Title: The Blind Bartender's Game
Archive date: 1 September 1994
Abstract: Consider the following problem: A blind bartender wearing heavy gloves is trying to align four glasses arranged in a square on a table in front of him. That is to say he is trying to make them all be right side up or all upside down. Because of the gloves he cannot feel the glasses in order to tell which is which. He can reach out with one or two hands, grab one or two glasses, and turn them over, repeating this process as long as the glasses are not all aligned. Unfortunately, some practical jokers amongst the patrons spin the table between his attempts. It turns out, as we shall see, that the bartender has a strategy for accomplishing his aim, despite all these handicaps.
We shall consider an even more difficult problem. Suppose we replace the four glasses with $n$ glasses placed at the vertices of a regular $n$-gon and replace the bartender with a blind octopus wearing heavy gloves on each of his $n/2$ hands. We shall show that the octopus has a strategy for success iff $n$ is a power of $2$.
We do not yet know the complete geneology of this problem. We heard it from a colleague in the PSU Math Department who in turn got it from a friend in the Computer Science Department who got it from his daughter at Amherst who got it from a graduate student who had heard it while visiting Bell Labs. It is quite possible that everything presented here is well known in New Jersey, but we are so pleased with the results that we have written them down anyway.
Available Formats: This article was prepared using AMS-LaTeX. It is available as bbg.tex or in dvi form as bbg.dvi .