What is the optimal way to cut B chocolate bars to share equally between N people, but all people receiving congruent shape parts?

Without the constraint of congruent shape parts, the question was solved here in this group.

I've found this article that uses unitary fractions (Egyptian Fractions) to minimize the arithmetic mean of the number cuts to produce congruent shape parts. But I'm looking for a procedure to minimize the number of cuts, not their mean, while sharing congruent shape parts.


  • 1
    $\begingroup$ I seem a bit confused. Wouldn't minimizing the arithmetic mean simultaneously minimize the total number? $\endgroup$ – Pat Devlin Dec 24 '16 at 21:45
  • $\begingroup$ If I'm not mistaken, by minimizing the arithmetic mean, the cited article admits that the number of pieces received by each people is not an integer number anymore, so it leaves the realm of integer programming and, doing so, it is not realistic. $\endgroup$ – Humberto José Bortolossi Dec 24 '16 at 22:56
  • $\begingroup$ I wonder why it is so hard to find any good references about a simple problem. :( $\endgroup$ – Humberto José Bortolossi Dec 24 '16 at 23:02
  • $\begingroup$ The problem is simple but not easy. Another example: If a baguette is randomly split into 3 pieces, what's the expected length of the largest piece ? The correct answer is far from would you'd expect. $\endgroup$ – dohmatob Dec 25 '16 at 16:16

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