I’ve been absent from math-fun for a while, but from a quick glance at recent posts I see mention of N-athlons and visual estimation of shapes. Strangely, these combine in a new, untested, race that involves parked cars. The idea is to have the runners shout out the N-fold symmetry of the parked car hubcaps as they are passing them. You’d have to space the runners, so they cannot hear each other. But I think you get the idea: to get a good time you can’t afford to stop and count spokes (or whatever) to determine N. For example, you can train your eye/brain to determine if there is a line of bilateral symmetry, and then the existence or non-existence of an equivalent line orthogonal to that. Now you are dealing with N congruent to 0 or 2 mod 4, and for N not too large (<20) the ball-park-estimate part of your brain should be able to quickly arrive at say, 18 (don’t ask me why, but they exist). In the movie Rain Man, the title character was able to count objects almost instantaneously, up to the hundreds. Such people would do very well in my proposed race, and without clever tricks … or so you would think. Although it’s been a long time since I saw that movie, I clearly recall that when he was counting the number of spilled matches on the floor he verbalized 62,62,62,62 … 248 (please correct me if I got the numbers wrong). So it seems the Rain Man was able to directly see the factorization! Alternative hypothesis: he really liked 62 as a unit, and it was a lucky accident that it came out even. -Veit