perplexus.info :: Probability : Happy Birthday (2)

Happy Birthday (2) (Posted on 2004-03-11)

Remember this one?

Well, this time, the question is:
Assuming that birthdays are evenly distributed around 365 days of the year...
what is the minimum number of people I must have in a room, such that the odds are that at least n people share the same birthday?

Let's limit this question to n values from 1 to 12.

We know that for n=1, 1 person is sufficient.

For n=2, as is described in Happy Birthday, 23 people are sufficient.

What are the minimum numbers for n=3 to 12?

See The Solution Submitted by SilverKnight

Rating: 2.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Thoughts

Comment 6 of 6 |

Let the required minimum number be M(n)

Then, the required minimum values are as follows:

M(1) M(2) M(3) M(4) M(5) M(6) M(7) M(8) M(9) M(10) M(11) M(12)

1 23 88 187 313 460 623 798 985 1181 1385 1596

The fuller list is provided in terms of:

Sloane's A014088: Minimal number of people to give a 50% probability of having at least n coincident birthdays in one year - in this location:

http://oeis.org/A014088

Edited on December 10, 2022, 1:54 am

Posted by K Sengupta on 2022-12-10 01:45:40

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