How many people do you need in a room in order to guarantee that there is a pair of people who were born in the same month?

Choose one of the following answers:
12
13
365
366

Well, consider that if you have more than 12, there has to be at least one pair of people with the same month.

Answer: 12

The question does not say that each person would have a different birthday month. I could invite 12 people to a party and there might be only 7 months represented for birthday months.

Should I assume the question is limited by assuming each person to have a different birthday month? I took the question to mean random selection of persons.

And if each person had a different birthday month, and there were only 12 people in the room, then there would not be two people in the room with the same month birthday.

Help my logic here.

If you have 12 people, and only 7 months represented, you already lost. You have folks who have the same birthday month in that group of 12.

goodness, I had a typo. You have to have 13 to guarantee two people have the same month birthday. I typed 12 in my answer, when I meant more than 12. Sorry.

I finally understand! Thanks for your explanation to this dense logic.

To find the minimum number of people needed in a room to guarantee that there is a pair of people born in the same month, we can use the Pigeonhole Principle.

According to the Pigeonhole Principle, if you have n items that need to be placed into m containers, and n > m, then at least one container must contain more than one item.

In this case, the "items" are the people in the room, and the "containers" are the 12 months of the year. We want to find the minimum number of people (items) needed to ensure that at least two people are born in the same month (a container with more than one item).

Since there are only 12 months in a year, the minimum number of people needed to guarantee that there is a pair of people born in the same month is 13 (n + 1, where n is the number of containers).

Therefore, the correct answer is 13.