 30 comment Is this modified coffee cup equivalent to some n-fold torus? Can you make a picture of it for us non mathematicians? This question makes me want to make the donut to complement the mug, but I don't know what a three-fold torus looks like. Is it a normal 3d structure, can it be made from dough? Jun 15 comment 'Obvious' theorems that are actually false @Joshua I have to yet meet a student who notices that this is the root of the problem, and explain how to avoid it in the logical "proof". You are right, of course, once we define the set of "everybody" not as "all humans" but "all humans who are capable of loving my baby", and decide that my baby is not in the set, the result is different. Jun 13 answered 'Obvious' theorems that are actually false Jun 13 comment 'Obvious' theorems that are actually false Good luck finding a layman whose eyes don't glaze at the term "propositional calculus", let alone one who finds something here obvious. May 21 awarded Nice Answer May 14 answered Gift advice: present for high school graduate interested in math Mar 18 comment Is Lewis Carroll's reasoning correct? After reading this question, I have to fight the urge to put two black backgammon stones in a bag. Mar 9 awarded Notable Question Mar 4 asked How to recognize if an algorithm working on ordinal data will also work if the ordering is reversed? Mar 4 comment Can I use the “Secretary Problem” to find the worst candidate, too? @JørgenFogh Interesting thought. Can you give examples which use ordinal (not interval/ratio) data which won't work? Or are interval/ratio algorithms the exceptions you were referring to? ACtually, I think maybe I should ask this in its own question. Jan 28 comment Why is it trivial that $\left(1+\frac{2\ln3}{3}\right)^{-3/2}\leq\frac{2}{3}$? +1. "Trivial" does not mean "obvious" or "quickly proven". It means that, whatever amount of work is needed for the proof, it is uninteresting grunt work. Of course, being obvious makes a proof also trivial, but people forget that not everything trivial is also obvious. Jan 24 comment Is computer science a branch of mathematics? As a computer scientist writing a Ph.D. on Requirements Engineering, I could argue that computer science is in fact a branch of social sciences, not mathematics :P