In a classroom, 9 students are talking, 5 are standing, and 4 are reading. 1 student is standing and not talking. 1 student is reading and not talking. What is the smallest possible number of students in the room?
Can anyone solve this? I tried PIE (principle of inclusion/exclusion), but I got the answer as 13. For some reason the answer was 10.
On
9 students must be talking. There is 1 student who is not talking.
That bring us to 10 students.
Consider that the student who is standing and not talking may also be reading. This would mean that of the 9 talking people, 3 are also reading (good multitaskers?), and the 1 student who is not talking is standing and reading.
It really depends on whether you consider talking and reading to be mutually exclusive. Duck's answer does not, and it seems to be what the given solution is implying as well. If you do, you will get that there must be 13 students; 9 are talking and 4 are reading, standing shouldn't be a factor here, and the not talking student(s) may just be reading.
However, the problem states that there is one student who is reading and not talking. If we interpret this as meaning only one student is reading and not talking, that means there must be 3 students who are reading and talking, and thus they cannot be mutually exclusive.