36-22 Some students sit around a round table, passing a small package containing 100 pieces of candy. Each person takes one piece when they receive the package, then passes it to the next person on their right. If a student gets both the first and the last piece, how many students could there be?
(A) 10.
(B) 11.
(C) 19.
(D) 20.
(E) 25.
(6th American Junior High School Mathematics Examination, 1990)
[Solution] If a student gets the first piece and also the last piece, then the total number of people should be a divisor of 99.
Among the five numbers given, only 11 fits.
Therefore, the answer is $(B)$.