1991 AHSME Problems/Problem 28

Initially an urn contains 100 white and 100 black marbles. Repeatedly 3 marbles are removed (at random) from the urn and replaced with some marbles from a pile outside the urn as follows: 3 blacks are replaced with 1 black, or 2 blacks and 1 white are replaced with a white and a black, or 1 black and 2 whites are replaced with 2 whites, or 3 whites are replaced with a black and a white. Which of the following could be the contents of the urn after repeated applications of this procedure?

(A) 2 black (B) 2 white (C) 1 black (D) 1 black and 1 white (E) 1 white The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.