There are many anecdotes that demonstrate the exceptional mathematical proficiency of the famous mathematician Karl Friedrich Gauss (1777–1855) even as a child. One of the best-known of these events occurred between him and his teacher, J.G. Büttner. Büttner posed a problem to his students, including Gauss, that would take a long time to solve. Gauss, who was only 10 years old at the time, solved this problem in a much shorter time than his teacher expected, using a method he discovered himself, and astonished him. Here is the problem his teacher posed, and here is Gauss’s solution…
What is the sum of the numbers from 1 to 100?
Gauss’s Solution
Gauss, while explaining his solution method, first wrote the numbers from 1 to 100 from left to right. Then, he wrote the same numbers in reverse order, from 100 to 1, below these numbers.
For example, 100 under the number 1, 99 under the number 2, 98 under the number 3, and so on.
You may have noticed that the sum of numbers placed one below the other always gives the same result, which is 101. In this case, we have 100 instances of the number 101.
But don’t think this is part of the problem. Because Gauss wrote the numbers from 1 to 100 twice. In this case, 10,100 needs to be divided by two.
In conclusion, the sum of the numbers from 1 to 100 is 5050.
Now it’s your turn!
What is the sum of the numbers from 1 to 200? Write it in the space provided.
One more question…
What is the sum of the odd numbers from 1 to 99? Write it in the space provided.
This is the last question…
What is the sum of the even numbers from 50 to 100? Write it in the space provided.
