either X2' (if it was not taken by Alice) or X1 (otherwise); Carl gets either X3' (if it was not taken by Alice) or X1 (otherwise). The trimmings, E2 and E3, are divided in a similar way to Case 1. Oskui also showed how to convert the following moving-knife procedures from cake-cutting to chore-cutting: Stromquist moving-knives procedure The rotating-knife procedure. Peterson and Su's continuous procedures for three and four partners Peterson and Su suggested a different procedure for three partners. It is simpler and more symmetric than Oskui's procedure, but it is not discrete, since it relies on a moving-knife procedure. Their key idea is to divide the chores into six pieces and then give each partner the two pieces that they feel are at least as small as the pieces the other players receive. Step One. Divide the chores into 3 pieces using any envy-free cake cutting method and assign each piece to the player that finds it the largest. Step Two. Using Austin moving-knife procedure, divide piece 1 to two slices that partners 1 and 2 consider equal. Let partner 3 choose the slice that is smaller in his eyes, and give the other slice to partner 2. Similarly, divide piece 2 to two slices that partners 2 and 3 consider equal, let partner 1 choose the smallest slice and give the other slice to partner 3. Similarly, divide piece 3 to two slices that partners 3 and 1 consider equal, let partner 2 choose the smallest slice and give the other slice to partner 1. Analysis. Partner 1 holds two slices: one from piece 2 and one from piece 3. In the eyes of partner 1, the slice from piece 2 is smaller than its slice given to partner 3, and the slice from piece 3 is smaller than its slice given to partner 2. Moreover, both these slices are smaller than the slices of piece 1, since piece 1 is larger than both piece 2 and piece 3 (by Step One). Therefore, partner 1 believes that his share is (weakly) smaller than each of the other two shares. The same considerations apply to partners 2 and 3. Therefore, the division is envy-free. Peterson and Su extend their continuous procedure to four partners. Peterson and Su's discrete procedure for any number of partners The existence of a discrete procedure for five or more partners remained an open