ABSTRACT
Presumably, a more satisfactory division in either case could be made if more cuts were allowed. So what could be done with n cuts (where one player would receive two pieces) or n+ 1 cuts? To define our problem more formally, suppose
n players are to share a cake X using k or fewer cuts. Motivated by the two possible points of view mentioned above, let us examine the two values
We have seen finite algorithms that accomplish simple fair division for three and four players using three cuts (Section 2.3) and four cuts (Section 2.6) respectively. Also, in Section 8.2 we saw that for n ~ 3, n - 1 cuts aren't enough to accomplish fair division for n players. What do we know for other numbers of players? Although the problem of determining the least number of cuts, F{n), needed to guarantee each of n players a piece of size 1/n using a finite algorithm seems very difficult, perhaps we can make some progress when the number of players is small.
