300 students participated in a symposium with 3 conferences in sequence.

Half of the students that attended the first conference, attended neither the other two.

One-third of the students that attended the second conference, attended neither the other two.

And one-fourth of the students that attended the third conference, attended neither the other two.

Knowing that the three conferences were attended by the same number of students, and that each of the 300 students attended at least one conference :

a) how many students attended each conference ?
b) how many students attended only one conference ?
c) how many students attended only two conferences ?
d) how many students attended all 3 conferences ?

One unique solution !

(In reply to No brute force is assumed? by Gamer)

Gamer, my preocupation is related to the fact that with the intensive use of computers to solve any type of problem (and certainly most, in fact, can be solved only with its aid), paradoxicaly, it is creating a generation that even before start to analyze and thinking how to simplify it, and then (perhaps) use the computer, here comes the brute force, the trial and error, etc...

And this, for me, is extremelly negative. Since I'm from the time when the computers didn't exist (at least, here in Brasil), I think (and I may be wrong) that we developed a sense of thinking and reasoning, that we can't find in most of the young people, today. I know many and many friends of my sons (in the 25-ages), and none of them will be interested in solve a problem if only logical thinking is necessary.

For this reason (and only for this), I didn't consider that the problem is solved, the solution was "found", not "achieved". But, since I didn't stated nothing about computers, there's nothing to do. Probably, my "public" for the next problems will be reduced, because I will not allow the use of computers.

And I still assure you all : the solution can be achieved without one single trial. It's directly found. And this is what I expected.

By the way, it has a digitation mistake in my previous coment : it's "guest".     

Posted by pcbouhid on 2005-05-12 15:18:35