Here is the problem a professor of physics had at the beginning of the XXth century:

“I received a call from a colleague about a student. He felt he had to give him a 0/20 to a physics question, while the student claimed a 20/20. Professor and student came to an agreement to select an impartial arbiter, and I was selected.
I read the examination question: “Show how it is possible to determine the height of a building with a barometer.”
The student replied: “I carry the barometer to the top of building, I attach a rope to it, I lower it to the ground, then I haul it back up and then I measure the length of the rope, which gives me the height of the building. “
The student was right, he had truly answered the question and accurately. On the other hand, I could not give him the exam: in this case, he?d receive his degree in physics without having shown me any knowledge in physics.
I offered to give another chance to the student giving him six minutes to answer the question with the caveat that for the answer he had to use his knowledge of physics. After five minutes, he had not yet written anything. I asked him if he wanted to give up but he said he had many answers to this problem and he wanted to choose the best one.
I excused myself for interrupting him and I asked him to continue.
In the next minute, he hastened to explain: “The barometer is placed at the height of the roof and is dropped: in calculating the fall time with a stopwatch, then using the formula: x=gt2/2, I find the height of the building. ”
At this point, I asked my colleague if he would give up. He replied in the affirmative and gave the student nearly 20/20
Leaving his office, I recalled the student because he said he had several solutions to this problem. “Well, he said, there are several ways to calculate the height of a skyscraper with a barometer. For example, you place it outside when the sun is shining. Height of the barometer is measured, then the length of its shadow and the length of the shadow of the building, then with a simple calculation of proportion, it?ll give you the height of the building. ”
“Good, I replied, what else??
“There is a pretty basic method that you will enjoy. You climb the stairs with a barometer and you mark the length of the barometer on the wall. Counting the number of lines gives the height of the building in barometer length. This is a very direct method.
Of course, if you want a more sophisticated method, you can tie the barometer to a string, swing it as a pendulum, and determine the value of g at the street level and at roof level. From the difference of g, the height of building can be calculated.
Similarly, you attach it to a long rope and on the roof, allow it to get down about the street level. You swing it like a pendulum and the height of the building is calculated from the period of precession. ”
Finally, he concludes: “There are other ways to solve this problem. Probably the best is to go to the basement, knock at the concierge?s door and say.” I have a nice barometer for you if you tell me the height of the building. ”
I then asked the student if he knew the answer I expected. He admitted that yes, but he was tired of school and teachers who tried to direct his way of thinking. ”
The student was supposed to be Niels Bohr and Rutherford the referee.
[Rutherford – Nobel Prize in Chemistry 1910]
[Bohr – Nobel Prize in Physics in 1922]
The links in the comments lead to question the authenticity of the anecdote.
The myth of Niels Bohr and the barometer question
Barometer question