It is based strictly on the rules of Towers of Hanoi, a well-known problem in the Computer Science world. You begin with three pegs, and a number of stones of varying sizes. The goal is to move all stones from the first peg to the third, by picking up a stone at once and under the constraint that a stone cannot be place on top of a smaller one.
In Burgers of Hanoi, Burly the bear returns, and he has to move a hamburger, ingredient by ingredient, to the spot marked with an arrow. The catch is that they must be kept in the same order, just like for the original game. You better not put the meat on top of the lettuce, or anything else crazy like that!
For bigger projects, I think it'd be useful to make your own tile maker. I drew the graphics in Excel, and calculated bit field values by hand. I included documentation for how tiles are stored in memory. Once you beat the game, it will lock up. I couldn't think of a nice ending to the game...
the Burgers of Hanoi rom. Should play in most Sega Master System emulators
the Burgers of Hanoi source code. Use it with the z88 dev kit
the z88 dev kit. Unzip it to C:\. It comes with an emulator, and the source code for Burgers of Hanoi (and another simpler example), found in the source directory
a good Sega emulator. I used it as a run-time environment to try out my homebrew code