Some may recall a scene from the movie Rain Man when Dustin Hoffman instantly counts how many toothpicks spilled on the floor: 214 (or so). In reality, how well can humans do in tasks like this? Given, let's say, five seconds to look at a collection of well-separated white ping-pong balls on a black rug, how many can the best-in-the-world-at-this count reliably? --Dan << At this juncture I can't resist observing that "bijective enumeration" is a very primitive counting technique. People well-practised in counting sets of cardinal up to (say) a few tens simply glance once at the whole assemblage, enumerating it instantaneously. Such a facility is necessary in order for example to count sheep in a field, or ducks on a pond --- neither of which are in the habit of waiting around obligingly for any such pedestrian procedure as bijection!
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele