why is it that every participant is able to perfectly cut a cake into pieces they themselves consider fair, but at the same time, are unable to cut them precisely into equally sizes pieces?\n\nthis is how i imagine it:\nmoderator: alice, cut it!\n*alice cuts*\nalice: oops, this one got too big. can i have a new cake?\nmoderator: no, you like all the pieces equally, as agreed upon in advance!\n*game continues, in the end nobody is satisfied*