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Among 100 people at least how many of them were born in the samemonth?

Question

Among 100 people at least how many of them were born in the samemonth?

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Solution

To answer this question, we need to apply the Pigeonhole Principle. The Pigeonhole Principle states that if you distribute more items than there are containers to hold them, then at least one container must contain more than one item.

In this case, the "items" are people and the "containers" are the months of the year. There are 100 people and 12 months.

If you distribute the 100 people across the 12 months, you will find that at least one month must contain more than one person. To find the minimum number of people born in the same month, you divide the number of people by the number of months:

100 people / 12 months = 8.33 people

Since you can't have a fraction of a person, you round up to the nearest whole number. So, at least 9 people must have been born in the same month.

This problem has been solved

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