While teaching a course on ethics, I proposed the following problem:
You are at an intersection, and you need to cross, but the light is red. The roads are straight and you see no cars for 500 m in all directions. Do you cross against the red? Justify your actions ethically.
I was expecting students to provide either a deontological or utilitarian response. The deontological approach likely would have ended with, "I don't cross because that's what the law is." The utilitarian response could go either way, but in general, you could justify crossing as you are benefitting (you are getting to your destination sooner) and no one is being harmed by you crossing against the red. The most humorous answer, however, was one where likely the student wanted to use the deontological argument, but instead provided a completely bogus excuse: "Cars move really quickly, and even if you can't see them, they could come out of the blue and hit you as you cross." At 60 km/h, it would take 30 s to travel 500 m, and at 120 km/h, it would still take 15 s, assuming the car comes into sight 500 m away just as you take your first step into the intersection. It was an absolutely hilarious answer.
Cheating on mass: during final examinations around 200n (for some small integer n), a group of students in a class discovered a unique means of cheating: after 90 min into the examination, as many students near the back of the room as there were invigilators (the instructor and teaching assistants) raised their hand and all invigilators went to answer those questions. While this happened, all the students in the front started to pass around notes. Then, 15 min later, just as many students in the front of the room reciprocated by raising their hands and asking questions. The faculty did not discover this until other students in the cohort reported on this behavior, which is one reason I don't allow any questions during a mid-term or final examination.
Cheating through hints: one student continued to ask for help, and the student had learned that he could get help as follows: The student would ask one teaching assistant for a hint to start the questions. The teaching assistant would perhaps initially hesitate, but the student managed to squeeze enough to start the answer by, for example, claiming the wording was ambiguous. Then, a few minutes later, the student would ask another teaching assistant for another hint to continue going, again, by making claims that something was ambiguous or poorly worded. After a while, I noted this behavior, and asked the teaching assistants what was going on, as this student was asking more questions than all others put together, and it was only after a long discussion with the teaching assistants that I determined what was likely happening. The student, however, did get away with it, as the teaching assistants were volunteering the information being requested. This is another reason I don't allow any questions during a mid-term or final examination.
One math professor once complained in a meeting, perhaps jokingly, about how he did not like how engineers used j instead of i for the square root of negative one. My response was along the lines of "Well, we're just using a different but isometrically isomorphic sub-field of the quaternions." Of course, there are good reasons for using j: complex numbers are intimately connected with alternating current, and long before complex numbers were used to model current, the letter used to represent current as a function of time is i or i(t). E.g., v = iR. As engineering concerns the application of mathematics where a failure may result in harm to health, life, property, finances, the environment, etc., it would be rather sad if someone designing your pacemaker wrote something like i = (4.52 - 0.325i)/v and was praying that the person interpreting this would understand the one i is current and the other is part of the complex impedance.