In March 1975, I started a science degree at ANU in Canberra Australia.
I was enrolled in Pure Math and Applied Math.
The first assignment in Applied Math was a Fortran problem, print out a statement, to a line printer, where each character was made up of individual letters of the character type
W W W
W W W W
Simple sample. I dropped Applied Math, personally a bad decision.
I have always wondered to this day how you would do it?
Doing the simple beam last night made me think of this problem.
The other interesting physics problem in the first exam. A semicircular block of ice sits on land, it has a height of R and a radius of R, a thing sits on the top of the block, it is given an infinitesimal push and ignoring friction where does it depart the ICE.
I did not solve the problem in the time, one boy in a class of 100 solved it. It has an elegant answer. I blame the beer I consumed instead of studying, of course I can solve it but not in 10 minutes.
When I had a bright student talking to me, out of the 1000s, I would drag out the problem and say can you solve this. 4 solved it in less than 10 minutes, no one else.
I used to then tell the class, Mr or Miss Such and Such is going to get an A in the class, I know this and he/she knows this, you are not being graded against them. I also said if they help you with your homework, not a problem as long as you note where they helped on the paper.
They always dragged the class average up.
Actually, the thing never touched the ICE other than for a momentary point in time when it makes first contact. Afterwards, the weight of the thing compresses the ICE, converting the ICE into water. Under this situation, it left the ICE at the top.
Also, conversely, depending on the shape of the thing, capillary action of the water between the thing and the ICE can provide a "suction" force, making the thing adhere to the surface as it glides over the ICE (iow it will not leave the ICE, but rather strike the ground).
But, the four students were 18 or 19, they walk in a start talking to me, you quickly realize how good they are and to test them you draw the problem, sit them at the desk outside your room and ask them to solve it, no computers, books, phones nothing, in 10 minutes. It was one of five problems on a three hour exam. Some gave up, 4 did not. This is at the start of classes.
The ones who solve it are super bright, usually socially awkward.