Mathematicians solve real-life problems

Out of toilet paper.

What is toilet paper? A tissue that through repeated contact transfers fluids and solids from the nether area to itself, after which the tissue plus fluids and solids can be disposed of.

The most common substitutes ignore this last part: using the person’s own hand, for example, is a highly suboptimal solution since the hand cannot be disposed of in any easy fashion. This is because the hand is attached to the body.

Likewise, the use of underpants, t-shirts, and overcoats is troublesome because of the disposal problem. Leaving overcoats with fluid and solid remnants at one’s local waste disposal point can result in loss of social prestige.

The optimal solution to running out of toilet paper are small birds. Their own motor effects serve to enhance the transfer of fluids and solids, and once released at a window, they dispose of themselves.

Exercise. (a) Compare the effectiveness of utilizing pet birds vs. wild birds, as regards costs of care vs. immediate availability. (b) How to catch birds when not wearing clothing on the waist-ankles interval. (c) Are specific toilet rooms necessary? Design a portable intra-rectal toilet with pneumatic compression.

Opening doors.

What is a locked door? A rotational system attached to a doorframe at n points, that can be orthogonalized from the frame if at most n-1 of those points are fixed, enabling access through the doorframe.

If, however, all n of those points are fixed (i.e. the key is lost), the usual layman solution is to “bust” the door, that is, to reduce the structural integrity of the door rectangle until (a) one of the points gives, or (b) a sufficient subset of the door rectangle orthogonalizes.

Such brute force methods are not elegant and cannot be recommended. The local order authority may react to them negatively and possibly induce unforeseen fatalities.

Exercise. (a) Formulate the door analogue in an arbitrary dimension. (b) Build a 5-dimensional door. Do not open it for any reason whatsoever. (c) Study the theory of doorknobs, e.g. T. Setting’s Mathematics for the Knobhead. (d) Write a search algorithm for arbitrary keys, then ask the author for a test key.

This problem of opening doors without keys is as of yet unsolved. Those interested in collaboration on the matter should contact Prof. Holzbein, Königstrasse 2a (the porch), Stuttgart.

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