While I was a student at Long Beach City College years ago, we had an IBM 1620
that students could actually touch.
IBM in those days left the schematics for the computer with the system for use by their service technicians. Being enterprising students we studied them to understand the inner workings of the machine.
This machine had 8K of read/write Core memory and 8K of read only that contained the operating system. The write line for the read-only memory was terminated on a test point about 6 inches from the write line on the read/write memory.
We decided to try jumpering the test points and found--wallaahh!--that you could actually write in the read-only memory.
We then found the square root routine and made a minor change to cause the console typewriter to type out "I ain't cut out for this high-falutin' math" and then would continue processing the square root.
Of course, our fun was to ask for the square root of some numbers and watch this sentence repeated for each calculation.
The real fun was watching the IBM techs in action. The first ones could only do routine maintenance and had no clue as to what was causing the problem. Of course we had removed our jumper right after writing our instructions. The second group could not fix it either.
The school's response was to build a wall around the computer and bar students from access; then, only the operator could put our punch card programs in it.
After about a month, an elderly IBM tech showed up in a white coat, not the three-piece suit the others always wore, and chased the other IBM techs away. He went to the operator's console and poked around.
We were watching from the other side of the fence. You could tell when the light came on in his head. He pulled a jumper from his pocket and opened the computer, and, with a few instructions, he put a jump around our routine and it was fixed!
The other IBM techs asked him what he had done, his response was "never mind, it is fixed."
I did not hear the word "hack" for some years after we had pulled this stunt.