Question

How many people must be in a room to guarantee that 3 of them were born in the same month?

36

25

33

93​

Answer 1

Answer:

36 people must be in a room to guarantee that 3 of them were born in the same month...

Answer 2

25 people must be in a room to guarantee that 3 of them were born in the same month.

• The Pigeonhole principle is a well-known concept. The Pigeonhole principle states that at least one cage must contain in itself, more than one pigeon. Thus, if there exist m cages then we will have an intention to place inside them, n > m number of pigeons inside of them.
• Let us consider a certain example to demonstrate this concept. We need to place pigeons in such a manner that there are 3 cages and we have to have atleast two of those pigeons in the same cage. The answer with the help of the Pigeonhole principle will be 4.
• Now, if one tries to fit exactly one pigeon in each cage, which is after one has already placed three pigeons in each cage, we will be left with only one pigeon. This one pigeon needs to be now placed in a cage which already holds a pigeon.

Similarly, we know that there are twelve months in a year.

Thus, if there are 24 guests, it will be feasible to assume that every two of them will have birthdays in the same month. But if we consider 25 individuals, three of their birthdays must fall in the same month and this occurs due to pigeonhole principle.

Hence, 25 people must be in a room to guarantee that 3 of them were born in the same month.

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