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.

The song goes:

n bottles of beer on the wall, n bottles of beer, take one down, pass it around, n-1 bottles of beer on the wall.

There are two solutions, depending on whether we treat the occurrence of "one" as a number or as a pronoun. If the former, as I suspect was intended, then the solution is the summation, with n ranging from 1 to 99, of n+n+n-1, which can easily be computed, and is 14850. If we ignore the occurrence of "one", then the answer would be: 14751.

Posted by RoyCook on 2003-10-20 08:39:04