$35 \cdot 26$ Initially, there are 100 black and 100 white marbles in the jar. Repeat the following operation: each time, take out three marbles from the jar, and put back a corresponding number of marbles from another pile of marbles, the specific number and color are:
After a certain number of times, the possible situation of the remaining marbles in the jar is
(A) 2 black marbles.
(B) 2 white marbles.
(C) 1 black marble.
(D) 1 black and 1 white marble.
(E) 1 white marble.
(42nd American High School Mathematics Examination, 1991)
[Solution] From the procedures of taking and placing marbles, we can see:
Regardless of the situation, the number of white marbles either remains unchanged or decreases by 2 after each operation. In other words:
After each take and place, the reduction in the number of white marbles is always even (0 is considered even).
Starting with 100 white marbles, which is an even number, the number will remain even no matter how many times the operations are performed. And the white marbles only decrease when there are more than 3, so at least 2 will be left. Therefore, the answer is $(B)$.