If memory serves, that's one point in the game that represents a major failing on Infocom's part, regarding a lot of later software: the bright idea that if they made the packaging materials essential to beating each game, they'd stop losing profits to pirates. People illegally copied the games anyway, of course, so all it did was to make the legitimate players suffer.
This almost ruined the otherwise fantastic
Spellbreaker for me. Once I learned that I needed the documentation that had been included in the original game package, I found the docs online and finally passed the silly in-game quiz about wizard names. It was always so intrusive, yanking you right out of the story and ruining the self-contained nature of the on-screen text.
In the case of
Zork Zero, I believe that the calendar that came with the game was necessary for beating the jester at Double Fanucci. I had trouble with that part too, which is probably why I'm remembering it.
Okay; I've just searched through the calendar, and I think I found the month that contains the hint. Here's a link to that image, found right here at the Zork Library. Zoom-in on the image, and read the prose about Babe Flathead for the clue:
http://thezorklibrary.com/zork0/zork0-calendar14.jpg
I think you're supposed to just play any card you want during each turn, waiting until the jester makes his fatal move (see the calendar for a hint about what this should be). Then make your "indefensible gambit" triple-play that supposedly can't fail. I'm pretty sure that should do it, and allow you to grab the broom (again, that's only if my memory of the game is intact). I hope I haven't given away too much; at least you can have fun looking for the hint on the calendar!