Abstract: In 1891,French mathematician Edouard Lucas gave his famous Married Couples Circular Table Problem:in how many ways can n married couples be seated around a circular table in such a manner that there is always one man between two women and none of the men is next to his own wife.In this article,we generalize this problem to Married Couples’ Trapezoidal Table Problem:in how many ways can n married couples be seated around a trapezoidal table with two sides having 1 and 2n-1 seats,respectively,in such a manner that there is always one man between two women and none of the men is next to his own wife.In this paper,the enumeration formula of this problem is obtained.

Key words: circular table problem, linear table problem, trapezoidal table problem