The Young Mathematician

Oct 09, 2021

Several hundred years ago, somewhere in Europe, in a classroom, a teacher is assigning the students some busy work as a kind of punishment because the class has been misbehaving.

The teacher says "Okay, wise guys, I want you to add up all the numbers between one and 100. I.e. one plus two, plus three, six. Four, plus five, plus six, plus seven."

As you can see, it begins to get tough. And don't forget, they were little kids, they could barely even make the numbers! After about a minute or so, one of the kids raises his hand and says, I have the answer.

And the teacher says, "The heck you do!"

But the student says, "The answer is 5050." And indeed that was the answer. The question is, how did he do it so quickly?

And part two for extra credit is, who was this kid? (He was a famous mathematician.) What's his name?



Have I got an answer for you!

Now I'm sure everyone will attribute this incorrectly to our pal, Al Einstein. But I gave a hint, a big hint!

That it was hundreds of years ago.

I don't even know if it was hundreds of years ago. In any event, it was the German mathematician, Carl Friedrich Gauss. Gauss, as a child, used to amaze his classmates and  his school teacher with the logic he used. He said, "Look, I took the first number in the last number, the first being one and the last being 100. I add them up and I got 101. The next one next pair, I added two and 99."

So basically what he did was he wrote the numbers in ascending order on one line, and right below me wrote the numbers in descending order.

So you add the first pair of numbers and get 101. Then the next pair is 99 + 2. And you get 101. 93 + 3 is also 101.

He said, "Gee, every line obviously comes out to 101. So I had 100 one 101s, which is 10,100. But since I used each number twice, I divided by two and got 5050."

And of course, he went on to become a renowned mathematician.


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