Talk:Birthday problem

Incorrect citation

The text says, “The problem of a non-uniform number of births occurring during each day of the year was first addressed by Murray Klamkin in 1967.” which points to a paper from 1967 by Klamkin and Newman. This paper does not actually address the problem of non-uniform numbers of births. So I think this sentence should be cut, or the proper citation should be tracked down. 100.36.247.162 (talk) 22:52, 5 December 2022 (UTC)

Indeed. Klamkin does not have any other relevant papers on MathSciNet, either. For the moment, I have tagged the statement as failing verification. JBL (talk) 18:50, 6 December 2022 (UTC)

Well, this goes way, way back. The attribution to Klamkin was added by AxelBoldt in April 2005, without citation. The footnote was added by Mikeblas in May 2020. @Mikeblas and AxelBoldt: Can you take a look at the discussion above? Thanks. --JBL (talk) 19:49, 10 December 2022 (UTC)

logarithms and combinations

I just noticed this, which I don't see in the article: ${\frac {\log(1/2)}{\log(364.25/365.25)}}\approx 252.83\approx {\binom {23}{2}}$ —Tamfang (talk) 18:01, 28 March 2024 (UTC)

So what? --Macrakis (talk) 20:37, 28 March 2024 (UTC)

364.25/365.25 is the probability that a given pair do not share a birthday. 253 is the number of pairs among 23 people. I never knew before why the threshold number is 23. —Tamfang (talk) 06:15, 29 March 2024 (UTC)

So you're saying that this is more than a coincidence? --Macrakis (talk) 15:45, 29 March 2024 (UTC)

Much closer, but equally meaningless: 365*log(2) = 252.999. --Macrakis (talk) 21:17, 28 March 2024 (UTC)

Or to put that another way, 23 is the smallest integer n such that $({\frac {364.25}{365.25}})^{\binom {n}{2}}\leq {\frac {1}{2}}$. —Tamfang (talk) 00:03, 30 March 2024 (UTC)

OK, I think I'm beginning to follow you here. Small detail: article says that leap years aren't taken into account, so it should be 364/365. --Macrakis (talk) 15:08, 1 April 2024 (UTC)

Is partition problem relevant to this article?

To me, the partition problem at the bottom of the article does not seem sufficiently related to the birthday problem. Is the motivation behind the inclusion that both problems have the "answer" 23? Zaspagety (talk) 13:59, 9 April 2024 (UTC)

I'm inclined to agree with you: although the content has been in the article a very long time, it doesn't seem actually relevant to the topic of this article except in a hand-wavy way. The unique citation does not mention the birthday problem. --JBL (talk) 18:03, 9 April 2024 (UTC)