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Overview

How good is your maths? Can you do better than 8 year old Fredrick Gauss?

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 Answer

500,500

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.

The tail

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 and the location of the bio.

John Sleigh has been applying adult learning principles to training design and workplace communication projects since 1988.

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