answer:I propose a much simpler division. A makes the first cut of the cake. Just one cut. If B and C both agree that that slice is fair, that is, no greater than any person was entitled to, then A gets to take it. This leaves the simpler problem of dividing a piece of cake in two pieces, to be shared by B & C. If B or C decides that the slice that A made was too big, then A gets to divide the remaining piece and take the last choice of pieces. B and C still have to decide how to split the two remaining pieces. If they both agree that the two larger slices are fair, then they can take those and leave A the remainder. If B or C believes that either piece is too large (and the other person is unwilling to concede that piece to the one who so believes), then they can decide who will trim the equalizing portion from that, and the other gets first choice of “apparently equal” portions, the person who made the final cut gets his choice as second, and A, as noted earlier, gets the last choice. Much less decision making, much quicker, and much less handling of the cake.