Literally. One. Single. Overhead cam.
The single cam operates both intake and exhaust valves through roller rocker arms - pretty clever stuff in 1901! Most cars still used atmospherically operated intake valves at this time. There are actually two lobes on the cam (although it is difficult to see), but since it is a single piece, I’m still considering it a single cam.
Technically speaking the Oldsmobile has a sideshaft, since the camshaft runs along the side of the engine. This was a common arrangement for early single cylinder engines, a multiple cylinder engine would require each cylinder to have its own sideshaft, so it’s easy to see why this mechanism disappeared.
Watch the full video from the Fountainhead Museum in Alaska: