Take a moment and add up the numbers 1, 2, 3, …, 98, 99, 100. Now, there’s a catch before you try. Do it in your head, and you have 10 minutes.
If you did it, congratulations! Please don’t share the result, though. If you did not do it, reflect on the fact that Carl Friedrich Gauss was able to do so at the young age of 10 years old. Apparently, his teacher had a hard time with keeping the lad busy, and she sent him off with this problem to get him out of her hair for a bit. I can just imagine her expression when he came back in just a few minutes with the correct answer!
I will decline from explaining for today. Tune in tomorrow for how Gauss tackled the problem. In the meantime, see if you can find not only the answer, but the technique.