Thread: The human calculator

G'day Rene,
I first heard about this kind of problem in connection with Fred Gauss,
who went on to pioneer symmetry arguments in Physics.
I think he did something with series like this too.
In that context it was only the numbers from 1 to 10 and his teacher wanted some time to rest while the students busied themselves with mindless addition. Gauss (in pre-calculator days) produced the answer instantly - much to the teacher's chagrin.
It was a collegue who told me this, but I have never verified it.

In this more advanced problem he would have noticed that
0 + 100 = 100,
1 + 99 = 100
...
49 + 51 =100
This happens 50 times with a 50 left over.

cheers
Peter

Very Good Peter,

That's exactly right. You group them up into a number that is easy to multiply. In this case, 50 groups of 100, and then you add the median number (50) therefore the answer is 5050.

If you wanted to add up 0 - 20, you would have 10 groups of 20 + the median which is 10, therefore the answer would be 210.

Have a great day.

Rene