The Question: What is the sum of all of the whole numbers between 1

and 1,000 inclusive?

Show all of the necessary calculations on a single sheet of paper.

The Workings: Pair the numbers at the extreme ends of the range:

1 + 1,000 = 1,001

Move up one at the lower end, and down one at the

higher end:

2 + 999 = 1,001

Continue moving away from the ends of the range, one

number at a time;

3 + 998 = 1,001

At the mid point, you will converge:

500 + 501 = 1,001

Thus there are 500 pairs, each of which adds to 1,001.

The answer is 500 times 1,001, or 500,500.

Allegedly this activity was set by a teacher as work to keep the class busy.

Unfortunately in 1885, it proved inadequate. One student, 8 year old Frederick Gauss, solved the problem in seconds. He later went on to become a significant mathematician.

Thanks to Duard Worthen for this information. He saw the article "Great games, but when does the learning start?" and e-mailed me the name of the mathematician.