I was trying to come up with a question for preliminary logic round for interviewing. I decided to form a tricky math series and tried to figure out 2 math series which looks same in the beginning and diverges after a while. Something on the lines of
1 2 3 4
So the question could be
To figure out these series, my approach was to start with some series x and find a pattern which doesn’t hold good after few numbers. After few unsuccessful attempts, tried my luck with series of squares
Voilà! difference of consecutive squares were not only a odd number, they were consecutive odd numbers. Tried it for a long series and found it true for all the squares!
From what I knew of squares of numbers, this wasn’t very obvious. I was very excited to check if this is already known or I was the first one to discover this :). Simple web search presented ton of articles on this observation.
That was disappointing but reading this link about a mathematician appreciating a student’s effort in similar finding was comforting and encouraging to carry on with my quest