Don't let yourself get very hungry...at the first pang of hunger, take a lemonade. I found that if I waited too long, the lemonade was not as satisfying as it is right away.
As Zoe suggested, the mental part of the Master-Cleanse is the biggest challenge. You really won't be hungry on this cleanse if you do it right (that is, drink enough lemonade). That fact is most startling to many people. But you will want to eat for other reasons - habit, boredom, socializing, etc. And THAT is where the mental challenge comes in. You have to be truly dedicated to doing this or it is pretty easy to talk yourself into eating something.