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.

If you only mentioned the number once per 'verse' the answer would simply be the triangular number of n - given by (n^2+n)/2.
I've only heard the song in movies, but I think it goes something like,

n bottles of beer on the wall
n bottles of beer, if
1 of those bottles should happen to fall there'd be
(n-1) bottles of beer on the wall.

for a total of 3n bottles mentioned per 'verse'.
The answer is therefore 3 x the triangular number of the bottles you start with on the wall.
Triangular number when n=99
(99^2 + 99)/2 = 4950
multiplied by 3 = 14850

The general formula is therefore 3(n^2+n)/2

Posted by Lee on 2003-10-20 12:16:04