This question discusses fair three-way sandwich division. Mentoined solutions include the Selfridge–Conway discrete procedure and the moving-knife procedure. I posed the question to the guys at the office and we can't think why this method would not be a solution:

  1. A makes the first cut.
  2. B makes the second cut.
  3. C chooses a piece.
  4. A chooses a piece.
  5. B gets the remaining piece.

Is this a solution? If not then why not?

  • $\begingroup$ If $A$ cuts the cake / sandwitch / whatever in more or less exactly half, then no matter what B cuts, he will end up with at most a quarter, and thus be unstatisfied. $\endgroup$
    – Arthur
    Feb 18, 2014 at 12:38
  • $\begingroup$ But A would have no motivation to cut in half because he will then always be left with less than a third. $\endgroup$
    – Daniel
    Feb 18, 2014 at 12:44
  • $\begingroup$ You might say that, but the point of the Selfridge-conway procedure is that no matter where you or anyone else actually cut, as long as you are under the impression that your own cuts are made fairly, and you always choose the biggest piece available, then it logically follows that your share is at least as big as anyone else's. That is not the case in the above procedure. $\endgroup$
    – Arthur
    Feb 18, 2014 at 12:47
  • $\begingroup$ Can you state the question in mathematical language? $\endgroup$ Feb 18, 2014 at 12:48

1 Answer 1


Suppose that A thinks that he has cut the sandwich into 1/3 and 2/3, but B then cuts the piece which A thought was 1/3. C can now take the piece which A thinks is 2/3, and A is going to be very unhappy.


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