30. There is a two-person moving-knife cake-division procedure due to A. K. Austin that leads to each player receiving a piece of cake that he or she considers to be of size exactly one-half. It begins by having one of the two players (Bob) place two knives over the cake, one of which is at the left edge and the other of which is parallel to the first and placed so that the piece between the knives (A in the picture below) is of size exactly one-half in Bob’s estimation.

If Carol agrees that this is a 50-50 division, we are done. Otherwise, Bob starts moving both knives to the right—perhaps at different rates—so that the piece between the knives remains of size one-half in his eyes. Carol calls “stop” at the point when she also thinks the piece between the two knives is of size exactly one-half.