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EN: Determine the minimum number of students required in a class to ensure that at least three of them celebrate their birthdays in the same month.
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Q. EN: Determine the minimum number of students required in a class to ensure that at least three of them celebrate their birthdays in the same month.
- Apply Pigeonhole Principle: Use the Pigeonhole Principle, which states that if items are put into containers, with , then at least one container must contain more than one item.
- Consider Months as Containers: There are months in a year, so think of each month as a container for birthdays.
- Ensure Students for Birthdays: To ensure that at least two students have their birthdays in the same month, we would need students ( months + ).
- Need Three Students in Same Month: But we need at least students to have their birthdays in the same month.
- Scenario with Students: If we have students for each of the months, that's students, and all months could have exactly birthdays.
- Adding One More Student: Adding one more student ensures that at least one month will have three birthdays.
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