Suppose that the song, "99 Bottles of Beer on the Wall" was sung in its entirety from beginning
to end.
What would be the sum of all the numbers (including repeats) in the song?
Solution to the Problem:
The answer is 14,850 (or 14,949 -- see correction at the bottom).Start with the first verse, "99 Bottles of Beer on the wall, 99 bottles of beer, take one down and pass it around, 98 bottles of beer on the wall."
The numbers of the song can be displayed as follows:
| 99 | 99 | 1 | 98 |
|---|---|---|---|
| 98 | 98 | 1 | 97 |
| 97 | 97 | 1 | 96 |
| ... | ... | ... | ... |
| 3 | 3 | 1 | 2 |
| 2 | 2 | 1 | 1 |
| 1 | 1 | 1 | 0 |
The sum of the third column is 99. If that 99 is placed on top of the fourth column, we have three columns from 1 to 99. The sum of the numbers from 1 to 99 is (1 + 99)* (99/2) = 4,950. So, three times 4950 = 14,850.
krishnanrk2000@yahoo.com and Elisa Arostegui added the following to their explanations:
The final two lines are
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
and these have a number 99
Adding this to 14850, we get the final sum as 14949. Thanks to both Elisa and krishnanrk for reminding of the last line of the song!
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. krishnanrk2000@yahoo.com | ---------- |
| 3. Keith Mealy | Cincinnati, Ohio |
| 4. Elisa Arostegui | Carmichael, California |
| 5. Chad Fore | Gate City, Virginia |