3 ms·

Knuth's Toilet Paper Problem

32 points by fogus 16y ago

Jun8 16y ago
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.
ryandvm 16y ago
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.
- pavel_lishin 16y ago
  This assumes perfectly logical actors.
- Stormbringer 16y ago
  Or you might always choose from the closest roll.
num1 16y ago
Is there some deep analogy that I'm missing, or is he just giving an example of how to analyze things?
- Stormbringer 16y ago
  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 16y ago
    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.
  - apetresc 16y ago
    This paper was published in the American Mathematical Monthly, a journal which is mainly known for its expository articles, not necessarily for original research. For that purpose (exposition) this paper does its job admirably. Whether it's useful research is not really important in evaluating whether it was worthy of its funding.
Stormbringer 16y ago
From the article: "When both rolls are empty, everybody has a problem." Indeed.
deleted 16y ago
[deleted]
iwwr 16y ago
Randall Munroe must be a fork of Knuth: http://blog.xkcd.com/2009/09/02/urinal-protocol-vulnerability/ http://blog.xkcd.com/2009/09/02/urinal-protocol-vulnerabilit...

32 points by fogus 16y ago

Jun8 16y ago

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.

ryandvm 16y ago

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.

pavel_lishin 16y ago
This assumes perfectly logical actors.
Stormbringer 16y ago
Or you might always choose from the closest roll.

num1 16y ago

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

Stormbringer 16y ago
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 16y ago
  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.
- apetresc 16y ago
  This paper was published in the American Mathematical Monthly, a journal which is mainly known for its expository articles, not necessarily for original research. For that purpose (exposition) this paper does its job admirably. Whether it's useful research is not really important in evaluating whether it was worthy of its funding.

Stormbringer 16y ago

From the article: "When both rolls are empty, everybody has a problem." Indeed.

deleted 16y ago

[deleted]

iwwr 16y ago

Randall Munroe must be a fork of Knuth: http://blog.xkcd.com/2009/09/02/urinal-protocol-vulnerability/ http://blog.xkcd.com/2009/09/02/urinal-protocol-vulnerabilit...