There are two kinds of students in a certain class, those who always lie and those who never lie. Each student know what kind each of the other students is. In a meeting today, each student tells what kind each of the other students is. The answer "liar" is given $240$ times. Yesterday a similar meeting took place, but one of the students did not attend. The answer "liar" was given $216$ times then. How many students are present today?
The question above, was posed, in the 2011 international mathematics competition. I have been studying, for quite a while, but to no avail. I am valiantly attempting, to create a logical connection, between the lies and the truths, without success. Can you guys please guide me, create a logical connection between the two and eventually, work out the answer, to this problem?