Elevator Paradox

A fact noticed by physicist G. Gamow when he had an office on the second floor and physicist M. Stern had an office on the sixth floor of a seven-story building (Gamow and Stern 1958, Gardner 1986). Gamow noticed that about 5/6 of the time, the first elevator to stop on his floor was going down, whereas about the same fraction of time, the first elevator to stop on the sixth floor was going up. This actually makes perfect sense, since 5 of the 6 floors 1, 3, 4, 5, 6, 7 are above the second, and 5 of the 6 floors 1, 2, 3, 4, 5, 7 are below the sixth. However, the situation takes some unexpected turns if more than one elevator is involved, as discussed by Gardner (1986). Furthermore, even worse, the analysis by Gamow and Stern (1958) turns out to be incorrect (Knuth 1969)!

Main character Charles Eppes discusses the elevator paradox in the Season 4 episode "Chinese Box" of the television crime drama NUMB3RS.

REFERENCES

Gamow, G. and Stern, M. Puzzle Math. New York: Viking, 1958.

Gardner, M. "Elevators." Ch. 10 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, pp. 123-132, 1986.

Knuth, D. E. "The Gamow-Stern Elevator Problem." J. Recr. Math. 2, 131-137, 1969.