Wikipedia Link

Does anyone know why this works? Conway's algorithms aren't making much sense to me, and the wikipedia page doesn't offer much explanation. Besides his calculations, one thing I'm having trouble with is this:

It takes advantage of the fact that within any calendar year, the days of 4/4, 6/6, 8/8, 10/10, 12/12, and the last day of February always occur on the same day of the week—the so-called "doomsday" (and furthermore that other months have "doomsday" on the pairs 5/9 and 9/5 as well as 7/11 and 11/7

This is true--In 2010, all those listed days were a Sunday, and wikipedia says that January 3rd and the last day of non-leap year Februarys are the doomsday...But how is that true? How does that just happen to line up?

And why do you need an "anchor" day?

I've copied some of the math below, if anyone's interested:

**Spoiler:**