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
