Barbanel–Brams moving-knives procedure

[1] It makes only two cuts, so each partner receives a single connected piece.

Its main advantage over the earlier Stromquist moving-knives procedure is that it requires only two moving knives, instead of four.

Initially, each partner marks a point such that the cake to its left is worth for them exactly 1/3.

Alice is then asked to mark another point such that the cake to its left is worth for her exactly 2/3.

There are several cases: The procedure can be adapted for chore division - dividing a cake with a negative value: in the initial step the rightmost cut should be selected instead of the leftmost cut, and in the following steps the directions of movement should be adapted such that the desired piece grows instead of shrinking.