The easiest way to save everybody would be for each gnome to take the party hat of the gnome in front and place it on their respective heads. This way, gnomes 2-10 would know their hat's color.

Once gnome number 10 finishes his turn, we know he "lives", and is is "freed". Gnome 10 doesn't need the party hat anymore, so he gives it to gnome 1 on his way out. All gnome 1 has to do is listen to what gnome 10 says.