Getting on Fifth Base?

I went to high school before electronic calculators and "slide rules" were the calculational devices of the time. My high school chemistry teacher said that we could do the test problems (as well as homework problems) anyway that we wanted as long as we showed the work. We could, of course, use our slide rules for calculations. Well, I had known how to use a slide rule since fourth grade, but I never actually looked carefully at the slide rule until that quarter in high school. Wow. It occurred to me that the slide rule, though intended for base 10 arithmetic could be used for any base arithmetic because the slide rule was just adding and subtracting logarithms.

I had done very well on the previous two chemistry exams and always had time left over, so I decided to do the next chemistry exam in base 5 rather than base 10. I practiced using my slide rule in base 5 a bit before the exam. There were something like 4 true/false questions worth 2 points apiece, and the rest of the exam required calculations. I barely finished the exam working in base 5, but I did finish and handed in the exam. When the exams came back a day or two later, my score was 8 points out of 100 points. There was also a note to see the teacher after class.

After class, the teacher said "Tom, what happened? You did extremely well on the previous two exams." I pointed to my note written at the top of the first page of the exam. The note said "Please note that all calculations and answers are in base 5." The teacher said "You did what!" I pointed out that he had said that we could do the exam any way we wanted. The expressions on his face in the next 30 to 60 seconds as he tried to decide what to do were fascinating. He went from astonishment, to exasperation, to annoyance, and finally to toleration. He finally simply said to convert all the numbers to base 10 and hand the exam back in. It was good fun. Maybe a bit risky, because he could have failed me, but I counted on his keeping his word.

Two or three years later I stopped by the high school and he recognized me at once. He told me that he now tells the class that if they show their work, they can do the exams anyway they like, within reason. And he gave my exam  as an example of what was not within reason. The teacher said that his classes were always amused by the example.

The moral of the story is that it took a little while  for the teacher to appreciate how students might follow his instructions  (and see the humor)...