MathDB

Bobo the clown was juggling his spherical cows again when he realized that when he drops a cow is related to how many cows he started off juggling. If he juggles

1

, he drops it after

64

seconds. When juggling

2

, he drops one after

55

seconds, and the other

55

seconds later. In fact, he was able to create the following table:
https://cdn.artofproblemsolving.com/attachments/1/0/554a9bace83b4b3595c6012dfdb42409465829.png
He can only juggle up to

22

cows. To juggle the cows the longest, what number of cows should he start off juggling? How long (in minutes) can he juggle for?

Problem Statement