I recall a question from my high school AP math or math SAT exam circa 1964: Two swimmers are swimming laps of a 25' pool, but they swim at different (constant) speeds, say S1 & S2. (Assume that they bounce elastically off the pool ends!) How many times do they pass one another in 30 minutes? This problem is pretty complicated, as one swimmer could pass the other in either the same or opposite direction. The time is also long enough, that you can't simply simulate the first 1,2,3 laps, but must come up with a more general answer. I don't recall how I solved it back then, but I must have gotten the right answer, because I did very well on that test. At 05:06 AM 11/11/2017, James Propp wrote:
Anyone have a favorite puzzle in which miscounting plays a role?
My favorite is the classic bookworm puzzle (see https://math.stackexchange.com/questions/1271651/how-is-this-true-bookworm-p... ).
Another example: A man was born in 50 BC and died on the same day in 50 AD. How old was he when he died?
I'm especially interested in puzzles that lend themselves to solvers committing fencepost errors, and off-by-one errors more generally.
Jim Propp