Question 28
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: Marbles removed 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 Which of the following sets of marbles could be the contents of the urn after repeated applications of this procedure?