This reminds me of a Uni exam that was soooo broken that answering “correctly” entailed guessing how exactly the professor designing the questions misunderstood the topic of his own lectures.
An interesting parallel to that is the "What's the next number in this sequence?" sort of questions.
If four numbers are provided, one can calculate the coefficients of a a quartic polynomial, for x values of 0, 1, 2 and 3, and then solve for x=4. Which does indeed provide a defensible "next number". And by similar reasoning, there are an infinite number of answers to this question.
Even worse. You could in fact provide any number as an answer, because there is always a quintic polynomial that fits the four initial numbers AND your arbitrary fifth number.
So these questions are actually not about what the next number is, but trying to imagine what the person who set the question thought was a "cool" answer, for some curious definition of "cool", for some person who isn't smart enough to realize that the premise on which the question is based is flawed.
Are you not allowed to ask the professor questions? We are, and it is not to seldom that the professor then walks to the black board and updates the question.
It was an examination with 300 students in a giant hall, overseen by university staff, not the individual professors.
So many people complained that they did eventually fetch him to come and clarify (correct) the questions.
I didn’t have the patience to wait for him to turn up, so I simply provided a matrix of solutions for every possible combination of potential original intent… with note next to it saying that anything other than a 100% mark will be met with official complaints about his lack of due diligence.
