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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