
How to hang a picture using n nails such that removing any k nails makes it fall - robinhouston
http://arxiv.org/abs/1203.3602v1
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losvedir
Why am I not surprised the Demaines are behind this? They're a hilarious
father-son team at MIT.

I worked next to Martin (the father) at CSAIL one summer. He excitedly ushered
me and some friends into his office one day to show us all a new video he had
finished shooting with Erik. It was a real-life demonstration of some
algorithmic problem about rolling a cube over a pattern on the ground. In the
video, Martin proceeded to put on a helmet and then climb into a box which
Erik then rolled everywhere. And by 'rolled', I mean, tipped the cube up onto
its edge to have it come crashing down onto a new face (with Martin inside,
sometimes upside down). It was very funny.

Also, looks like Ron Rivest of RSA fame is an author.

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cperciva
This is the first time I've come across an algorithm which is proven to
operate in _O(n^56556)_ time.

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willvarfar
One can imagine a guillotine that chops the king's head off only if K members
of the revolutionary council reach agreement and turn their keys...

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mad44
I see what you did there. A professor of mine once said that humans remember
stories related to violence or sex (which is a no-no in class). I guess,
hence, two-generals problem, byzantine-generals.

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Jun8
And you can combine the two, e.g. another paper from the same conference: "The
Byzantine Brides Problem" Swan Dubois, Sébastien Tixeuil and Nini Zhu.

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arihant
Almost every paper or artwork by Erik Demaine opens me to something I wouldn't
ever imagine. I encourage everyone to look at his website. He is closest to
the da Vinci of our times.

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cs702
Agree.

I enjoy the annual origami puzzles too: <http://erikdemaine.org/puzzles/>

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kapitalx
I enjoyed his 'family' tree. Showing his academic ancestry to the likes of
Fourier and Euler at the bottom of this page: <http://erikdemaine.org/family/>

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JadeNB
As the note at the bottom of the page mentions, the 'tree' part of that can be
got for any mathematician from the wonderful Mathematics Genealogy Project:
<http://genealogy.math.ndsu.nodak.edu/index.php>.

While we're on collaborations and curiosities, I could have sworn that there
was a page out there that would try to calculate your Erdös number
automatically (maybe through MathSciNet?), but I can't seem to find it.

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kylec
Bad title, "removing any k nails makes it fall" is NOT the same thing as "the
picture remains hanging when fewer than k nails get removed".

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willvarfar
You mean it may fall sooner?

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kylec
The title implies that removing _at most_ k nails makes it fall, the actual
paper deals requires _at least_ k nails to be removed to make it fall.

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willvarfar
"such that the picture falls whenever any k out of the n nails get removed,
and the picture remains hanging when fewer than k nails get removed."

I interpret that to mean _exactly_ K nails; no more, no less.

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kiiski
If it falls when exactly K nails are removed, I don't think it will go back up
when you remove the K+1th nail. And if you remove k-1 nails first, and then
remove 2 more simultaneously, the picture will fall anyway. So it's ">= K".

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spicyj
"At least k" might imply that removing more than k nails is necessary to make
the picture fall, which is not the case. I think "exactly k" is perfectly
clear.

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aplusbi
"Exactly k" is not clear because the picture will still fall if you remove k+1
nails. I think it's harder to get clearer than the way it's stated in the
paper: "the picture falls whenever any k out of the n nails get removed, and
the picture remains hanging when fewer than k nails get removed."

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thebooktocome
That's really weird. My complex analysis professor assigned a few cases of
these as joke homework problems (vaguely related to winding numbers around
poles) around two years ago.

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lell
the case where n=2, k=1 was an IMO problem around 2001/2002 (and the parent
article says it is first from spivak '97) and it's pretty easy to see the
generalization if you know about fundamental groups. I used to pose the n
arbitrary, k=1 case to other math students :D (parent article claims this
version is first from mathpuzzle.com, 2002)

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ma2rten
This was published at the The Sixth International conference on Fun with
Algorithms (FUN 2012). Maybe it's worth looking looking into other papers from
that conference. I am wondering what a keynote of such a conference might
sound like.

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powrtoch
Simple. Let n = k.

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meepmorp
Right, from the title, that's what I first thought, and figured that the lower
bound on the value of n is 1.

