It took me the entire freshman year to figure out what the hell the numbers meant, but I finally got it when I took genetics.
A chromosome can be one of two things:
A. A chromosome with TWO chromatids connected at the centromere (a "duplicated chromosome")
B. A chromosome with ONE chromatid connected by a centromere. (an undiplicated chromosome)
You see, you have to define what a "chromosome" is before you can count them.
Now, let's examine the actual chromosomes in an egg or sperm. They will be n (meaning half the number of normal chromosomes), so 23.
Now, what do those chromosomes look like? Do they have 2 chromatids apiece, or just one?
Take a look here...
http://publications.nigms.nih.gov/thenewgenetics/images/ch1_meiosis.jpg
You can see the meiosis I is reductive, that is, the number of chromosomes is halved, and in meiosis II, the number of chromosomes stays the same, but the number of chromatids in each cell is halved.
So each gamete is composed of 23 chromosomes, each with 1 chromatid, for a total of 23 chromatids!