A thousand light years away from Earth, there is a planet that orbits its sun every 100 days. That planet is called Omicron Persei 8, it is inhabitated by living creatures known as Omicronians and they too have the ritual to celebrate the anniversary of their birthday.

What is the maximum number of randomly selected Omnicrons needed such that the probability of all of their birthdays are different exceeds 50%?

Assume that there is a uniform distribution of birthdays across all days of the 100 day year.