David Bevan
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 Dec 11 awarded Nice Answer Sep 29 comment $N$ perfect logicians wearing hats @ghosts_in_the_code: See my answer below for an alternative presentation of what Joriki and Ross are describing. It works for any number of blind logicians and any number of hat colours. I was unaware of this discussion (hidden in the comments) when I posted my solution. Sep 29 comment $N$ perfect logicians wearing hats @mercio: in fact it does work with more than 2 hat colours! Sep 29 revised $N$ perfect logicians wearing hats generalized for an arbitrary number of colours Sep 28 awarded Custodian Sep 28 reviewed Approve How many extrema for the function $f(x)=3x^4-4x^3+6x^2+ax+b$ Sep 28 comment $N$ perfect logicians wearing hats @mercio, answer updated Sep 28 revised $N$ perfect logicians wearing hats updated in light of Marcio's comments; deleted 2 characters in body Sep 28 revised $N$ perfect logicians wearing hats added 20 characters in body Sep 28 answered $N$ perfect logicians wearing hats Sep 25 comment What's the property of this series? Is it special? Coefficients of $\left(x\frac{d}{dx}\right)^n f(x)$ @ClémentGuérin: I've added a combinatorial explanation. Sep 25 answered What's the property of this series? Is it special? Coefficients of $\left(x\frac{d}{dx}\right)^n f(x)$ Sep 25 answered How to formulate $(1-x)^k(1+x)^{n-k}$ as a polynomial sum expression Sep 10 comment How many different sums of parts of a vector @ColmBhandal: I'd see the first chapter (only) of Analytic Combinatorics by Flajolet & Sedgewick for a well written intro to the relevant stuff about generating functions. A PDF of the book is available online. Sequences and runs aren't really different, although in the context of this answer, you'll see that I've use them consistently to refer to different aspects of the argument. Btw, I've corrected a typo in the table. Sep 10 revised How many different sums of parts of a vector corrected typo in table Sep 9 revised How many different sums of parts of a vector simplified explicit answer Sep 9 revised How many different sums of parts of a vector added explicit form for answer Sep 9 comment Proving you *can't* make $2011$ out of $1,2,3,4$: nice twist on the usual @BhaskarVashishth: Percentage divides by 100. E.g. 5%=1/20. Sep 9 revised How many different sums of parts of a vector improved wording Sep 9 answered How many different sums of parts of a vector