Anecdotes from school: Divisibility test for Seven

This is a new series on this blog, called Anecdotes from school. I realize I’ve had so many awesome anecdotes in school that I should tell you people about it. Of course I won’t write about the incidents when I beat up people or got beaten up by people (both were common). Even leaving them out, school was quite an awesome time so I think I should write about it.

One fine morning when I was in 9th standard, I arrived at school to find the rest of my class raving over this little guy called Ramu. He had apparently made some major mathematical breakthrough, and the school had called the Deccan Herrald to interview this prodigy. He is the next Ramanujan, people claimed (no, Ramu wasn’t short for Ramanujan). Efforts were made by all parties to hurt my class topper ego – what is the use of being a topper if you can’t come up with breakthrough discoveries, they said.

A few days back, we had studied divisibiility tests. Powers of two were simple, as were 5, and 3 and 9. 11 was also quite simple, and that left only 7 among the “simple primes” for which there didn’t exist an elegant divisibility test. “This is an unsolved problem”, Matki, our maths teacher, had declared. “Any one who can solve this is sure to win a Nobel Prize” (evidently she didn’t know that no Nobel is given out for Math. Of course, us 13-14yearolds also had no clue about such finer details.

So Ramu had woken up one morning with a divisibility test for seven. As I mentioned earlier, by the time I reached, the entire class had been convinced. I’m not sure if Matki had heard about it yet. It was a weird test, and I must admit I don’t remember it. It was extremely inelegant, with different operations to be done with different digits of the number. If it were elegant, I had reasoned, this problem wouldn’t have been unsolved for so long, I had reasoned. So inelegance would not really take away any greatness from the method.So I asked Ramu to demonstrate it to me.

He wrote down a few numbers on the blackboard – all known multiples of seven. Actually he picked only powers of seven (49,343 and 2401). The reason he did this (picking powers) is unclear. So he takes the numbers, puts his magical algorithm on it, and there it is. Done. Hence proved. QED.

Of course this was too much for my class topper ego to take, and I spent the rest of the day trying to find holes in this argument. In the meantime Matki and the other senior maths teachers in school had learnt about this, and had gotten convinced of the greatness of Ramu and his algorithm. The team from Deccan Herald was supposed to arrive at 4 o’clock, we were informed.

It was sometime in the afternoon. Maybe during the history lesson. My ego had been hurt so much that I obviously didn’t care about the lesson. All I cared for was to poke holes in Ramu’s algorithm. I decided to stress-test it. I picked 8. And ran the “divisibility test for seven”. The algorithm said “divisible”. I picked 9. Again the algorithm said “divisible”. 1. Divisible by 7. 2. Divisible by 7.

I had confronted Ramu during the lunch break regarding my “experiments” with his algorithm. “You obviously know that 8 is not divisible by 7. Why do you even bother running the test on that?” He countered. “Errrr.. Isn’t that the point of the divisibility test?”, I asked. I had already started to become unpopular in class. I then started picking random large numbers whose divisibility by 7 I had no clue about. According to Ramu’s algorithm, all were supposed ot be divisible by 7.

Deccan Herald was hurriedly contacted again, and asked not to come. I don’t know how Matki or any of the other maths teachers had reacted to this. I was “boycotted” by the class for the next one week for destroying the career of a budding mathematician. Ramu, however, wasn’t finished. A week later, he came up with an algorithm for trisecting an angle using only a straight edge and a compass.