Recently, Howard Bergerson proposed the following research problem in logology:
I have had one research problem in mind for a long time -- I once did some preliminary work on it -- which could turn out to be anything from easy to formidable to practically impossible. It is this: Imagine the one thousand vigintillion minus one (if you don't include zero) consecutively named numbers arranged in alphabetical order and also in numerical order. How many (if any) numbers have their positions the same in both lists? What is the least such number? ... Does this intrigue you enough to have a shot at it?
When I first read this, my reaction was that of a mathematician. Isn't this merely a verbal version of the well-known matching problem in probability -- the game in which two well-shuffled decks of cards are matched, one card at a time from one deck against one card from the other, until identical cards appear?
Eckler, A. Ross
"Alphabetizing the Integers,"
Word Ways: Vol. 14
, Article 6.
Available at: https://digitalcommons.butler.edu/wordways/vol14/iss1/6