The contest rules are pretty simple:

1. Each unique National Parks Passport cancellation stamp that you acquire counts as 1 muffin stamp.
2. You must do something in that park, as far as it is possible, in order to qualify for the muffin stamp.
3. At least one contest year must elapse before you can reacquire a muffin stamp that counts towards your total.
4. In the event of a tie, the person(s) with the most unique muffin stamps for that year will be declared the winner.
5. Specially issued stamps can count as “half-stamps” and can serve as a first tie-breaker.

Examples of the above:

1. Getting the Lincoln Memorial stamp at the Lincoln Memorial and at the Washington Monument bookstore would not work, because it is the same stamp. Plus, that would be dumb. In contrast, if you visited the C&O Canal visitor centers at Great Falls, Brunswick, Hancock and Cumberland, which each have their own, unique stamp, that would easily count as 4 stamps.
2. For stamps like the George Washington Parkway and the Suitland Parkway, which are just roads, driving them is about all that you can do. In pursuit of The 19 I didn’t collect on the Washington Monument, even though I was standing outside of it, because I didn’t really do anything other than look at it. When I collected the Catoctin Mountain NP stamp, back in 2003, I at least walked one of the trails, even if it was the shortest.
3. Monocacy NB is about 3 miles away from where I live. I went there in 2007, shortly after the new visitor center opened up, and got a stamp. I could go there as many times as I want this year, but a stamp from Monocacy NB will not count again towards The Muffin until January 1, 2009.
4. Pretty self-explanatory. There have been 2 ties already. Although it’s a shame if you go to some far flung place for a muffin stamp, like Hawaii or the U.S. Virgin Islands, and somebody else wins because they walked the National Mall–like yours truly–that’s tough cheese. Go get some more stamps! Although so far, whether intentionally or incidentally, we don’t seem to aggressively pursue the trophy in years when someone else has gotten far away stamps.
5. Golden Spike NHS in Promontory, Utah, had a stamp with the date that the first transcontinental railroad line was completed, which we got on the 140th Anniversary. Of course, I don’t know whether or not they have that stamp there every day, like the little choo-choo stamp they had.

Update: Looks like I haven’t been admiring my trophy enough, since Eric correctly pointed out that there has only been one tie in the history of The Muffin. Mom has always threatened to force a tie whenever she has been trailing in the muffin count. I guess I just assumed that she followed through on her threat one of these last few contest years.