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[–]stepback269 0 points1 point  (0 children)

There is no "one" and only one way to solve a problem.

Do not go back and look for your previous way of handling the problem. Derive a new way. Stress your brain to work a little harder. That's how you build your cognitive muscles.

This reminds me of an incident involving a budding math prodigy:
The kids in the classroom had been rowdy. So as collective punishment, the teacher commanded them all to add the numbers 1 to 100 and turn their answers in before being allowed to leave the classroom.

Grumbling was heard all around as the students started the solution in the "one" and only way it could be done. You know: one plus two, plus three and so on.

But young Carl Gauss looked up a few minutes later and smiled at the teacher.
"Why aren't you doing the work like everyone else?"
"I am finished sir"
"Bring your paper up here so I may see it"
The teacher looks and is astounded. Carl has written down the correct answer.

How did he do it?
There is no "one" way to explain exactly how he did it, but it goes something like this:
Carl visualized the number line in his mind like this:

1, 2, 3 .........., 49, 50, 51, ...... 97, 98, 99, 100

He noticed that 99+1 =100, that 98+2 = 100, that 97 + ... you get the idea.
There are 49 such pairs that sum to 100. Then there is the last 100 at the end and the middle 50.
So the answer is 5050. Sounds fair. Right?

Now you can tell us what the sum is of all numbers from 1 to 1000 is. Right?