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There are about 6 billion people alive on Earth, and its increasing everyday. Therefore, you would have to know more than 365/6 billion people to have any chance of being invited to birthday parties everyday in a year.

This is incorrect. I assume you mean 365 billion / 6 = 61 billion people to have a greater than 50% chance of knowing someone with a birthday on every day.

I have about 350 friends on facebook and on average I know someone with a birthday on every 2 days. Further, if you knew everyone on earth, you would be certain to know thousands of people with a birthday on every single day.

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Q: How many people would you have to know for it to be more likely than not that at least one person had a birthday on every single day of the year?
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