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Interview Brain Teasers Hard 2 min

You are asked in an interview: A room contains 100 people. At least two people in the room must share the same birthday. What is the minimum number of people required to guarantee this?

Hint
Think about the number of possible birthdays.

Answer

367 people, assuming 366 possible birthdays including February 29.

Explanation

There are 366 possible birthdays if leap day is included. With 366 people, everyone could theoretically have a different birthday. The 367th person guarantees a repeated birthday by the pigeonhole principle.

Step-by-Step Solution

Number of possible birthdays = 366.
Maximum people without repetition = 366.
Therefore 366 + 1 = 367 guarantees a shared birthday.
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