Adding algorithmic class attribute to widget box

I’m working on a theme that has widgets running horizontally across the footer. The theme is styled to have three across.

It would be helpful if I could hack something to put a different class in the first, second, and third widget-wrapping divs. This would allow me to roll back to the beginning if there’s a 4th (or 7th, etc) widget. I’m guessing somewhere I’d need code along the lines of

switch $countOfThisWidget mod 3 {
case 1:
echo "<div class='firstwidget'>";
case 2:
echo "<div class='secondwidget'>";
case 0:
echo "<div class='lastwidget'>";
}

Clearly I’d need to hack an existing function; I’d like to do this in a portable way so that I can distribute the theme and not need to worry about hacking on future copies of WP.

If we lived in the magical future of CSS3, I wouldn’t need to bother with this at all.