The mystery of linear superposition of state in EM exercise class 
During the EM exercise class, I asked the students to do a simple problem. Then after several minutes, I asked them whether they had finished it. At first, I asked, “For those who have finished, please raise your hand.” No one moved. Then I asked, “For those who haven’t, please raise your hand.” Again no one moved. So here comes the problem: They are in the middle of having finished and not having finished. I told them about the story of Schroedinger's cat. If you open the box, either the cat is alive, or the cat is not alive. Here is my argument for the existence of the problem. Assumption: The voting measurement is successful. The student could only finish (|f>) or not finish (|nf> the problem. So before I asked them, they should be in a linear-superposition state |psi>=(|f>+|nf>)/ sqrt(2). So when I asked whether they are in the state of |f> (|nf>), (i.e. P|f>|psi>=|f><f| |psi> (P|nf>|psi>=|nf><nf||psi>)), the state should be collapsed into |f> (|nf>). Now the state doesn’t collapse. So, hum, this measurement is not successful?? I have never learnt about an unsuccessful measurement in Quantum Mechanics. >< | 
