[math-fun] The fummin problem
(Please delete my e-mail address from any such documents before distributing them — thanks.) The multi-author muffin paper begins as follows: ----- You have m muffins and s students. You want to divide the muffins into pieces and give the shares to students such that every student has m muffins. Find a divide-and-distribute protocol that maximizes the minimum piece. ----- Apologies for not remembering whether I posted the following already, or merely thought it: Suppose we change the problem by changing the objective criterion, from maximizes the minimum piece. (the muffin problem) to minimizes the *number* of pieces (the fummin problem). (I think now I proposed this criterion for finding nice geometric dissections like regular polygon-to-regular polygon ones, but not for a muffin problem.) Minor simplification: Given M disjoint circles of unit circumference, What is the smallest number of pieces to chop them into that can be reassembled into S disjoint congruent circles? (Of course, each would have circumference M/S.) First question: What is the smallest case, if any, where the solution to this problem uses a different dissection from that used in the muffin problem for the same M and S ? —Dan
Surely the quote of the beginning of the muffin paper is incorrect. The authors could not have meant "each student has m muffins". Perhaps the words were "each student has m/s muffins" or "each student has an equal quantity of muffins". On Mon, Apr 2, 2018 at 1:33 PM, Dan Asimov <dasimov@earthlink.net> wrote:
(Please delete my e-mail address from any such documents before distributing them — thanks.)
The multi-author muffin paper begins as follows:
----- You have m muffins and s students. You want to divide the muffins into pieces and give the shares to students such that every student has m muffins. Find a divide-and-distribute protocol that maximizes the minimum piece. -----
Apologies for not remembering whether I posted the following already, or merely thought it:
Suppose we change the problem by changing the objective criterion, from
maximizes the minimum piece. (the muffin problem)
to
minimizes the *number* of pieces (the fummin problem).
(I think now I proposed this criterion for finding nice geometric dissections like regular polygon-to-regular polygon ones, but not for a muffin problem.)
Minor simplification: Given M disjoint circles of unit circumference,
What is the smallest number of pieces to chop them into that can be reassembled into S disjoint congruent circles?
(Of course, each would have circumference M/S.)
First question: What is the smallest case, if any, where the solution to this problem uses a different dissection from that used in the muffin problem for the same M and S ?
—Dan
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Bill Gasarch here. If you are referring to my paper then I am puzzled. I could not find any place where the paper says: ``each student has m muffins'' please clarify so either I can fix a mistake if there is one. bill g. On Mon, Apr 2, 2018 at 2:16 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Surely the quote of the beginning of the muffin paper is incorrect. The authors could not have meant "each student has m muffins". Perhaps the words were "each student has m/s muffins" or "each student has an equal quantity of muffins".
On Mon, Apr 2, 2018 at 1:33 PM, Dan Asimov <dasimov@earthlink.net> wrote:
(Please delete my e-mail address from any such documents before distributing them — thanks.)
The multi-author muffin paper begins as follows:
----- You have m muffins and s students. You want to divide the muffins into pieces and give the shares to students such that every student has m muffins. Find a divide-and-distribute protocol that maximizes the minimum piece. -----
Apologies for not remembering whether I posted the following already, or merely thought it:
Suppose we change the problem by changing the objective criterion, from
maximizes the minimum piece. (the muffin problem)
to
minimizes the *number* of pieces (the fummin problem).
(I think now I proposed this criterion for finding nice geometric dissections like regular polygon-to-regular polygon ones, but not for a muffin problem.)
Minor simplification: Given M disjoint circles of unit circumference,
What is the smallest number of pieces to chop them into that can be reassembled into S disjoint congruent circles?
(Of course, each would have circumference M/S.)
First question: What is the smallest case, if any, where the solution to this problem uses a different dissection from that used in the muffin problem for the same M and S ?
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Allan Wechsler -
Dan Asimov -
William Gasarch