Dr. Monadnock, the myopic but lovable precalculus teacher, got up so early each morning that he had to dress in the dark. Every day he would put on two socks grabbed at random from his sock drawer. At the end of the day he would wash them, dry them, and return them to the drawer.

Dr. Monadnock's exceptionally perceptive math students saw him on various days in matching pairs of black, gray, or blue socks, and also in mismatched pairs of these same three colors. After taking careful sock color statistics over an extended period of time, they concluded (quite correctly, as it turns out) that their teacher had exactly a 50% chance of wearing matching socks on any given day.

Assuming that he owned more black socks than gray, and more gray than blue, what is the smallest possible number of each color of sock that Dr. Monadnock might own?

Extra Credit: Same question if we knew that Dr. Monadnock always bought socks in matched pairs, and that he never lost a sock.

Extra Extra Credit: Both questions above, but with greater numbers of sock colors.