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1800s Classroom Game

Picture of Karl Friedrich

Pictured on the left is one of the most famous mathematicians, Karl Gauss. One of the earliest stories about Karl is set in a 19th century classroom.

In an attempt to get some nap time at the back of the classroom, the teacher posed a summation problem that assuredly will keep the children busy for the entirety of the class.  “Add all the whole numbers from one to one hundred. That is, 1+2+3+4+5 …98+99+100.”

To the teacher’s dismay, whilst some children were still busy writing down the question, Karl came forward with the correct answer within a few seconds!

Are you able to provide the right answer & understand what method Karl used to solve this problem so easily.

 

Answer
The answer is 5050.

Here is how young Karl arrived at his answer so quickly. He noticed in the series of 1, 2, 3, … 98, 99, 100 that sum of the first (1) and last number (100) is 101. The sum of the next pair (2) and (99) is also 101. Working toward the middle, the same holds for the next pairs. There are 50 pairs in total, so 50 pairs x 101 = 5050.

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Stating the obvious here, but I enjoy riddles & puzzles. Anyone else also struggling with seemingly simple 5th grade math problems?

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