MathDB
Marble choosing problem

Source: AHSME 1991 problem 28

November 2, 2011
AMC

Problem Statement

Initially an urn contains 100 black marbles and 100 white marbles. Repeatedly, three marbles are removed from the urn and replaced from a pile outside the urn as follows: \begin{tabular}{ccc} \underline{MARBLES REMOVED} & & \underline{REPLACED WITH} \\ 3 black & & 1 black \\ 2 black, 1 white & &1 black, 1 white\\ 1 black, 2 white & & 2 white \\ 3 white & & 1 black, 1 white \end{tabular} Which of the following sets of marbles could be the contents of the urn after repeated applications of this procedure?
<spanclass=latexbold>(A)</span> 2 black marbles <span class='latex-bold'>(A)</span>\ \text{2 black marbles} <spanclass=latexbold>(B)</span> 2 white marbles<span class='latex-bold'>(B)</span>\ \text{2 white marbles} <spanclass=latexbold>(C)</span> 1 black marble<span class='latex-bold'>(C)</span>\ \text{1 black marble} <spanclass=latexbold>(D)</span> 1 black and 1 white marble<span class='latex-bold'>(D)</span>\ \text{1 black and 1 white marble} <spanclass=latexbold>(E)</span> 1 white marble<span class='latex-bold'>(E)</span>\ \text{1 white marble}