![]() Wait - what about an odd number of items?Īh, I’m glad you brought it up. And how many pairs do we have? Well, we have 2 equal rows, we must have n/2 pairs. As the top row increases, the bottom row decreases, so the sum stays the same.īecause 1 is paired with 10 (our n), we can say that each column has (n+1). Instead of writing all the numbers in a single column, let’s wrap the numbers around, like this: 1 2 3 4 5Īn interesting pattern emerges: the sum of each column is 11. Pairing numbers is a common approach to this problem. For these examples we’ll add 1 to 10, and then see how it applies for 1 to 100 (or 1 to any number). ![]() Let’s share a few explanations of this result and really understand it intuitively. Manual addition was for suckers, and Gauss found a formula to sidestep the problem: So soon? The teacher suspected a cheat, but no. The so-called educator wanted to keep the kids busy so he could take a nap he asked the class to add the numbers 1 to 100. There’s a popular story that Gauss, mathematician extraordinaire, had a lazy teacher.
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