
Knuth's Toilet Paper Problem - fogus
http://gi.cebitec.uni-bielefeld.de/teaching/2007summer/jclub/papers/toiletPaper.pdf
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Jun8
Interesting problem that we face everyday. Knuth assumes that people are
either big or little choosers. I don't think this is the case, e.g. my
strategy is dependent on the size of the rolls.

When the roll is really big (i.e almost brand new), the low quality toilet
paper (that my company thinks we're worth, if you're working in a better place
this is a moot point) tends to tear, so that I can't get a piece of adequate
length. This is because the tension on the paper is proportional to the moment
of inertia of the roll and larger rolls have higher inertia. So, given a
choice, I avoid these rolls.

On the other hand, really small rolls are annoying, too, since it's hard to
estimate if the amount left is enough, i.e. while pulling a piece of paper
they may finish unexpectedly, which is annoying.

So, my strategy is: avoid the very big and very small rolls. Around medium
size, go for the smaller roll. I wonder how Knuth's analysis could accommodate
such dynamic strategies based on roll size.

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ryandvm
Wait - what kind of person would draw from the big roll?

The goal isn't to use them both up simultaneously. You use all of one and then
the stall still has the other one during the period it takes the janitorial
staff to notice and replace the empty.

~~~
Stormbringer
Or you might always choose from the closest roll.

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iwwr
Randall Munroe must be a fork of Knuth:

[http://blog.xkcd.com/2009/09/02/urinal-protocol-
vulnerabilit...](http://blog.xkcd.com/2009/09/02/urinal-protocol-
vulnerability/)

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Stormbringer
From the article:

"When both rolls are empty, everybody has a problem."

Indeed.

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num1
Is there some deep analogy that I'm missing, or is he just giving an example
of how to analyze things?

~~~
Stormbringer
I think the deeper analogy, if there is one, is that this is the difference
between Computer _Science_ and Computer _Programming_.

Or perhaps that the govt will pay for any old shit:

"My research was supported in part by National Science Foundation grant
MCS-83-00984."

~~~
jcl
Or perhaps we should be asking: What are all the _other_ NSF-funded scientists
doing on their bathroom breaks? Knuth's output has clearly been accounted for.

