Suppose that the song "99 Bottles of Beer on the Wall" was sung from beginning to end.

What would be the sum of all the numbers (including repeats, of course) in the song?

Then, suppose you have some arbitrary number n bottles, which you would like to sing about. Find a formula in terms of n for the sum of all the numbers you will be singing.

(In reply to Solution by RoyCook)

Assuming that 'one' is a number rather than a pronoun then in the general case the sum is...

(1+...+n) + (1+....+n) + (1+...+1) + (0+....(n-1))

which is equal to

3 x (1+....+n)

= 3 x n x (n+1) / 2

In the traditional song this gives...

3 x 99 x 100 / 2 = 14850 as per Roy's answer

Posted by fwaff on 2003-10-20 09:15:17