Puzzles with numbers and things

[The Statman]

when theres 23 people at the party (including host)

?

I forgot to mention, please show evidence of your working. If you looked it up on the internet, the link will suffice .

[davis_greatest]

when theres 23 people at the party (including host)

?

I agree (as long as we assume that the birthdays are independent and uniformly distributed through the year - so, we don't, for instance, invite the Olsen twins).

[Semih_Sayginer]

I forgot to mention, please show evidence of your working. If you looked it up on the internet, the link will suffice .

i forgot to mention that ive done this question before, and also read up on "birthday paradox" and remembered the figure

[davis_greatest]

Edit 2 - deleted ugly table... now appears 2 posts below.


Edit 1 - sorry - that looks horrible. I can't do tables. I'll see if I can paste it somehow as a picture

[davis_greatest]

I've tried to put the table in as a .bmp or Word document but whatever I do, it says the file size is too big...

[davis_greatest]

Hopefully this is semi-legible

Person . Col. A...Column B...Column C

1
2 ….. 364/365 ….. 99.73% ….. 0.27%
3 ….. 363/365 ….. 99.18% ….. 0.82%
4 ….. 362/365 ….. 98.36% ….. 1.64%
5 ….. 361/365 ….. 97.29% ….. 2.71%
6 ….. 360/365 ….. 95.95% ….. 4.05%
7 ….. 359/365 ….. 94.38% ….. 5.62%
8 ….. 358/365 ….. 92.57% ….. 7.43%
9 ….. 357/365 ….. 90.54% ….. 9.46%
10 ….. 356/365 ….. 88.31% ….. 11.69%
11 ….. 355/365 ….. 85.89% ….. 14.11%
12 ….. 354/365 ….. 83.30% ….. 16.70%
13 ….. 353/365 ….. 80.56% ….. 19.44%
14 ….. 352/365 ….. 77.69% ….. 22.31%
15 ….. 351/365 ….. 74.71% ….. 25.29%
16 ….. 350/365 ….. 71.64% ….. 28.36%
17 ….. 349/365 ….. 68.50% ….. 31.50%
18 ….. 348/365 ….. 65.31% ….. 34.69%
19 ….. 347/365 ….. 62.09% ….. 37.91%
20 ….. 346/365 ….. 58.86% ….. 41.14%
21 ….. 345/365 ….. 55.63% ….. 44.37%
22 ….. 344/365 ….. 52.43% ….. 47.57%
23 ….. 343/365 ….. 49.27% ….. 50.73%



Column A = Probability birthday of latest arrival differs from others here so far
Column B = Probability all birthdays differ of those here so far (cumulative product of column A)
Column C = 100% - column B = Probability at least 2 people share a birthday.

Assumes 365 days a year (ignores leap years)

[snookersfun]

test
but don't worry, it is all readable....

now this has size limitations, anything bigger and not doable...

[davis_greatest]

Yes, that's what it looked like on my screen!

[snookersfun]

Recall that in round 52, Oliver, my pet orang utan was sitting in a circle during his birthday party with 9 of his friends from this forum. For the next game, Charlie the chimpanzee and Gordon the gorilla decide to join in, so they each squeeze in somewhere into the circle, their positions chosen at random. (So there are now 12 in the circle.)

D_G check me on this question please
In continuation to the circle puzzles. The circle meanwhile has 12 members, each sitting at different distances from eachother (thus each pair with different distance). Now each member rolls one snookerball to the player closest in distance.

What is the highest # of balls one player can thus receive
and how would the answer change when adding new members to the ring?

[davis_greatest]

D_G check me on this question please

Sorry, snookersfun - what do you mean?


Edit: oh, do you mean that you would like me to check the answer to the question you have just posed? I was thinking maybe you meant that you had answered question 52 somewhere and that I had missed it.

[davis_greatest]

D_G check me on this question please
In continuation to the circle puzzles. The circle meanwhile has 12 members, each sitting at different distances from eachother (thus each pair with different distance). Now each member rolls one snookerball to the player closest in distance.

What is the highest # of balls one player can thus receive
and how would the answer change when adding new members to the ring?

Um.... 2? And the answer wouldn't change?

[snookersfun]

no, check, if it is a valid question
and I think it is more than 2...

[snookersfun]

D_G check me on this question please
In continuation to the circle puzzles. The circle meanwhile has 12 members, each sitting at different distances from eachother (thus each pair with different distance). Now each member rolls one snookerball to the player closest in distance.

What is the highest # of balls one player can thus receive
and how would the answer change when adding new members to the ring?

sorry, rethink!
The members are not forming a circle anymore....

[davis_greatest]

sorry, rethink!
The members are not forming a circle anymore....

So how are they positioned?

[davis_greatest]

ROUND 54:

You are invited to a party.

You are the first to arrive, so at that time there is just you and the host. Gradually, and individually, other invitees turn up.

At what point does the chance of any two people at the party sharing a birthday reach 50%?

By which I mean, when the n-1th person arrives the chacne is less than 50%, and when the nth person arrives, the chance has reached/exceeded 50%.

The Statman, has this been answered as intended - and if so, how are you scoring it - or is it still open?