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Sandy Wood
Brain Game: We’re Gonna Have a Party, Party
by Sandy Wood - June 27, 2008 - 6:30 AM

Answer: Twenty-three. If you want to see the numbers crunched, there’s a detailed explanation here.

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Comments (17)

  1. Love the Beatles reference, btw.

    I was just thinking about the “birthday” problem yesterday. That’s a really weird coincidence.

    posted by Benjamin M. Strozykowski on 6-27-2008 at 8:03 am

  2. That raises the question. How many people have to be in a room together before two of them are thinking of the birthday problem?

    posted by Jacquilynne on 6-27-2008 at 8:36 am

  3. I learned about this in one of my excessively daunting statistics/probability classes, and this guy’s explanation is almost as long as my teachers!

    posted by mle on 6-27-2008 at 9:06 am

  4. Indeed, mle – that’s why I linked it instead of even attempting to come up with an abbreviated version. I can figure out factorials and probabilities to an extent… but not that!

    posted by Sandy on 6-27-2008 at 9:16 am

  5. Sorry… but i don’t think you’re asking the same question the number-crunching website is. If the odds are better than 2:1, you can either be saying that the probability is better than 2/3 (if you mean odds for) or that the probability is better than 1/3 (if you mean odds against)… but if you’re trying to ask how many people need to be around in order to achieve a probability greater than 1/2, then if you want to talk in terms of odds you’d want to say 1:1 odds.

    posted by Jason on 6-27-2008 at 9:38 am

  6. Here is how I look at the problem. There is a high probability that I am wrong… I took 2/3 of 365 and got 243. I set up an algebra problem like this: (1 + n) x n / 2 = 243. I multiplied 243×2 and got 486, set up a quadratic equation and solved with the quadratic formula. I discounted the negative value of n. I got 22. Seems like a very low number…

    posted by Loni on 6-27-2008 at 9:55 am

  7. To my surprise I got it – I knew it was 20 for 1:1 (even odds).

    2/3 of 365 is about 244, so just look for lowest pair of consecutive numbers where half their product is greater than 244. That happens to be 23 and 22 (253) so 23 is the answer.

    posted by dant on 6-27-2008 at 11:22 am

  8. I think it is 29…

    posted by Emily S S on 6-27-2008 at 12:02 pm

  9. 23 – we spent an entire class period deriving this in my college Statistics class. And 10 years later, it’s the only thing I retained from that entire semester. What are the odds?!

    posted by Humaira on 6-27-2008 at 12:49 pm

  10. Actually 29 happens to be the minimum number of people for the odds to be better than 9:1! It goes up fast.

    posted by dant on 6-27-2008 at 1:13 pm

  11. so.. i’m september 29th.
    any one else?

    posted by lindsey on 6-27-2008 at 2:25 pm

  12. This was in an old Scientific American magazine–a one page math problem/example. They used a soccer game (with 23 people on the field, players plus officials) as an example.

    posted by Patrick on 6-27-2008 at 2:37 pm

  13. Sept 29 here also

    posted by Patrick on 6-27-2008 at 2:53 pm

  14. I have to agree with Jason, and with Emily. Sandy asked one question but then posted the answer to a different question and linked to how the other question was solved.

    The question asked is “how many people are necessary for odds better than 2:1″, which means better than 66.6% (or possibly better than 33.3%, depending on how you look at it.)

    The answer (23) is the answer to “how many people are necessary for odds better than 1:1″, which means better than 50% or “even” odds.

    The answer to the question asked is 29 (or 18, if you are looking for better than 33%)

    Look at the linked “detailed explanation” if you don’t believe me.

    posted by MrTisoy on 6-27-2008 at 5:53 pm

  15. UPDATE: Yes, you folks are correct. I meant to say a 50 percent chance, not 2:1 odds. They’re two quite different things, and it was my bad. I’ve changed the phrasing of the question to make it correct.

    Thanks for the heads-up, all!

    posted by Sandy on 6-27-2008 at 6:16 pm

  16. Um, the answer is 2. You said nothing about random people, or not knowing their birthdays.

    And fix the Tab problem in the commenting form.

    posted by Just Al on 6-28-2008 at 11:57 am

  17. If I plan for a party of 23 people, it’s a sure bet 100 will show up.

    posted by Miss Cellania on 6-29-2008 at 9:11 am

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