A local ice creamery gave the principal of the high school 295 ice cream certificates, good for a huge order of ice cream, to be awarded to any
student with a B average or better. As it happened, 297 students had at
least a B average. Since there were 2 more students than ice cream
certificates, the principal started a long, agonizing process of giving
them out and determining who didn't get one. Each day the principal
chose 3 students at random. If all 3 were freshmen, they were each
awarded a certificate. If 2 of the 3 were sophomores, the principal
awarded the certificates to the 2 sophomores and put the third's name
back in the hat. If all 3 were from a different class, he awarded all 3.
If any other combination of students was selected, no certificates were
awarded that day and the names went back in the hat. At the end of
many days, there were only two B-average students left who had not
received a certificate. At the beginning there had been 101 freshmen,
99 sophomores, and 97 juniors. From which class were the two
remaining students?