Devising a Plan: Strategy

Strategy

We need to figure out a strategy to find the sum of all the numbers from 1 to 50. Here are some questions to note:

• Can we simply sum all the numbers on paper?

• Do we need to use a calculator to add these numbers?

While it’s possible to add these 50 numbers using a calculator or pen and paper, the process is quite difficult and prone to errors.

Forgetting to include a number or accidentally adding one more than once are common mistakes. Furthermore, when dealing with a larger set of numbers, verifying the accuracy of the result becomes difficult.

These are tough challenges. Is there a way to tackle these issues? Has anyone previously solved a similar problem?

The genius of Gauss

The brilliant mathematician Carl Friedrich Gauss was just a young student when he astounded his teacher by discovering a quick and elegant method to find the sum of consecutive numbers.

One day, Gauss’s teacher asked his class to add all the numbers from 1 to 100, assuming that this task would occupy them for quite a while. He was shocked when young Gauss, after only a few minutes, wrote down the answer. The teacher couldn’t understand how his pupil had calculated the correct solution so quickly in his head, but the eight-year-old Gauss pointed out that the problem was actually quite simple.

It was undoubtedly a challenging problem, especially for young children. Nevertheless, the eight-year-old Gauss devised a solution that ingeniously solved the problem.

He observed that there are a total of 100 numbers from 1 to 100, and if we add the first and last numbers in the sequence, the second and second-last numbers in the sequence, and so on, they will add to 101 for each pair.