What is the minimum size of a randomly selected group of people such that there is a greater than 50% chance they can celebrate the birthday of at least one person in the group on every day of the year? Assume that all years have 365 days, and that birthdays are evenly spread throughout the year.

As always, you can use whatever techniques/resources you want to try and answer this puzzle, and we don’t expect you to submit anything other than your answer. That said, if you want to challenge yourself, see how far you can get just using your intuition! How about if you add pencil & paper? How about if you add a calculator? It could be difficult to arrive at an exact answer via these methods, but if so, how tightly can you bound the answer?